A bank finds that the estimated proportion of clients defaulting on a loan, given the interest rate is below 15%, is 0.34, They also find that the estimated proportion of clients defaulting on a loan, given the interest is greater than or equal to 15%, is 0.52. a) What is the odds ratio of defaulting given the interest rate is greater than or equal to 15% relative to the interest rate is lower than 15%? Interpret this odds ratio. b) If we were to analyze this data using the following logistic regression model, what are the estimates of β0 and β1? Show your work. lg{(p1−p)}=β0+β1x 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% and 0 when the interest rate is less than 15%.

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A bank finds that the estimated proportion of clients defaulting on a loan, given the interest rate is below 15%, is 0.34, They also find that the estimated proportion of clients defaulting on a loan, given the interest is greater than or equal to 15%, is 0.52.    a) What is the odds ratio of defaulting given the interest rate is greater than or equal to 15% relative to the interest rate is lower than 15%? Interpret this odds ratio.    b) If we were to analyze this data using the following logistic regression model, what are the estimates  of β0 and β1? Show your work.    lg{(p1−p)}=β0+β1x    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% and 0 when the interest rate is less than 15%.

Aubree Mcintyre · Accepted Answer

SOLUTION: we translate data into tabular formate. CasesContolDefaultingnon−Defaultingexposed&amp;lt;15%0.340.66unexposed≥15%0.520.48 a) What is the odds ratio of defaulting given the interest rate is greater than or equal to 15% relative to the interest rate is lower than 15%? Interpret this odds ratio. ANS: odds of defaulting given interest rate 15≥15% is odd1=(0.520.48)=1.083 odds of defaulting given interest rate &amp;lt;15% is odd1=(0.340.66)=0.5151 SO odds ratio is given by, addratio=odds1odds20=1.0830.5151=2.1025 Interpretation: odds of defaulting given interest rate 15≥15% is greater than odds of defaulting given interest rate &amp;lt;15%, that is high intereset rate 15≥15% may be a risk factor for defualting a loan. b) If we were to analyze this data using the following logistic regression model, what are the estimates of β0 and β1? Show your work. lg{(p1−p)}=β0+β1x ANS: where bl and bo are b1=log⁡ (base catergory) and b1=log⁡ (odd ratio) bo=log⁡ (odds of defaulting given interest rate 15≥15%=log⁡(1.083)=0.03462 b1=log⁡ (oddratio of defaulting given interest rate 15≥15% relative to the defaulting given interest rate &amp;lt;15%=log⁡(2.1025)

A bank finds that the estimated proportion of clients defaulting on a loan, give

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