I have two data sets and there are some questions that you need to answer for both data sets for regression. The questions are pretty short it won't take long enough to complete it.
Data set 1: Annual domestic sales and advertising of Lydia E. Pinkham Medicine Company: both in thousands of dollars. 1907-1960. (Pankratz, 1991)
Data set 2: Advertising and sales data: 36 consecutive monthly sales and advertising expenditures of a dietary weight control product
Both data sets contain a) advertising expenditure for particular periods of time, and b) sales (revenue) in the corresponding period. The key business question is: how advertising expenditure affects sales?
In your report, for each data set, you MUST:
1) Write down the linear model (7 points)
2) Identify the dependent, and the independent variable (7 points)
3) Conduct a regression analysis, and cut & paste the results to your report (16 points)
a. Identify estimates of β0 and β1
b. R-square
c. Standard error
4) Provide a line fit plot (scatter plot of the data, and the predicted y line, with the axis clearly labeled) (8 points)
5) Provide a histogram of the residues (8 points)
6) Provide a plot of residues against the predicted y (8 points)
7) Provide a plot of residues over time (8 points)
Answer the following questions, in complete sentences, for each data set. (7 points each) 8) Does advertising have an impact on sales? If so, how much? Explain.
9) Does the model fit well with the data? Explain.
10) Are all the required conditions of the regression met?
11) When there is no advertising, does the company have positive sales?
The following question is for both data sets (i.e. do not have to answer for each individual data set)
12) Compare the two businesses. Which business is more effective in advertising? How much more? Explain. (20 points)
EXTRA CREDIT QUESTIONS (12.5 points each)
E1) Does the advertising effect (if any) have diminishing returns (that is, the impact of advertising becomes smaller when more is spent))? Can you construct a regression model to test that? Show the analysis for at least one of the data sets.
E2) Does advertising expenditure in a previous time period (last month in data set 2, for example) have an impact on sales in the current period? Can you construct a regression model to test that? Show the analysis for at least one of the data sets.