The Dodge City Bank is planning its loans for the next several years, and is usi

Question

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 - 0.5P + 0.6Y + 0 .2H,             

R2 = .844                            (17)   (0.13) (0.08)   (.06)   

Number of observation (N) = 14

Here, Q denotes mortgage loan demand (in $ millions), P denotes the prime interest rate (%), Y is per capita income ($ thousands), and H is an index of average city housing prices ($ thousands). The standard error of a coefficient is shown in each parenthesis.

1.Interpret the each coefficient except for the intercept.

2.Test the overall statistical significance of the regression equation at 95 % confidence. And interpret your result.

3.Test the statistical significance of each individual right-hand variable at 95 % confidence. And interpret your results.

Economics

Explanation / Answer

1) Results from regression model shows that prime interest rate is -vely related to Mortgage loan demand , where as per capita income and index if average city house price are +vely realted to Mortgage loan demand . With 1 unit increase in H ,with every thing remaining same, Q will rise by 0.5 units.

2) To test overall significance , Compute F stat = R^2 *(k-1) / ( (1-R^2)* (n-k))

with k = 4 , n= 14 , R^2 = 0.844 , F = 1.62307

F at 0.95 level of significance at k-1 , n-k dof is 3.7082 ,

hence oveall model is not significant. as 1.623 < 3.70

3)test for individual coefficient significance : T = coefficient / std error

For P T_p = (-0.5/0.13) = - 3.846

For Y T_y = 0.6/0.08 = 7.5

For H T_h = 0.2 / 0.06 = 3.333

T at 1 - 0.05/2 level of significance for 13 dof is 2.16 ;

since T _ p , T_y, T_h > 2.16 ; then all the cofficient are significant.

hence P , H , Y have statistical signifincat effect on Q

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