## Monday, April 13, 2020

### Odds Ratios for Impact of Medical Debt on Home Equity

Odds Ratios for Impact of Medical
Debt on Home Equity

Question:   Information on people with and without medical debt and people with and without home equity is presented in the contingency table below.   Use this data to calculate the odds ratio for the existence of medical debt on negative home equity.

Follow up to Calculation of Odds Ratio Calculation:   The respondent level data obtainable from the 2018 Financial Capability Survey can be used to estimate a logistical regression model of the impact of medical debt on negative house equity.  What is the odds ratio obtained from this logistical regression model where the dependent variable is a dummy variable set to 1 if the respondent has negative home equity and the explanatory variable is a dummy variable set to 1 if the respondent has medical debt?

Follow up discussion of impact of medical debt on negative house equity:  What do the results presented here indicate about the impact of medical debt on negative house equity?

 Contingency Table for Medical Debt  and Home Equity Positive House Equity Negative House Equity Total No Medical Debt 13,175 456 13,631 Medical Debt 2,105 772 2,877 Total 15,280 1,228 16,508
Sample of all homeowners in 2018 track of the national capability study.

The odds ratio calculation from the contingency table:

Step One:  Calculate the probability of having medical conditional on negative house equity and the probability of have medical debt conditional on positive house equity.

P(medical debt/negative house equity) = 772/1228 = 0.629.

P(medical debt/positive house equity) = 2105/15280 = 0.138.

Step Two:  Calculated the odd for the two conditional ratios above.

O1= 0.629/(1-0.629) = 1.6929

O2= 0.138/(1-0.13) = 0.1597.

Step Three:  Calculate the odds ratio by taking the ratio of the two odds, which is 1.6929/0.1597 or 10.6.

Follow up to Calculation of Odds Ratio Calculation:

I used survey questions to generate dummy variables for existence of negative house equity and existence of medical debt.  The analysis is limited to homeowners on the 2018 survey.

The code used to estimate the logistical regression model is presented below.

logistic underwater medical_debt if track==2018 & home_owner==1

The results are presented below.

 underwater Odds Ratio Std. Err. z P>z [95% Conf. Interval] medical_debt 10.59622 .6734463 37.14 0.000 9.35519 12.00188 _cons .034611 .0016486 -70.61 0.000 .031526 .0379979

Note the odds ratio from the logistical regression model is 10.6 same as from the contingency table.

What is the impact of medical debt on negative equity?

Medical debt has a huge impact on negative equity.  It is likely that people with medical bills are taking out home equity lines or refinancing their mortgages.  Very large implications for retirement security.

I have a larger paper on medical debt and financial distress under review.  Also, please look at my policy primer Defying Magnets: Centrist Policies in a Polarized World.

## Tuesday, August 20, 2019

### Monopoly PR2: Throwing Doubles and Probability of Turn Outcomes.

What is the probability of throwing doubles?

Each turn of monopoly starts with a roll of two dice.   If the player rolls doubles (the same value on each dice) the person rolls again.   If the player rolls three doubles in a row the person goes directly to jail.   The player who rolls three doubles in a row does not get to buy a property or use a community chest or chance card.

The monopoly turn ends after the first roll of the dice if the dice roll is not doubles and after the third roll of the dice regardless of the dice roll outcomes.

Question one:  The Chance Square exists seven squares away from GO.  What is the probability that a player starts as Go and lands on Chance on the first turn of the game?

Analysis

The person can roll a seven on the first roll or roll a double go again and hope the sum of all rolls adds to seven.   One also can get to chance on three rolls.

As noted in a previous post 7 is the most common outcome from the sum of two dice rolls.   There are six combos of two dice rolls that add to 7 – (1,6), (6, 1), (2,5), (5,2), (3,4), and (4,3).   Each of these outcomes has probability 1/36.   The sum of the six mutually exclusive outcomes is 1/6 or 0.16667.

The person can also reach 7 by throwing a (1,1) or a (2,2) on the first turn and throwing and taking a second turn.   (Note (3,3) even though sum is less than 7 is not an option.  Explain why.)

To get to seven on two throws of the dice after throwing (1,1) one must throw (4,1) (1,4), (2,3) or (3,2).    The probability of this occurring is 4/36 or 0.11111.  The probability of getting to seven after two throws of the dice after throwing (1,1) on the first throw of the dice is probability of throwing (1,1) (1/36) multiplied by probability of getting dice rolls to sum to 5 (4/36).  This product is (1/(9x36)) or 1/324 or 0.00308642.

To get to seven after throwing (2,2) on two throws of the dice one must throw (1,2) or (2,1).   The probability of throwing (2.2) is 1/36.   The probability of throwing dice that sum to 3 is 1/18.   The product of both occurring is the product of the two or (1/(36x18)) or 1/648 or 0.00154321.

There is one other way to get to seven on one turn.  Throw (1,1) on the first turn, (1,1) on the second turn and dice that sum to 3 on the third turn.   The probability of this sequence happening is (1/36) x (1/36) x (1/18) 1/23328  or 0.0000428669.

The probability of getting to seven on the first turn is the sum of the probabilities of all the ways to get to seven, which is 0.171339163

More monopoly probability problems will follow.
.

## Friday, August 2, 2019

### The earth's actual orbit

Issue:  In a previous post I calculated the speed of the earth under the assumption that the earth’s orbit was circular.

The earth’s orbit is elliptical, not circular.    The link below provides a description of the actual orbit of the earth around the sun.  At its nearest point the earth is

Describes the orbit of the earth around the sun

According to this web site at its nearest point the earth is 147 million kilometers away from the sun and at its furthest point the earth is 152 million kilometers away from the sun.

Find an equation for an ellipse that approximates the earth’s orbit around the sun.

What is the perimeter of an object that travels around this ellipse?

How do estimates of the earth’s speed and distance traveled based on the elliptical-orbit estimate differ from the earth’s distance traveled and speed based on the circular orbit assumption.

Answer:  The equation of an ellipse with the center at (0,0) is of the form

X2/a2 + Y2/b2 = 1

It has been a really long time since I thought about ellipses.  (The web site below has a nice explanation.)

If we set a=147 and b=152 we get an ellipse where the furthest point is 147 kilometers and the nearest point is 152 kilometers.

The formulas for the perimeter of an ellipse are actually very difficult.  See the link below for an explanation.

The approximation for the ellipse perimeter that we use is

PER = pi x [ 3 x (a+b) – ((3a+b)(a+3b)}0.5 ]

Plugging in values of a=147 and b=152 we find that the earth’s annual orbit around the sun is approximately 939.4 million kilometers.  Our estimate of the earth’s orbit assuming a circle (radius 149.7 kilometers) is 940.4 kilometers.

The circular orbit and elliptical orbit estimates are in fact quite similar.

## Thursday, August 1, 2019

### Speed of an object going around the sun

This post evaluates the speed of an object going around the sun assuming a circular orbit.

Question:  An object travels in a circle around the sun.  The radius of the circle is 93 million miles.  It takes 365 ¼ days for the object to make one complete revolution around the sun.  What is the average speed in miles per hour for this object?

Answer:  The distance traveled is the circumference of the circle, which is

2 x 3.1416 x 93,000,000

or 584,337,600 miles.

(Note to self.  Remember to multiply by 2.)

The number of hours in 365 ¼ days is 8,766.

The average speed in miles per hour is (585,337,600)/(8766) or 66,661 miles per hour.

Note:  The earth is 93 million miles from the sun but I do not know the exact nature of its orbit.  Does it travel in a circle or ellipse?  I am clueless.   If science students wants to create more questions of this type I will publish guest posts.