A marketer is interested in the relation between the width of the shelf space for her brand of coffee (x) and weekly sales (y) of the product in a suburban supermarket (assume the height is always at eye level). Marketers are well aware of the concept of 'compulsive purchases', and know that the more shelf space their product takes up, the higher the frequency of such purchases. She believes that in the range of 3 to 9 feet, the mean weekly sales will be linearly related to the width of the shelf space. Suppose the marketer conducted the experiment over a twelve week period (4 weeks with 3' of shelf space, 4 weeks with 6', and 4 weeks with 9'), and observed the sample data in Table 1

Table 1: Coffee Sales data

Shelf space (x)	6	3	6	9	3	9	6	3	9	6	3	9
Weekly sales (y)	526	421	581	630	412	560	434	443	590	570	346	672

Assume the Marketer is interested to estimated the following model

, where is an error term and and are parameters to be estimated.

a) Find the least square regression line of weekly sales on shelf space b) Construct 95% confidence interval of gradient and slope coefficients c) Test that , using 5% level of significance d) Analyze the variance from the given information and present your answers in ANOVA table e) Use results in ANOVA table to test if there is a significant linear relationship between dependent and independent variables at 5% level of significance.

Hint: You may use the following information

Estimated residual standard error (deviation) = 51.63, =112772.9, =26660.4