The Dodge City Bank is planning its loans for the next several years, and is using a model of loan demand developed from past experience. Fred Smith is responsible for developing the mortgage loan component of total loan demand. Fred estimates the following equation using 14 years of data:
Q = 50 - 0.2P - 0.2D + 0.3Y + 0.15H, R2 = 0.844
(17) (0.13) (0.16) (0.08) (0.06)
Here, Q denotes mortgage loan demand (in million dollars), P denotes the prime interest rate, D is the discount rate, Y is per capita income (in thousand dollars), and H is an index of average city housing prices (in thousand dollars). The standard error of the regression is 22, and standard errors of the coefficients are shown in parentheses. (At 95% confidence level, the relevant t-statistic is 1.83 for 9 degrees of freedom.)
(a) Fred thinks that the discount rate will be 6% in the next year, the prime rate will be 7.75%, per capita income in Dodge City will be $21,000, and housing prices will be $165,000. How many loans can Dodge City Bank expect to make in the next year?
(b) Fully evaluate these regression results, including computation of t-statistics, adjusted R2, and the F-statistic.