Question

The following regression equation for quantity supplied was estimated
using a sample of fiftyobservations.
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.
a)Establish a 99% confidence interval for slope and intercept coefficient.
b)Test the hypothesis that slope coefficient (ß1) = 0 falls within this
interval. Can we saytheprice has no effect on the quantity supplied? Use
the test of significant approach at 1% significance levelto test the above
hypothesis?

Answer 1

a) The 99% confidence interval for the slope coefficient (ß1) is (0.094, 0.114). The 99% confidence interval for the intercept coefficient (ß0) is (1.9, 2.5).

b) To test the hypothesis that the slope coefficient (ß1) = 0, we can use the t-test. The t-statistic is 10.4, which is greater than the critical value of 2.58 at the 1% significance level. Therefore, we can reject the null hypothesis that the slope coefficient (ß1) = 0 and conclude that the price has an effect on the quantity supplied.