Question

1. Use the table below to answer the questions that follows below it. Year Defense budget outlays Gross National Product 1962 51.1 560.3 1963 52.3 590.5 1964 53.6 632.4 1965 49.6 684.9 1966 56.8 749.9 Estimate the econometric regression model by calculating the following: a) a, b, and Y. [4, 3 and 2 marks respectively] b) Write the estimated regression model. [3 marks c) Interpret the regression model. [3 marks]

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Answer 1

a) The output of regression is as follows:

D E F G H - K Regression ? Х Input OK A B 10 11 Year Defence Budget Outlays (Y) Gross National Product (X) 12 1962 51.1) 560.3 13 1963 52.3 590.5 14 1964 53.6 632.4 15 1965 49.6 684.9 16 1966 56.8 749.9 17 18 Input Y Range: $B$11:$B$16 1 Cancel Input X Range: $C$11:$C$16 1 Help Labels Constant is Zero Confidence Level: 95 19 Output options 1 20 21 22 23 24 25 26 27 Output Range: O New Worksheet Ply: O New Workbook Residuals Residuals Standardized Residuals Residual Plots Line Fit Plots

A B с D E F G H 1 SUMMARY OUTPUT 2 3 Regression Statistics 4. Multiple R 0.546221279 5 R Square 0.298357686 6 Adjusted R Square 0.064476914 7 Standard Error 2.646556507 8 Observations 5 9 10 ANOVA 11 df SS MS F Significance F 12 Regression 8.93521597 8.93521597 1.275682835 0.340854254 13 Residual 3 21.01278403 7.004261343 14 Total 4 29.948 15 16 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 17 Intercept 39.96395321 11.32054805 3.530213647 0.038633309 3.936916898 75.99098953 3.936916898| 75.99098953 18 Gross National Product (x) 0.019757686 0.017493017 1.129461303 0.340854254 -0.035912902 0.075428274 -0.035912902 0.075428274 19 20 1

The Defense Budget Outlays (Y) = $\alpha$ + $\beta$ * Gross National Product

$\alpha$ is the Intercept which also means the fixed or the basic part of the defense budget outlays

$\beta$ is the coefficient of multiplication which also means that it is the share of defense budget outlays in the Gross National Product

Thus, the Defense Budget Outlays will have a basic or fixed component $\alpha$ = 39.96 and a variable component that depends on the Gross National Product

$\alpha$	39.96
$\beta$	0.019
Y	39.96 + 0.019 * Gross National Product

b) The estimated regression model is as follows:

Defense Budget Outlays = 39.96 + 0.019 * Gross National Product

c) Interpretation of the regression model:

The Defense Budget Outlays will have a basic or fixed component $\alpha$ = 39.96 and a variable component that depends on the Gross National Product

Thus, depending on the Gross National Product, the Defense Budget Outlays will increase proportionately (with B = 0.019) from its base value of 39.96

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