Consider the simple regression model Yt = a + b Xt + ut in which Yt is total expenditure on travel and Xt is total income for the t th State. Including the District of Columbia, you have data for 51 observations. Both variables are measured in billions of dollars. The following is a atrial computer output for the above data.
VARIABLE COEFFICIENT STDERROR
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)(5 points) What is the econometric interpretation of the estimated coefficient for income? Does the numerical value appear reasonable?
ii)(14 points) Test individually whether the coefficients for the constant term and income are significantly different from zero at the 5% level. Be sure to state the null and alternative hypotheses, the test statistic and its distribution, the critical value (or range), and the criterion. What is your conclusion?
iii)(3 points) Compute the measure of goodness of fit.
iv)(5 points) Compute the 95% confidence intervals for the intercept and the slope coefficient.