An executive of a firm wants to measure the influence of advertising expenditures on sales. She collected data on advertising expenditures (ADV), and sales revenues (SALES). Data was collected for the period 2011 -2020 and reported below. (Hints: sales revenue is the dependent variable).

Note: For this question 1, please do not use Excel Regression Tool and do not write any number from the output file. Do it by hand.

(i). Find the equation of the regression line using least-squares methods including sales revenues (SALES), and advertising expenditures (ADV). Interpret the slope and the co-efficient. (ii). Compute the co-efficient of determination and comment on the strength of the relationship between the two variables. (Hint: calculate SSE and SST). Explain it.

(iii). Compute the sample correlation co-efficient. Explain it.

(iv). Using F test, determine if the two variables are related. Use α=0.05. Write the null and alternative hypotheses and use both the p-value and the critical value approaches. Write your conclusion.

(v). Using t test, determine if the two variables are related. Write the null and alternative hypotheses and use both the p-value and the critical value approaches. Write your conclusion.

(vi). Determine the expected sales volume when the advertising expenditure is 3.5 million dollars.

(vii) Develop a 95% confidence interval estimate for the slope and interpret it (3 points).

(viii). Develop a 95% confidence interval for estimating the mean sales volume with advertising expenditures of 3.5 million dollars. Interpret it.

(ix). Develop a 95% prediction interval for estimating the sales volume for a specific advertising expenditure of 3.5 million dollars. Interpret it.

Transcribed Image Text:

SALES ADV Y X 36.00 3.80 41.00 4.30 38.00 4.60 40.00 4.40 44.00 4.80 48.00 5.00 51.00 5.40 54.00 5.20 50.00 5.60 53.00 5.80 SALES ADV Y X 36.00 3.80 41.00 4.30 38.00 4.60 40.00 4.40 44.00 4.80 48.00 5.00 51.00 5.40 54.00 5.20 50.00 5.60 53.00 5.80