Answer to Question #274761 in Accounting for wahu

Question

The saving function of a random sample of ten families is given as where denote aggregate savings, denotes disposable income real interest rate. The sample data are given in the following table:-

20 25 25 30 35 40 43 42 50 55

100 110 115 120 140 145 145 140 150 160

2 2 3 2 3 4 3 4 5 5

Required:

a) Find the regression equation of the savings on disposable income and real interest rate

b) Estimate the savings when the disposable income is 180 and real interest rate is 6

c) Compute the coefficient of multiple determination and adjusted value

d) Test the significance of the individual regression coefficient at the 5% level of significance

e) Estimate the confidence limits of the individual regression coefficient at the 95% confidence level.

f) Test the overall significance of regression at 5% level.

Answer 1

The computations were done using Microsoft Excel. The results are shown in the figure below(Image).

Solution

a) From the results in the figure above, the regression equation of the savings on disposable income and real interest rate is given by:

Savings = -29.885 + 0.440 Disposable Income + 2.418 Real Interest Rate

b)

When the disposable income is 180 and the real interest rate is 6, saving is:

Savings = -29.885 + 0.440 (180) + 2.418 (6) = 63.823

c)

From the Figure above, the coefficient of multiple determination and the adjusted value are given by

Multiple determination = R-Square = 0.9505

Adjusted value = Adjusted R-Square = 0.9364

d)

Test for the significance of the individual regression coefficient at the 5% level of significance:

From the regression equation in part (a), the coefficients of disposable income and real interest rate are 0.440 and 2.418 respectively.

Hypotheses tests: Done using t-test

1) H₀: B₁ = 0

H_a: B₁ ≠ 0

2) H₀: B₁ = 0

H_a: B₁ ≠ 0

From the results in the figure above, the t-statistics for the coefficients of disposable income and real interest rate are 4.5813 and 1.4751. The p-values for the two variables are 0.0025 and 0.1837 respectively.

It's clear that the t-statistics for the coefficients of disposable income is greater than 1.96(critical value) and its p-value is less than 0.05 significance level. Thus, at a 5% significance level, the coefficient of disposable income is greater than 0, and it's significant.

It's also clear that the t-statistics for the coefficients of real interest rate is less than 1.96(critical value) and its p-value is greater than the 0.05 significance level. Thus, at a 5% significance level, the coefficient of the real interest rate is less than 0, and it's not significant.

e)

From the figure above, the confidence limits of the individual regression coefficient at the 95% confidence level are:

Coefficient of disposable income Limit = (0.2133, 0.6683)

Coefficients of real interest rate Limit = (-1.4582, 6.2945 )

f)

is determined using the F-test's statistic p-value of the regression. From the figure above the p-value(f-significance) of the regression is 0.000026912, which is less than 0.05 significance level. This suggests that overall regression is significant.