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where * denotes extremely small.

First, let us interpret this regression. As expected, there is a positive relationship between expenditure on food and total expenditure. If total expenditure went up by a rupee, on average, expenditure on food increased by about 44 paise. If total expenditure were zero, the average expenditure on food would be about 94 rupees. Of course, this mechanical interpretation of the intercept may not make much economic sense. The r2 value of about 0.37 means that 37 percent of the variation in food expenditure is explained by total expenditure, a proxy for income.

Suppose we want to test the null hypothesis that there is no relationship between food expenditure and total expenditure, that is, the true slope coefficient fS2 = 0. The estimated value of ft2 is 0.4368. If the null hypothesis

The probability of obtaining a |t | of 0.8071 is greater than 20 percent. Hence we do not reject the hypothesis that the true ft2 is 0.5.

Notice that, under the null hypothesis, the true slope coefficient is zero, the F value is 31.1034, as shown in (5.12.2). Under the same null hypothesis, we obtained a t value of 5.5770. If we square this value, we obtain 31.1029, which is about the same as the F value, again showing the close relationship between the t and the F statistic. (Note: The numerator df for the Fstatistic must be 1, which is the case here.)

Using the estimated residuals from the regression, what can we say about the probability distribution of the error term? The information is given in Figure 5.8. As the figure shows, the residuals from the food expenditure regression seem to be symmetrically distributed. Application of the Jarque-Bera test shows that the JB statistic is about 0.2576, and the probability of obtaining such a statistic under the normality assumption is about

(Continued)

Gujarati: Basic I I. Single-Equation I 5. Two-Variable I I © The McGraw-Hill

Econometrics, Fourth Regression Models Regression: Interval Companies, 2004 Edition Estimation and Hypothesis

Testing

150 PART ONE: SINGLE-EQUATION REGRESSION MODELS

A CONCLUDING EXAMPLE (Continued) 14 r

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