Consider the simple regression model Y, =a+BX, +u in which Y is total expenditure on travel...

 

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Consider the simple regression model Y, =a+BX, +u in which Y is total expenditure on travel and X, is total income for the t" state. Including the District of Columbia, you have data for 51 observations. Both variables are measured in billions of dollars. The following is a partial computer output for the data: Variable Coefficient Standard Error Constant 0.4981 0.5355 Income 0.0556 0.0033 Error Sum of Squares (ESS) 417.110 Total Sum of Squares (TSS) 2841.330 (i) What is the economic interpretation of the estimated coefficient for income? Does the numerical value appear reasonable? (ii) Test individually whether the coefficients for the constant term and income are significantly different from zero at the 5 percent level. Be sure to state the null and alternate hypotheses, the test statistic and its distribution, the critical value (or range), and the criterion. What is your conclusion? (iii) Compute the measure of goodness-of-fit. (iv) Compute the 95% confidence intervals for the intercept and the slope coefficient. Consider the simple regression model Y, =a+BX, +u in which Y is total expenditure on travel and X, is total income for the t" state. Including the District of Columbia, you have data for 51 observations. Both variables are measured in billions of dollars. The following is a partial computer output for the data: Variable Coefficient Standard Error Constant 0.4981 0.5355 Income 0.0556 0.0033 Error Sum of Squares (ESS) 417.110 Total Sum of Squares (TSS) 2841.330 (i) What is the economic interpretation of the estimated coefficient for income? Does the numerical value appear reasonable? (ii) Test individually whether the coefficients for the constant term and income are significantly different from zero at the 5 percent level. Be sure to state the null and alternate hypotheses, the test statistic and its distribution, the critical value (or range), and the criterion. What is your conclusion? (iii) Compute the measure of goodness-of-fit. (iv) Compute the 95% confidence intervals for the intercept and the slope coefficient.

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