Exercise 2.30
(a)
variableNmeanp50minmaxskewnesskurtosisp10p90
AMOUNT100024.4620.81.4110.32.0188.4587.99445.7
FICO1000686688.5500809−0.42332.713596.5767
RATE10006.0246.251.2514.40.25433.4543.1258.387
TERM3010000.853101−1.9944.97501
The average amount borrowed is $244,600. The 90th percentile FICO score is 767. The median interest rate paid was 6.25%. 85.3% of the loans were for 30 years.
(b) The empirical distribution of the loan amount is skewed with a long tail to the right. The empirical distribution for ln(AMOUNT) is less noticeably skewed. The skewness coefficient is −0.6341 and kurtosis is 4.3028 so the distribution is far from normal. The FICO score ranges from 500 to 800 and has a bit of left skew. The loan rate is “bi-modal” (two modes) with the most common rates about 3.1% and 6.5%.
Figures xr2.30(b) Histograms
Exercise 2.30 (continued)
(c)
For each additional point on the FICO score we predict loan amount will increase by $429, holding other factors fixed.
For each additional point on the FICO score we predict loan amount will increase by 0.08%, holding other factors fixed.
(d)
For each one percent increase in the mortgage rate we predict the amount borrowed will fall by $18,306 other factors held constant.
For each one percent increase in the mortgage rate we predict the amount borrowed will fall by 12.11%, other factors held constant.
(e)
There are 853 loans with 30-year terms, and the average borrowed is $255,976.40. For the 147 loans of something other than 30-year terms the average borrowed is $178,400.80. In the regression model, the estimated intercept is the average amount borrowed when TERM30 = 0. The estimated coefficient of TERM30 is the difference between the amounts borrowed when TERM30 = 0 and when TERM30 = 1.