(The following problem requires an Excel spreadsheet. You may use appropriate Excel formulas where useful)
20. Circulation is the lifeblood of the publishing business. The greater the number of magazines sold, the more it can charge advertisers. Recently, a circulation gap has appeared between the publishers' reports of newsstand sales of magazines and subsequent audits by the Audit Bureau of Circulations. The following data represent the reported and audited newsstand sales (in thousands of magazines) in 2001 for the following ten magazines.
Magazine Reported Audited
YM 621.0 299.6
CosmoGirl 359.7 207.7
Rosie 530.0 325.0
Playboy 492.1 336.3
Esquire 70.5 48.6
TeenPeople 567.0 400.3
More 125.5 91.2
Spin 50.6 39.1
Vogue 353.3 268.6
Elle 263.6 214.3
a. Is there a causal relationship between reported and audited sales? If so, what is the independent variable and what is the dependent variable?
b. Write the algebraic expression for a general theoretical regression line, identifying the variables x and y and all other symbols.
c. Write the algebraic expression for a general estimated regression line
d. What is the interpretation of β1
e. Construct a scatter diagram for the data above
f. What are the estimates of β0 and β1; write the expression for this particular estimated line
g. Predict the mean audited newsstand sales for a magazine that reports newsstand sales of 150,000 magazines
h. What type of data, cross-section or time-series, is used in this regression analysis? Explain your answer
i. Test the hypothesis that there is no relationship between reported and audited sales.
j. Is the estimate of β1 statistically significant at the 99% level? Explain why it is or why it is not?