You have estimated the following model for demand of grape juice using one
hundred observations.
Qg= 150.83–0.75Pg+ 0.37Po+0.65Y.
(0.04) (0.23) (0.02) (0.52)R-square=0.78
Where, Qg=quantity demanded of grape juicebbottles.
Pg=price of grape juice per unit.
Po=Priceoforangejuice.
Y=Income.
Standard errors are in parenthesis.
a)Test the significance of the estimated R-square.
b)Calculate thevalueofadjustedR-square.
a) To test the significance of the estimated R-square, we can use the F-test. The F-test is used to test the null hypothesis that the R-square is equal to zero. The F-test statistic is calculated by dividing the R-square by its standard error. In this case, the F-test statistic is 78/0.04 = 1950. The critical value of the F-test statistic at a 5% significance level is 3.84. Since the F-test statistic is greater than the critical value, we can reject the null hypothesis and conclude that the R-square is significantly different from zero.
b) The adjusted R-square is calculated by subtracting the number of independent variables from the R-square and dividing the result by one minus the R-square. In this case, the adjusted R-square is (0.78 - 4)/(1 - 0.78) = 0.75.