8. The following regression equation for quantity supplied was estimatedusing a
sample of fifty observations.
Q = 2.2 + 0.104P.
(3.4) (0.005)
Standard errors are in the brackets. The total sum of squares was 132 and the residual
sum of squares was 19.5
i. Establish a 99% confidence interval for slope and intercept coefficient.
ii. Test the hypothesis that slope coefficient (ß1) = 0 falls within this interval. Can
we say the price has no effect on the quantity supplied? Use the test of significant
approach at 1% significance level to test the above hypothesis?
iii. Calculate and interpret R-square. What other factors could possibly explain
variations in the quantity supplied?
iv. From (c) can we say the model best fit in the data set?
i. The 99% confidence interval for the slope coefficient is (0.094, 0.114) and for the intercept coefficient is (1.9, 2.5).
ii. The hypothesis that the slope coefficient is 0 falls outside of the confidence interval, so we can reject the hypothesis that the price has no effect on the quantity supplied at the 1% significance level.
iii. The R-square is 0.85, which indicates that 85% of the variation in the quantity supplied can be explained by the price. Other factors that could explain variations in the quantity supplied include the availability of substitutes, the cost of production, and consumer preferences.
iv. From the R-square value, we can say that the model fits the data set well.