Fwd: Linear Probability Interpretation

[Nicholas Woo]

Hey guys, does anyone know the answer to the question posed below?

---------- Forwarded message ----------
From: Nicholas Woo <nichol...@gmail.com>
Date: Sun, Apr 24, 2011 at 10:04 AM
Subject: Linear Probability Interpretation
To: rcol...@scu.edu


Professor Collins,

In the class #5 notes on linear probability, I have a question on slide #10, "More complex example: credit union failures"

When interpreting the coefficient outputs relative to "x" where "x" equals some ratio (i.e. liquid assets/total assets), which of the following is the correct interpretation?

1. When the liquid assets/total assets ratio increases TO 1, the chance of failure decreases by .52
2. When the liquid assets/total assets ratio increases by 0.01, the chance of failure decreases by .52
3. When the liquid assets/total assets ration increases by 0.10, the chance of failure decreases by .52 

Thanks,
Nick

[Ajay Goyal]

Hi

What were the two boxes the Prof was saying we need to interpret?

the r-square? and the intercept?

 

what about the t-values for each independent variable?

thanks

ajay

[alex smirnov]

Hi Nick,

Technically the first choice is correct I believe, but because this is a ratio and it won't go above 1, you're more interested in the increments.  So if the ratio increases by 1%, chance of default decreases by %.52%, if the ratio increases by 0.1 (10%), the chance of default decreases by 0.052 (5.2%), etc

Hi Ajay,

I'm not sure what exactly your're asking, but you do need to look at R2 (which shows how much of the variation of the dependent variable is explained by the independent variable), and you do need to look at t-values for each dependent variable (which shows you how many standard deviation is your answer from 0).  That is to say that if the t-stat is "2", are 95% confident that your answer is different from "0" ( there's a 95% chance that a value falls within 2 std deviations).  You can also look at the p-value which tells you the same information.  If your p-value is ".01", that means there's a 1% chance that your regression value for that independent variable is "0"

If on the other hand your t-stat is 0.5, and your p-value is .6, you would conclude that your value is only .5 std deviation away from 0, and that there is a 60% chance that that variable is indeed 0 and hence discard that variable as not having any explanatory value.

Everyone else,

Please correct me if I'm wrong.