e1s2kat26

2021-09-10

TD Canada Trust discovers that the estimated proportion of clients defaulting on a loan, if the interest rate is lower than$15\mathrm{%}$ , is 0.34. They also discover that the estimated proportion of clients defaulting on a loan, given the interest is greater than or equal to $15\mathrm{%}$ , is 0.52.
a) What is the odds ratio of defaulting given the interest rate is greater than or equal to $15\mathrm{%}$ relative to the interest rate is lower than $15\mathrm{%}$? Interpret this odds ratio.
b) If we were to analyze this data using the following logistic regression model, what are the estimates of ${\beta }_{0}$ and ${\beta }_{1}$? Showyourwork.
l$\mathrm{log}\left(\frac{p}{1}-p\right)={\beta }_{0}+{\beta }_{1}x$
(Where p is the probability of defaulting on a loan and x is an indicator variable that is 1 when the interest rate is greater than or equal to $15\mathrm{%}$ and 0 when the interest rate is less than $15\mathrm{%}$)

unett

Here estimated proportion of clients defaulting on a loan, given the interest rate is below $15\mathrm{%}=0.34$
estimated proportion of clients defaulting on a loan, given the interest rate is greater than or equal to $15\mathrm{%}=0.52$
Odds Ratio = $p\frac{1}{p}2=\frac{0.52}{0.34}=1.529$
Here the odds ratio is 1.529 that means there is 1.529 times more chance of default interest rate is greater than or equal to $15\mathrm{%}$ than when it is less than $15\mathrm{%}$.

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