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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$\mathrm{log}(\frac{p}{1}-p)={\beta}_{0}+{\beta}_{1}x$

(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 $15\mathrm{\%}$ )

a) What is the odds ratio of defaulting given the interest rate is greater than or equal to

b) If we were to analyze this data using the following logistic regression model, what are the estimates of

l

(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

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Skilled2021-09-11Added 119 answers

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 $15\mathrm{\%}$ .

estimated proportion of clients defaulting on a loan, given the interest rate is greater than or equal to

Odds Ratio =

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

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