Regression analysis:

This is a term that is used extensively in AI, and is the starting point in AI. In statistics, regression analysis is a set of statistical processes for estimating relationship b/w a dependent variable (also commonly called outcome variable) and one or more independent variables (often called 'predictors', 'covariates', or 'features'). For ex: heart attack vs weight. Here heart attack is dependent var (on Y axis), which depends on weight, an independent var (on X axis). Here, we are trying to find a relationship b/w the 2, and see if they are related. i.e does higher weight causes more heart attack, etc.

Correlation Coefficient (R):  R is a correlation coeff that measures how well X,Y in given dataset are correlated, i.e if X changes by a certain amount, does Y also change by a proportional amount. The correlation of 2 random variables X and Y is the strength of the linear relationship between them. It's a number b/w -1 and +1 (-1 meaning perfect -ve correlation, while +1 meaning perfect +ve correlation, and 0 meaning no correlation).

There are many types of correlation coeff, but the most commonly used is Pearson's correlation coeff (rep by "r" or "R"). To measure R mathematically, we define it as follows

Pearson's r = R = Correlation (X,Y) = Cov(X,Y) / (σ(X) * σ(Y)) => Correlation exhibites same properties as covariance, as it is defined the same way. However we divide it by std debviation terms to normalize it, so that correlation remains b/w -1 to +1. See statistics section for definition of variance and covariance.

The most common form of regression analysis is Linear Regression. A special case of Linear Regression is logistic regression.

 


 

Linear Regression:

Linear Regression is a linear approach used in statistics to model a relationship b/w o/p response (dependent var Y) and i/p parameter (independent explanatory var x0, x1, x2 ...). In simple terms, it's a X,Y plot, where numerous (X,Y) data points are given. Our goal is to find an eqn that very closely fits all the data point. This is linear approach, so data is fitted with a linear line (Y = mX + b), and loss or error is calculated by taking the squares of difference for each data point. Minimizing this loss gives us the best fit, and is called "least squares" approach to fit models to data. Liner fitting or linear regression is the simplest approach, and works well, so it's very widely used.

NOTE: We need both Fitting func and Error func. W/O defining Error func, we have no definitive way to quantify how well our fitting func fitted with the data. Genrally by getting insight into the fitting func, we are able to come up with an error func. Finding the Fitiing func is the harder part.

There are 2 kinds of Linear regression.

1. Simple linear regression:  Here there is only one explanatory var on which o/p response depends. Let's say weight of a person depends on his height, then we can have Y(weight of person) plotted against X(height of person). We'll collect lot of (X,Y) data, plot it, and then do a best linear fit, by drawing a line Y=mX+b thru that data. This is simple linear regression

2. Multiple linear regression:  Here there is more than one explanatory var on which o/p response depends. Let's say in above ex, weight of a person depends on race along with his height. Then we have 2 explanatory var (height and race) on which o/p Y (weight) depends. We'll collect lot of (X0 , X1 ,Y) data, plot it, and then do a best linear fit, by drawing a line  Y=m0X0 + m1X1 + b (Here X0 is height and X1 is weight) thru it. This is a 3D plot (i.e equation of a plane in 3 var) where there are 3 axis, X, Y, Z. where X,Y are two i/p axis, and Z is o/p axis. Similarly it's n dimensional plot (eqn of a plane in n dimensions) for "n" i/p var. Since it's eqn of a plane, it flat and can't be zig-zag, so if data is zig-zag, it may not fit very well. NOTE: here we don't have b0 , b1, separately since all of them can be clubbed into 1 var b (as b= b0 ,+ b1 + ...)

Error func:

We choose our error func for best fit to be something that sums up the differences b/w the actual and predicted value. We take squares, since we want to treat both +ve and -ve differences to be treated as errors, an NOt to cancel each other out. So, our error func to determine best fit is ( Ygiven - Ypredicted )^2 and we try to minimize it. We use calculus to come up with values of m, b to minimize this error. Mean Square error (MSE) measures the mean of this square by dividing it by number of samples. We divide it by "m" to get avg error, so that error func doesn't keep on going up as we increase the number of samples. Root mean square error (RMSE) is taking the root of MSE so that the units of RMSE are same dimension as those of Y.

Coefficient of determination (R2 or  r2 or R-squared): Above we saw that R specifies extent of linear relationship b/w var X,Y. R2 is other term used to specify goodness of fit for a model. It has multiple definitions. Most widely used is that it is the proportion of the variance in the dependent variable that is predictable from the independent variable(s). This link explains it nicely: http://danshiebler.com/2017-06-25-metrics/

Pearson's r2 (square of regression coefficient) is simply the square of pearson's r value, and is a number b/w 0 and 1. It's not the same as R2 that we talked above, but in special cases, it becomes the same.

R2 is most commonly used in regression analysis, where we are more interested in how well our predicted data fits with the actual data. This R-squared is different than "squared error" we talked above. R2 measures how much better does the data fit compared to the mean. it is a number b/w 0 and 1, and is calculated as follows:

R2 = 1-  (MSE / variance(Y)) =>  Variance(Y) is the mean line we draw which doesn't change at all with change in X. So, this is the worst fit that we can do, where it returns mean value of Y for any given X. Since MSE is always going to be smaller than variance(Y), our R2 value = 0 to 1. In worst case, we may have Y_predicted to be the same as mean line, so R2 = 0 (very bad correlation of predicted data), while in best case, Y_predicted is exactly same as Y_given, implying R2 = 1 (very good correlation of predicted data), Hypothetically R2  can be -ve infinity to 1, since we can always do worse than mean prediction by choosing a line for Y_predicted which is going in opposite direction to the real direction. However, this would be intentional. We choose mean as the worst case, since we can always choose mean line as our starting point, and see if we can do better than mean, else we stay at mean line for our predicted values too. From the formula, we can see why we call it square (since we don't take square root, but instead keep square terms in both numerator and denominator).

R2 = (variance(Y) - variance(Y_predicted)) / variance(Y) = 1 - ( variance(Y_predicted) / variance(Y)) => This is another formula for R2 and boils down to same formula as above. FIXME? Above link explains it, but couldn't figure out yet?

R2=0.25 means that only 25% of the original variation in the data is explained by the given relationship, other 75% of variation is going from some other relationship that we don't know yet. So, here correlation is weak (in other words we are only 25% in between mean and perfect fit). On the other hand, R2=0.9 means that 90% of the original variation in the data is explained by the given relationship, so correlation is very strong.

Higher order non linear eqn: Above we used linear regression, which used eqn Y=f(X). But for a better fit, We could go to higher order eqn (i.e Y=f(X2), Y=f(X3), ...) and those will fit the plot better, but those get more complex. Turns out that higher order eqn that look non linear, are actually linear regression. Let's say we have 2 i/p var, X0 and X1. In linear regression Y=f(X0 , X1). However, if we go to 2nd order eqn, then Y=f(X0 , X1,  (X0)^2, (X1)^2, X0*X1). If we choose X2=(X0)^2, X3=(X1)^2, X4=X0*X1, then the eqn ican be expressed as Y=(X0 , X1,  X2, X3, X4). This eqn is linear eqn, it just happens to have 5 i/p var, instead of 2 that we had before. So, Higher order non linear eqn can be treated as Multiple linear regression for all analysis.However, be careful as these higher order eqn may cause overfitting, and may not represent real world effect.

 


 

Logistic Regression:

Logistic regression (or Logit) is a special case of linear regression. In many textbooks, it's not even referred to as logistic regression, but rather as logistic classification. Here the o/p Y can't have infinite values (i.e Y is not a continuous function) but can only have a certain number of distinct possibilities. I.e there may be only 4 outcomes as a shape is a square, circle, rectangle or triangle. However, there are key differences b/w linear and logistic regression. One is that logistic regression predicts the probability of particular outcomes rather than the outcomes themselves, so they are restricted to values 0 to 1. So, o/p Y reps probability of that event happening for given X. Second is that conditional distribution is a "Bernoulli distribution" rather than a "Gaussian distribution" because the dependent variable is binary. FIXME Not sure how ??

Logistic regression is very nicely explained on StatQuest: https://www.youtube.com/watch?v=yIYKR4sgzI8

There are multiple types of logistic regression:

1. Binomial or binary logistic regression: They deal with situations in which the observed outcome for a dependent variable can have only two possible types, "0" and "1" (which may represent, for example, "dead" vs. "alive" or "win" vs. "loss").

2. Multinomial logistic regression: They deal with situations where the outcome can have three or more possible types (e.g., "disease A" vs. "disease B" vs. "disease C") that are not ordered

Since in Logistic regression, Y is not continuous but has distinct values, we don't try to fit Y, but instead try to fit the probability of Y employing the same curve fitting methods , 

Linear model: Y=m0X0 + m1X1 + b => Linear model with 2 predictors X0,  X1

Logistic Model: L = logb(p/(1-p)) = m0X0 + m1X1 + c, where p = P(Y=1), L=log odds of event that Y=1. => Logit model with 2 predictors X0,  X1. Logistic model predicts probability p that Y=1 for given X. It assumes linear relationship between predictors X0,  X1 and log odd of event that Y=1. Base b is usually taken as "e", but sometimes base 10 and 2 are used too. I changed the Y intercept to c here, so as not to confuse with base b.

NOTE: we are doing probability of "odds of event that Y=1", and NOT "probability of event that Y=1". Odds of event that Y=1 is "probability of event that Y=1 / probability of event that Y≠1". So, if P(Y=1) =0.5, then P(Y≠1)=0.5, so odds of event that Y=1 is 1 and NOT 0.5, implying that odd of Y=1 is same as odd of Y≠1. If P(Y=1)=0.8, then P(Y≠1)=0.2, so odds of event that Y=1 is 0.8/0.2 = 4, implying that odd of Y=1 is 4 times the odd of Y≠1.

Now, the question is why do we do logistic regression this way, why don't we just use the same fitting methodology as Linear Regression, i.e why not do "Y=m0X0 + m1X1 + b" , instead of doing "logb(p/(1-p)) = m0X0 + m1X1 + b". The reason is because such linear line will never be able to achieve a good curve fit, as it will have to run thru the middle to fit data. A portion of the data is saturated on lower end, while the remaining portion is saturated on higher end. No matter what slope or C-intercept we choose, the error will be enormous, as line will always run thru middle to minimize error, basically always predicting that the value is 0.5 or so (which makes no sense). For binary classification, we need something non-linear like S shape, which will fit values with least error. Also, we need probability here as we'll never be able to get 0 or 1 values when predicting Y, i.e if we try to predict using Y=m0X0 + m1X1 + b, then for given X, we may get Y=0.7, but that value is meaningless as Y is either 0 or 1. But if we use probability here, then p(Y=1) for a given X makes more sense, as p(y=1) = 0.7 means there is a 70% chance that Y=1 for given X.

If we choose base b=e, and solve for p=P(Y=1) using the eqn above, we get a sigmoid function . i.e p = σ(z) = 1 / (1 - e^(-z)) where z = m0X0 + m1X1 + b. So, it's easier to understand if we assume that sigmoid func came first. It constrained our o/p values to b/w 0 and 1, gave a probability func, and that fitted our requirement well. So, by taking sigmoid of our predicted value, we ended getting that log func of p/(1-p).

This sigmoid is the standard logistic func used to fit data. It gives us the probability of o/p Y for a given i/p X, rather than giving the value of o/p Y. So, our Y data (which is the probability) is always between  0 to 1.

We could have chosen some other eqn too, i.e "logb(p) = m0X0 + m1X1 + b", however that may give a worse fit. It's just a conjecture, I don't know that. Assuming sigmoid is the best function  fitting our requirement, let's calculate the error.

Error func:

Now the question that comes to mind is how do we calculate error for this function to get best fit. Can we do "residual square" method used in linear regression? Turns out that if we do residual square, we end up getting non convex graph with many local minima for Logistic regression. For linear regression, we ended up getting a beautiful convex graph, that had 1 local mimima, so it was easy to find lowest cost. This link explains it very well.

https://towardsdatascience.com/optimization-loss-function-under-the-hood-part-ii-d20a239cde11

As explained in the link, a better function to minimize error is Ygiven * Log( Ypredicted ) +  (1-Ygiven ) * Log( 1-Ypredicted )

If we plot this error function using desmos.com graphing utility, we'll see that the function is a parabola (like umbrella), with 0 at both ends (at x=0 and x=1). It reaches a max value around x=0.5. Here, we chose  Ygiven  to be the same as Ypredicted. So, when both are the same value (i.e both are 0 or both are 1), that means, we predicted perfectly and error func is 0 (as seen at the 2 ends). Anywhere in between, even if both  Ygiven  and Ypredicted  are both same (i.e 0.5, etc), the error func will throw out a non zero value. this is OK as we never have Ygiven to be anything other than 0 or 1. The respective terms, either Log( Ypredicted )  or  Log( 1-Ypredicted ) will take over when Ygiven = 1 and Ygiven = 0 respectively. This will take the error value to very large numbers (to infinity if we predict totally opposite value of what Y is supposed to be. So, the algorithm will try to stay away from predicting totally opposite values.  This is exactly how we wanted our error func to lo behave as.

The above eqn is what we use in all logistic regression as our error function that we try to minimize. We calculate error for each sample using above eqn, sum them up and try to minimize that sum. For logistic regression, we call our cost approach "maximum likelihood", instead of "residual square".

 


 

AI logistic regr example

M pictures with 1 pixel value each. Let's say we have m pictures, each with 1 pixel (each pixel has a value from 0 to 255 representing 256 possible colors), and we try to plot that pictures popularity based on that pixel value. So, on X axis, we will have these pixel values, and on Y axis, their popularity number. We can do simple linear regr, and plot a best fit line: Y=mX+b.

However, if we have 2 pixel values for each pic, then this becomes Multiple linear regr, and best fit plane becomes Y=m0X0 + m1X1 + b. Similarly if we had nx pixel values, then, we would have  Y=m0X0 + m1X1 + ... + mnX+ b as the best fit plane. This is exactly what we do in AI in finding best fit. We call these slopes (m) as weights as w0, w1, ... and so on.

Gradient Descent (GD):

This method is used to find plane with best fit. A very good video about gradient descent is here: https://www.youtube.com/watch?v=sDv4f4s2SB8

Finding these weights or slopes to minimize the error when fitting the plane to the data is a difficult problem. However, calculus comes to our rescue here, and gives us "gradient descent" method, that allows up to find such a plane (weights w0, w1, ... ), so that total error across all X is minimized. It works amazingly well (like magic) !!

Andrew Ng's Course on coursera.org called "Supervised Machine Learning: Regression and Classification" talks about gradient descent, and has labs on it. Try it, if you want to know the basics of Gradient descent. Instead of doing gradient descent, we could also just find the slope of the cost function and equate it to 0 to find the minima. GD allows you to see what's going on, Also, computers won' t be able to just solve the derivative of cost function and equate it to 0. Instead, they can always do GD to come to a point where derivative is close to 0. So, that's why we learn and implement GD in computer programs.

 


 

Health Insurance in USA:

Health insurance is one of the highest expense after income taxes. Health insurance premiums are very high in this country, as doctors and medical facilities are ridiculously expensive. Good news is that if you are employed by a business, then a big chunk of your health insurance premium is paid by your employer. The health insurance plans are offered bythe employer, and you choose from one of their plans. You don't have the option of going and buying your own insurance plan. This works in your favor, as the plans offered by employers are way better than what you can buy in open market place.

Insurance Coverage:

When you say health insurance, what does it cover. turns out that general health insurance plans offered by your employer cover everything except Vision and dental expenses. So, employers offer these optional plans to cover dental and vision expenses. Here are 3 types of insurance plans offered by most employers:

1. Health insurance: This is the regular plan for which you pay the highest premium. It covers all medical expenses incurred by you. It costs about $5K in premiums.

2. Dental insurance: This is optional insurance that pays for your dental visits. It costs about $1K - $3K depending on the type of plans your employer offers. This is optional, but I would highly recommend getting this dental insurance, as you will need to get your regular teeth cleanup and checkup. It will pay for itself.

3. Vision Insurance: This is optional insurance that pays for your eye doctor visits. A lot of confusion here is what exactly vision insurance covers. What if I get a eye problem or disese, is that covered by your regular health insurance or by your vision insurance? Almost all eye issues are covered by your regular health insurance as it's considered a medical expense and not a vision expense. The only thing that Vision insurance covers is your regular eye checkup (once a year0 and your prescription glasses or your contact lenses. So, if you don't wear glasses, you can get away without getting any Vision Insurance. However, vision insurance is very cheap. For the whole family, you can get this insurance for less than $500/year. Since this insurance pays a large portion of your eye glasses cost, you can recover all the money that you paid in premium. So, I would highly recommend getting Vision Insurance too.

Health Insurance Plans:

Your company may offer various plans for your health insurance. A new law called "Obamacare" was passed under Obama's president ship. Many older plans were replaced by new plans. IRS dictates what is covered by these plans, how much deductible plans can have, who can be covered, etc. More details for 2019 available on publication 969 of IRS website:

https://www.irs.gov/publications/p969

There are 2 kinds of health insurance plans offered by employers as of 2020:

1. Co-pay plan: This is the traditional copay plan where you pay a $20 or $30 co-pay for visiting any doctor, and the rest is covered by the insurance company. The health premiums in these co-pay plans are higher. Health insurance premium used to be about $15K - $20K for a family of 4 (husband, wife and 2 kids) before Obmacare. However, as you are employed, your employer pays about 80% of your health insurance premium while you pay only 20% of the premium. So, your share of the premium is about $2500. This used to be superb plan as you didn't have to worry about any medical expenses except for your co-pay. Even for baby delivery, these plans charged you a flat $250 co-pay, to cover the entire cost of baby delivery, which actually costed north of $10K to the insurance company. For this reason, babies used to be called "$250 baby", as $250 was all that it would cost to bring a baby in this world.

However, with the Obama Health care reform that came in full force in year 2014, the premiums for these co-pay plans rose fast, and as of 2015, employee share of the premium has gone from $2.5K to about $8K. Also, health insurance companies are increasing co-pay for these kinds of plans. For ex, for baby delivery or other hospital visits, the co-pay is now $500 instead of $250. So, employees and employers are switching to the other pan, which is what the intent of the govt was when it initiated the health care reform. Now, most of the employers don't even give you the option of "co-pay plan". Co-pay plan are guaranteed to be expensive than the other plan, so it makes no sense for anyone to get a co-pay plan anymore. This other plan, in lieu of co-pay plan, is called the High Deductible Healthcare plan (HDHP).

2. HDHP (High Deductible Healthcare Plan): In this plan, there is no concept of co-pay. You pay 100% of medical expenses out of your pocket, until you meet a deductible limit. The health premium in these HDHP plans are lower (at about $1K/year for the employee share of the premium), but the deductible is usually set at $3K, so first $3K of medical expenses have to be borne entirely by you. After you meet this deductible, that is when insurance companies pick up 80%-90% of the medical expense. Then once you hit $6K in total expenses out of your pocket, they start covering 100% of your medical expenses. That typically happens once you have amassed about $30K in medical expenses.

Premiunm: For my HDHP plan at my employer, I pay about $3K per year in premium for a family plan. Family plans are the most expensive, but they cover all the children irrespective of the number (for the same premium). This is one of the places where having more kids pays off.

HSA (Health Savings account): To compensate for the financial hit, govt allows you to set up a HSA (health savings account) in which you can contribute money upto a certain limit (limit was $7000 for the year 2019) free of federal taxes, and use money from this HSA to pay for any qualified medical expenses. You still have to pay SSN and medicare taxes on this money, but it's exempt from federal taxes and state taxes (in most of the states). Also, the money grows tax free, and funds in this HSA never expire. The HSA is just like a normal savings account, and most of the banks will open it for free. However, any money that is moved in or out of HSA is reported to IRS, as IRS wants to make sure that you are using money in this account only for qualified medical expenses, and not for Walmart shopping spree. The bank or custodian of HSA doesn't care about what you do with money in this account. It will approve money for anything that you ask for. It's between you and IRS to figure out in case of any discrepancy. One sweetener that most of the employers add to this plan, is that they contribute free money every year if you have an HSA. Most companies contribute $1K for family plans and $500 for individual plans every year in the HSA. This contribution by employer is tax free from federal taxes, SSN taxes and Medicare taxes. So, this $1K or $500 gets deposited in full without any tax bite. Also, this money never gets reported anywhere as your income, so it's 100% free money.

How much to contribute in HSA:

You should always contribute the maximum amount allowed in HSA. For 2020, it's $7.1K. This is because the money that you or your employer puts in HSA is your money, and remains with you no matter who you work for. So, in the end, you add about $8K money in your HSA every year which you can use for almost all medical expenses. Even if you don't use part of it, there is no penalty and the money remains there until you reach age 65. Most HSA custodians allow you to put money in stock market, that also grows tax free. So, people use it as a kind of retirement account, where they put a big chunk of their balance in the stock market, and try to take out as little as possible, by keeping their medical expenses low. (some people I know of don't even use their HSA for medical expenses, preferring to pay out of their pocket, and keep 100% of their HSA money invested in stocks. I don't see any rational in that). If you withdraw money for any non-medical expense before age 65, then you have to pay a 20% penalty, and applicable income tax. However, if you use it for any medical expense, then there is no penalty and no tax, no matter when you use it.

The best part with HSA comes now. After age 65, you are free to withdraw all the money from HSA for any expense, without any penalty. You just have to pay income tax on that withdrawal, if you are using it for non-medical expense. That's what makes HDHP plans with HSA so lucrative. $8K/year is almost half of your 401K retirement account contribution for a given year. So, once you have maxed out on your 401K contribution, many people try to max out on HSA contribution.

Then upon reaching age 65, you can treat your HSA in 2 ways:

  1. You can treat it as regular 401K account and pay taxes on money that you withdraw. HSA account is no different than 401K account in this case.
  2. You can treat it as regular medical account, and use it for any qualified medical expense. Then you pay no taxes on withdrawal.

Dental Insurance Plans:

Your company may offer various plans for your dental insurance. Choose the one that is lowest cost, as that should suffice to cover most of the regular dental expenses. You can keep following up with your dentist, and if he/she suggests some expensive dental work, then you can sign up for the more expensive dental plan for next year, and get that treatment done the next year.

Vision Insurance Plans:

Your company may offer just one plan for your vision insurance. As I stated before, it's worth taking if any one in your family wears glasses or contact lenses. For me and my family, it's offered at $75/year by my employer. It pays for itself with just 1 pair of eyeglasses bought every year. You can pay a little out of pocket or get the eyeglass entirely free. All regular vision tests are also covered. Your real cost is less than $75, since you are not taxed on this part of income (since it's deducted from your income before any taxation is done). So, assuming 25% tax bracket, your real cost is more like $55. There is absolutely no reason not to get it.

FSA (Flexible Spending account):

We saw one kind of account called HSA that's allowed with HDHP plans. There's another kind of account for eligible medical expenses that used to be allowed before Obamacare came into existence. It was called FSA. FSA accounts could be used with both Co-pay plans and HDHP plans. Previously there used to be only 1 kind of FSA account (aka traditional FSA accounts). Now, there are 2 kinds of FSA accounts:

  1. GPFSA (General Purpose FSA) or Traditional FSA or Traditional Healthcare FSA: This account is offered in lieu of HSA. It is known by so many different names. Your employer may call it by yet another name. We'll call it GPFSA here, but we mean any of these accounts. If you have an HSA account, you can't have a GPFSA account. Your employer offers this account, and you can choose only one: either HSA or LPFSA. LPFSA is what is generally referred to as FSA account in regular talks and on websites (FSA eligible). After Obamacare passed in 2012, FSA was what used to be offered with co-pay plans. But with advent of HDHP plans, HSA accounts were introduced to be used with HDHP plans. IRS disallowed having both HSA and FSA accounts, you could choose only one. So, people on co-pay plan chose FSA (since co-pay plans didn't offer HSA). However people on HDHP plan had the option to choose HSA or FSA. They could choose FSA only if they didn't opt for HSA plan.These kind of FSA were started being called Traditional FSA or GPFSA. GPFSA is inferior compared to HSA account. So if your employer offers HSA, you should always opt for HSA with HDHP plan (don't go for GPFSA).
  2. LPFSA (Limited Purpose FSA): This is another account that is offered by employers. In above section, I said that FSA accounts were dis allowed with HSA. However that was not entirely right. Only traditional FSA (or GPFSA) accounts were dis allowed. A different kind of FSA accounts were still allowed to be used with HDHP plans, but the the kind of expenses you could deduct in these FSA were a lot strict than the LPFSA that were offered above. To alleviate confusion, these FSA accounts that could be used with HSA  were called LPFSA. The good news is that this account can be had on top of having an HSA account. The bad news is that this account can only be used to pay dental and vision expenses (and NO other expenses). Anytime you pay at a eye doctor's office or a dentist, the expense is considered an eligible expense for LPFSA. Any medical expense other than these 2 expenses (vision and dental) can be paid via HSA or GPFSA, but not via LPFSA.

Looks like both of these accounts are referred to as FSA accounts on IRS website, and that is the main source of confusion. In GPFSA any qualified medical expense is eligible, while in LPFSA, only vision and dental expenses mentioned below are eligible (this list is from my employer, but most employers have a similar list for LPFSA. NOTE: this list comes from IRS, so they will be similar irrespective of which employer is offering the plan):

  • Vision expenses not covered by a medical or vision plan, including examinations, treatment, corrective lenses, and contact lenses
  • Dental deductibles, coinsurance, and many other dental care expenses not covered by your dental plan
  • Over-the-counter (OTC) drugs that are prescribed by a physician and related to vision or dental care

A sample list of eligible LPFSA expenses is on this website (this is some employer somewhere, but whatever they list here applies to everyone in USA, since the list eventually comes from IRS):

https://fsafeds.com/explore/lex-hcfsa/expenses?take=100

Any prescribed eye/dental medication (that is available over the counter only) is eligible for LPFSA. No other medication is eligible. For ex let's say you get eye drops for your eyes which are needed because of some medical condition in your eyes. If those eye drops are not available OTC, then they are considered medical expense, and NOT vision expense for LPFSA purposes. So, they won't be covered. Any eye doctor visit or any dental work should be covered by both GPFSA and LPFSA. However, there is again a fine line between medical expense vs vision/dental expense even if performed at the optometrist or the dentist. The dentist or the optometrist will mark each expense with a code that marks that expense as "medical" or "vision/dental". If he/she marked it as "vision or dental", then LPFSA will cover it, else it will not be covered by LPFSA. I've seen almost same kind of eye tests getting marked as "vision" by some optometrist/opthalmologist, while some others will mark it as "medical".

Insurance companies will outright reject any LPFSA claim that you file, if it's marked under "medical" by the eye/dental office. You may ask the doctor's office to classify the treatment as dental/vision. Sometimes they may do it, many times they won't. So, even if the expense should have been a "vision" expense, just the code that these doctors or pharmacy put determines the fate of that expense. It's not worth fighting, as it's just a mentally draining process. If it's not the right code, you are out of luck. Sometimes having a FSA debit card helps a lot. Any expense that you incur at eye doctor's office or at dentist office will automatically be eligible if you pay using this debit card. The debit card is designed specifically to work at only these locations, so you don't have to file claims for expenses that are approved via this card.

There is publication 502 on IRS website that talks about eligible expenses for FSA (it doesn't specify GPFSA or LPFSA). This is the publication that is used by all insurance companies to either grant or deny your claim:

https://www.irs.gov/publications/p502

NOTE: FSA rules were different before Obamacare came (as there was only 1 kind of FSA). You will still see websites which refer to FSA eligible items from that era. They are no longer valid. Also, no one mentions LPFSA. They all talk about FSA eligible (when they really mean GPFSA). We don't really want to have GPFSA as HSA is lot superior. The only account we are interested in is LPFSA. Also note that most of the co-pay/hdhp plans now cover routine checkup for free (thanks to obama healthcare).

Let's see in detail a LPFSA account:

Irrespective of whether you are in traditional co-pay plan or HDHP, you should consider about opening a Limited Purpose flexible spending account (LPFSA). This is beneficial mostly for people, who make < $150K, as you don't pay SSN or medicare taxes on money set aside in your FSA. You don't pay federal taxes either. So, the main advantage of LPFSA over HSA is that you pay no SSN and medicare taxes (about 7.5% of your contribution amount) in your LPFSA, but do so in HSA. So, LPFSA saves you even more money than HSA.

How much to contribute in LPFSA:

There is a maximum limit of $2700 for year 2020 that you can put in your FSA (GPFSA or LPFSA). You can contribute the maximum. The only caveat is that any funds that are unused in FSA account, get confiscated by the employer at the end of the year. However, your emploter may offer you one the 2 choices: 

  • Allow you to roll over $500 from your unused funds to next year or
  • provide you a maximum of 2 and 1/2 month of grace period to use the funds after the end of the year. 

Your employer can allow you only one option, and that's already pre decided by your employer for all employees. So, read your employer's FSA documents to which option your employer offers. $500 rollover is a better option, and is offered by more employers.

Since it's use it or lose it, you have to be very careful about how much you put aside in your LPFSA amount. This amount has to be decided by you before the start of the year, and you can't change it during the year. I think, it's very risky, trying to save an extra 7.5% on tax. Based on my personal experience, $1000 is a reasonable amount to put in an FSA. Especially, if your salary is < $150K and you don't have any big medical expenses pre planned for that year. These are the 2 categories where you can spend most of your FSA money.

Vision expenses: Assuming 4 members in a family, since all 4 of you are going to go for a eye checkup atleast once a year, you will pay about $100 for 4 visits. On top of that, you can buy eye glasses or contact lenses, so you can easily use $100-$200 from your FSA for glasses.

Dental expenses: For dental expenses, you could easily end up spending $200-$500 every year. You are going to make 2 dental visits every year for each of you, but those visits should be totally free as they are mostly covered by your dental insurance. Sometimes you might need to pay $10-$20 per sperson, depending in the type of insurance you have.

So, in the end, you will have no difficulty spending $500 on dental and vision expense. With $1000 as the starting balance in your account, you will easily spend $500, and can rollover remaining $500 to next year (if they are unused). Then depending on how much money you spend from LPFSA, you can readjust how much you want to contribute for next year's FSA. So, risk is pretty low of losing money in LPFSA. People usually go for an FSA account, when they are sure, they are going to have an expensive treatment, such as braces, dental surgery, eye surgery, etc. They get a quote before hand, and contribute exactly that amount of money in FSA to save some extra money on taxes. I put the maximum of $2700 in my LPFSA account, as I'm pretty sure I'll be able to use at least $2200 each year, with all the eye and dental expenses of kids.

Remember: both FSA and HSA reduce your AGI, by the amount that you contribute towards these accounts, so if you looking to bring your AGI down, you can max out the contribution to both of these accounts (about $2.7K for FSA and $7K for HSA for a total of $10K per year). Lowering your AGI, can allow you to take some deductions or get credits when filing your income taxes. Look in the income tax section for more details.

Conclusion:

So, in a nutshell, if you are employed, your total health care expenses can vary between $1K to $6K depending on the plan. Whether co-pay plan or HDHP plan is better depends on your health level. But since 2015, premium costs for co-pay plan are lot higher than premium costs for HDHP plan. Also many employers offer only the HDHP plan. So, it's wise to stick to HDHP plans, and just forget that co-pay plans even exist.

As an example, with my employer, premiums for co-pay plan are about $4K, while the premium for HDHP plan are about $1K. With HDHP plan, upto $3K have to be borne entirely by the employee, between $3K to $6K is borne 80% by insurance company and anything over $6K is borne 100% by the insurance company. So, with HDHP, the min I would ever spend out of my pocket is $0K ($1K in premium - $1K in employer contribution) while the max is around $6K ($6K in expense + $1K in premium - $1K that my employer contributes), while with co-pay plan, the min I would ever spend is $4K while the max is around $5K (just an assumption, as co-pays for visits,emergencies, medicines, etc shouldn't exceed $1K) . So, for my case, going with an HDHP is almost always better, as that can save me a lot of money, if I don't go to a doctor every week. However, when you are going to have a baby, you can save maybe $500 by being in co-pay plan, But that's the only scenario where it may be financially better to stick with co-pay plan.

My advise would be to go with an HDHP, with an HSA and a LPFSA, and use the money in HSA to invest in stock market. Within 30 years, you would be looking at $100K or more in returns in your HSA account, provided FED keeps on printing money !!

 

SCAMS:

There are so many scams going on that you may lose a good chunk of money if you are not careful when dealing with anyone in USA. Here's a good link on FTC website about how to identify scams and protect yourself from it:

https://www.consumer.ftc.gov/features/scam-alerts

Here are few scams that i've personally been hit with :(

 

1. Moving Companies Scam:

There are Moving companies on internet that move your stuff from one pace to another. The kind that you hire when changing houses, apartments, etc. There are 2 kind of Moving companies. One that are registered with the state, and others that are not registered. Different states have different requirments for registration. The companies that are not registered are in general scammers and corrupt. Craigslist is littered with such companies. They will tell you that they are registered and bonded, and have insurance, but if you ask them their DoT number or any paperwork, they will hang up the phone. The company name and owner names 9i.e The Moving company, owner: Joe) are very generic. They will have a website, and a phone number which changes frequently. They have no address or a fake address, social media page links to some other company with sm=imilar names and good feedback.

What these scammers do is that they will hire a guy or two and a truck to move your stuff. They will not give you any paperwork. They start loading the heavy stuff. If you don't like their loading, you can't back out. They will refuse to unload the stuff. On reaching the destination, they will demand extra money or threaten to never give your stuff back. They basically hold your stuff hostage. At that point, you try to go to the state's transportation website to complain, only to realize that they are unregistered, have no name or address. They may even be criminals who may loot you, take all your stuff, and in extreme cases kill you.

Here's a link to Moving company regulations across all 50 states: https://www.mymovingreviews.com/move/moving-companies-regulations/

Most companies are not limited to a state, but move stff across states. In that case, they are required to have a US DOT number. You can check more details here:

https://www.moving.com/tips/how-to-check-a-moving-companys-usdot-number/

The very first thing to do when hiring any Moving companies is to ask for their USDOT number. If they don't give you one, it's a scammer. Only hire companies which have a USDOT number, and a state license to transport. It will cost you a little more, but you will have ensure your safety and a route to resolution in case things go wrong.Never ever go with unregulated companies. Craigslist has "warning on the bottom" below the liasting for any moving company, warning you about all such pitfalls.

 

2. Utility Bill scam:

This is a very common scam in USA targeting hindi or urdu speaking community. I'm not sure how they get your phone number, but they call you and tell you that they have a great offer for your utllity bill. They usually speak in hindi and are extrememely friendly and courteous. They will say that they pay the bill on your behalf and you pay only 50% of what you owe. When you grow suspicious and ask how do they make money, they will say that have tieup with these utility companies, and they are trying to pass the savings to you. They ask for your utility bill details. Things go ok for first couple of months, and they start adding other bills to your discount.

Over time, the amount of money you pay them grows, and someday they will just disappear with all your money. No bills will be paid to any of the utility companies. I've gotten dozens of such phone calls. So stay clear.

 

3. Survey scam:

The survey scam is a very common scam, there's a high chance that you probably encountered them at least once in your life. If not consider yourself lucky.

Most survey scams start by a text message claiming to be a big company ex: Whole foods, Walmart, Apple, you get the point. They have very authentic looking logo, and text looks credible. They then say that if you do a survey or do a task you will get $100-$500 in return for your survey. But what happens is after you do the task the "Big company" ditches you and you don't get what your promised. In fact, you are out of a couple of thousands of dollars.

Here's a example: The "Big company" sends you a fake check thru ups overnight delivery for a large amount like $2000. The ups envelope and the content inside it including the survey form is very authentic looking. They ask you to go to a store (usually store like walmart) and buy may be 3 giftcards for $500 each and send them the code in 24 hours. They call you a "mystery shopper" or "secret shopper" and advise you not to talk to anybody about the survey. Since they sent you $2000 check, and you sent them only $1500 worth of gift cards, you make $500 in the process, which is yours to keep.

They instruct you "Do not tell the bank about this offer". The check is very real looking, and usually from a local bank. Since you are a smart person, you don't buy the giftcards immediately. You take the check to the bank to cash it out. You ask the bank person about the authenticity of the check. The cashier sees no issues with the check. So, you deposit the check and the money comes to your account in a day or so. You get the money and you feel good about yourself. You go ahead and buy the giftcards and send the code to the "Big company" via text. You are all laughing to yourself as to how easily you made $500 doing virtually nothing.

Now, 4-5 days later you get a cursed email... (this is around what they say) "Hello this is (insert bank name) we regret to tell you the check turned out fake and we withdrew all the money back. You have been charged $35 for the bounced check". Not only you lost $1500, you are stuck with charges for "bounced check" too. You contact the "Big company" via text/phone call. There's no response, as they have moved on to their next "customer". Oops, losing that $1500 hurt. 

Some of these stories with not so happy ending ....

https://www.consumer.ftc.gov/blog/2018/05/scam-story-secret-shopping-and-fake-checks

https://www.consumer.ftc.gov/blog/2020/03/fake-offers-secret-shopper-jobs

 

4. Home Warranty scam:

This may not be termed as a a scam, as it's a business that provides warranty services. You are typically lured into buying this, when purchasing a home. However, all these are utter scam. Never ever buy any of these Home Warranty Plans. See more details under Housing section in "Home Insurance and Warranty".

 

5. General Scams:

Any email or phone call or text saying that your account or credit card has been frozen, and they need to verifying you by clicking on a link are all impersonators. They try to get your login id and password or your credit card details or bank account details. Never ever click or text or call such numbers. Always call the customer service directly by looking at the phone numbers on the back of your card or by going to their website. Doesn't matter how serious that email or text appears to be, disregard it. Nothing is going to happn to your money if you decide to wait. Scammers try to get more details about you or your account with banks or merchants and then try to target you so that they appear legitimate. There are 1000's of posts on FTC website. Read those posts to see how people are getting scammed. As a rule, i never click on any link, even if it appears legitimate. I always call customer service.

Few links below on scams reported to FTC:

Amazon impersonator: https://www.consumer.ftc.gov/blog/2021/10/amazon-impersonators-what-you-need-know?utm_source=govdelivery

 

 

 

US Passport:

If you are a US citizen, you are eligible for a US passport. You are a US citizen if you were born here, or if got naturalized here (meaning you applied for US citizenship and got one).

US Passport website: Below is official website, which provides more info on applying

https://travel.state.gov/content/travel/en/passports.html/

Apply for a Passport:

Passport in USA can either be done by mail or in person by going to a USPS post office. There are few instances where you can apply by mail, instead of in-person at a post office.If you are just renewing the passport and are an adult (over 16 years), then you can skip the post office visit and apply via mail. Unfortunately for most of us, a post office visit is required.

Adults (over 16): Your passport is issued for a term of 10 years from the date your passport is processed. Your passport can be renewed by mail, but if you applying for the first time, then you have to apply in person at the passport office.

Minors (below 16): Your passport is issued for a term of 5 years only and can only be renewed in person at the post office.

USPS: Before you apply for a passport, you will need to schedule an appointment with USPS, where you will hand over your application and required fees to the clerk. You will need to go to the below USPS appointment link, and schedule an appointment. You can schedule an appointment at any location in USA.

https://www.usps.com/international/passports.htm

Once you have gotten a confirmation email from USPS for an appointment, follow these steps:

1. Form: Fill up form DS-11. This will take a couple of minutes. Fill up the form online (choose the filler link, since that allows you to fill online and then generate a pdf for you). You then print page 5 and page 6 of this pdf file (you don't need to print other pages). Print the 2 pages on 2 sheets (i.e do NOT print duplex). Pages 1-4 of this form lists all the other details regarding passport application, so read thru it.

https://travel.state.gov/content/travel/en/passports/how-apply/forms.html

2. Evidence: To apply for a passport, you need to be a US citizen, and you need to show proof of a US citizenship. US citizenship is attained 2 ways:

  • Birth: by being born in USA (irrespective of your parent's nationality, you are a US citizen, if you are born in USA).
  • Naturalization: by applying for a US citizenship (see other section on how to acquire citizenship in USA)

Best way to show US citizenship is via birth certificate (if you were born in USA) or via citizenship certificate (the one that was given to you at the naturalization ceremony). If you are renewing the passport, then your current US passport (expired or not) can be used as evidence. You need to get a black and white photocopy of the evidence (which you will submit with application). The original document will be returned to you once it's verified by the USPS clerk. NOTE: if yo are nenewing the passport, then the old passport will also be taken for processing (It will not be returned back to you by the USPS staff. It will come to you in mail)

There is separate set for requirements for minors and adults.

  • Adults (born or naturalized):
    • Proof of citizenship: Bring original birth certificate or citizenship certificate (if you weren't born here) or current US passport, along with a black and white photocopy of that document.
    • Proof of identity: Original Citizenship certificate, current US passport or driver's License can be used as identity proof. Bring a a black and white photocopy of that document. If you are using the same document (Birth certificate or US passport) for both as proof of citizenship and proof of identity, then just photo copy suffices.

 

  • Minors (born in USA):
    • Proof of citizenship: Bring original birth certificate (current US passport won't suffice), along with a black and white photocopy of that document.
    • Presence of parents: Both parents need to be physically present with the minor at the postal office.
    • Proof of identity: Both parents need to bring their original driver's license or passport (US or non-US, doesn't matter). Driver's license is preferred since it's just easy to carry. Both of the parents need to also submit a photocopy of their driver's license. Birth certificate of minor has the name of parents, so the USPS person will check and make sure that the parent's name match with what's in the birth certificate.

3. Photo: You need a passport size photo to go with the application. You can get passport size photo printed at USPS location (where you have your appointment scheduled), but these are expensive. See my link on "Passport photo" section on how to get passport size printed for 10 cents or less. Make sure that passport size has strict "white" background, or else the central passport office will keep rejecting your photos (even though the post office may accept it)

4. Payment: We are applying for a passport book (passport card is not needed). We are not going to use expedited service unless there's an emergency (since it costs extra). It will cost $110+$35=$145 for an adult passport while $80+$35=$115 for a minor passport. You can pay the application fee ($80 or $110) + execution fee ($35) at the post office using a credit card (use credit card so that you can get some cashback. It doesn't cost any extra to pay using a credit card). Some post offices may refuse to take credit card for application fee and/or execution fee, so have a personal check book handy. If you don't have a check book, they will force you to buy a money order to pay the fees, which will cost you extra.

Delivery:

Once the clerk at USPS has taken your application and documents, you just sit back and wait for the passport to come in mail. They will send you an email about the status when it's processed and mailed. You will get your new passport by mail. If you had also sent your old passport too (if renewing), then the old passport will come in a separate mail a few days later. So, don't panic if you don't see your old passport in the first mail. It is on it's way, just a little slower. You can also track the progress on above govt website. They say 10-12 weeks for regular processing, but all my passports have come much sooner than that.Make a colored photocopy of your US passport, and keep it in some other safe place (preferably at your work just as a backup).

Once you get your US passport, you are eligible to travel to a lot of countries without any visa (unfortunately India is not in that list). So make good use of the US passport wink

 

 

Household Supplies:

This section includes all household items that are needed on daily basis. Target is the best place to buy these household supplies. they usually have $10 GC with $40 household purchase or something similar. These promotions pop up every week, but in different categories. So, if you can wait a couple of months for household supply, you can always get them at a nice discount (and lot cheaper than at walmart, which never have discount on any of these items).

Toilet papers:

Buy from target or Lowes. You can get 1000 sheet roll for a couple of dollars, which will probably last you a year, if you use bidets (see below). There's really no need for toilet paper when you have a bidet, but they do help for extra cleanliness.

Bidets:

In lieu of toilet papers, you can install bidets, which clean your butt hole much more economically and leaves you in a much more hyegenic state. There are tons of bidets available starting from $20 and going all the way up to $1000's of dollars. However, the cheapest ones do the job just fine.

I had purchased over 5 bidets so far, and all of them worked flawless;y for over 5 years. 2 of them died after 6 years of continuous use (one of them started getting no pressure due to torn plastic pipe, while the other started leaking). It's best to throw them away instead of trying to fix it. All of these bidets fit over all the toilet seats that you have installed in toilets. They take less than 10 minutes to install, and you do not need any tools except for maybe a screwdriver to unscrew plastic screws. You can find a lot of youtube videos on how to install your exact model. They are very very easy to install, so don't let anyone talk you out of it.

Few things to keep in mind when purchasing these bidets:

  • There are both single and double nozzle versions available. double nozzle ones are supposed to clean you better. I've never tried double nozzle ones, as they are little expensive. single zozzle ones do the job just fine.
  • There are self cleaning ones now. Not sure if there's any advantage, but nicer to have it.
  • These bidets are very simple design. So, if if something is not working right, you can usually troubleshoot it pretty quick.
  • Always look for leaks. You need to tighten everything with hand, so don't use plier or other tools. There shouldn't be any leak. Make sure the valve that you get with the bidet is put in the connection, else water will start leaking. This rubber may also break over time causing leaks, though I haven't seen one fail so far.

These are the few that I've purchased, and would recommend.

  • Brondell Bidet: Bought this from amazon for $40+tax (for a single nozzle version). I've been using it for a year with no issues so far. It's very thin, and self cleaning. It's on the expensive side, so won't really recommend it price wise. https://www.amazon.com/gp/product/B075MMHQX7

 

  • Luxe Bidet MB110: Bought this in 2012 from amazon for $32. Worked for 8 years before leaking. When I bought it, it didn't spray water at all. I emailed "Vie de Luxe", the official seller for Bidel Luxe on Amazon. Their customer service was extremely friendly and they shipped me a new one entirely free. Later I found out that the hole was not big enough, and that was the reason for water not getting sprayed. On making the hole bigger by pushing in a screw driver, I was able to get it to work.  So, I ended up with 2 for the price of one. https://www.amazon.com/gp/product/B001KKRCFA

 

  • Joy Bidet C1: Bought this from amazon for $24. This also bought from same seller "Vie de Luxe". This also worked flawlessly. Just recently it started leaking after being in service for 8 years. Looks like this brand is discontinued and this seller just sells Luxe Bidets now.

 

  • Dalmo Bidet: Bought this for around $20 on sale, even though the list price is $32. It has self cleaning fetature, and has dual nozzle for feminine/posterior wash. Don't really know what that means. This works great too. https://www.amazon.com/gp/product/B07VGCT4XH

 

 

Paper towels:

This is one of the other time that is totally unneeded, but is sold in huge quantities all over the country. They are made from cutting trees, cost so much to ransport, take up so much shelve space in stores, and are used on a regular basis. If everyone just kept a handkerchief or a peice of cloth with them and wash it regularly, 99% of this wastage could be eliminated, Anyway, married people with kids can't imagine a life if they didn't buy this wastage. I personally don't use these paper towels, but do buy them. Paper towels shouldn't cost more than 0.5 cents per sheet. Ones with 1 ply (real thin ones) go for 0.25 cents/sheet. Good thick ones cost 0.5 cents/sheet. Look for ones that have "choose a size" or smaller cut sheets, as larger sheets just get wasted.Most of the times you just need a paper sheet to clean something, smallest size paper works just as fine as a large sheet.

Best place to buy these are  from Walgreens and Home Depot. They go on sale on Walgreens quite often. Combined with their cash rewards and coupons, you can get 86sheet paper towel for $0.40 (implying 0.5 cents per sheet). I have also seen these on clearance pretty often at Home depot, where they go for 50% off. There it goes for $3 for a pack of 6, costing about the same as walgreens one, but little better quality.

Paper towels usually go on sale on amazon too. This is a link that's expired, but the same deal keeps on coming every few months like a clockwork. There list price is $80 which is nonsense. Here 250 sheets cost a dollar when on sale, implying 0.4 cents per sheet. Papers are of better quality though.

Amazon deal on scotts paper sheet:

https://slickdeals.net/f/15548869-16-pack-of-250-count-scott-essential-multifold-paper-towels-14-45-w-subscribe-save

https://www.amazon.com/gp/product/B0040ZOD04

 

Soap:

Shampoo/conditioner:

 

Cloth Washing detergent:

Dish washing detergent

dish cleaning detergent