## Consider the following model used to estimate how a hamburger chain’s weekly revenue tr depends on price p, and advertising expenditure a

### economics

##### Description

Section A

Consider the following model used to estimate how a hamburger chain’s weekly revenue tr depends on price p, and advertising expenditure a

tr   1  2 p   3at   t

where price p is measured in Euro while total revenue tr and advertising expenditure a are measured in Euro (000s).

The least squares output from estimating this equation appears in TABLE 1.0 below

(a) Calculate estimated error variance  ˆ  2 and standard error. (10%)

(b) Calculate the R 2 . (15%)

(c) Calculate the t-statistic for  ˆ 2 and using the test of significance approach, without using the reported p-value, explain how you would test the null hypothesis that 0 2   . (10%)

(d) Interpret the p-value = 0.0427 given above, and say how this can be used to test for significance (i.e. to test the null hypothesis that 0 2   ). (15%)

(e) Calculate a 95% confidence interval for the true population parameter  3 . (15%) What does the interval tell you (i.e. in what are you 95% confident)? (5%) Test the hypothesis that advertising expenditure has no effect on the firm’s weekly total revenue. (5%) 3

(f) Test the joint hypothesis that 0 2   and 0 3   (that is, 0 2 3     ) using the F-test at the 5 per cent level of significance.