Audited Sales

     12.5

Circulation is the lifeblood of the publishing business.   The larger the sales of a magazine, the more it can charge advertisers.   Recently, a circulation gap has appeared between the publishers’ reports of   magazines’ newsstand sales and subsequent audits by the Audit Bureau of   Circulations. The data in the file represent the reported and audited   newsstand yearly sales (in thousands) for the following 10 magazines:       

 Magazine   Reported (X) Audited (Y)   YM 621 299.6    CosmoGirl   359.7 207.7   Rosie 530   325    Playboy   492.1 336.3    Esquire 70.5   48.6    TeenPeople   567 400.3   More 125.5   91.2    Spin 50.6   39.1    Vogue 353.3   268.6    Elle 263.6   214.3         

a. Construct   a scatter plot.   For these   data, b0 = 26.724 and b1 = 0.5719.   

b. Interpret   the meaning of the slope, b1, in this problem.   

c. Predict   the audited newsstand sales for a magazine that reports newsstand sales of   400,000.    

     12.9

An agent for a   residential real estate company in a large city would like to be able to   predict the monthly rental cost for apartments, based on the size of the   apartment, as defined by square footage. A sample of 25 apartments (stored in   the file Rent) in a particular residential neighborhood was selected, and the   information gathered revealed the following:    

a. Construct a scatter plot.   

b. Use the least-squares method to find   the regression coefficients b0 and b1.

  c. Interpret the meaning of b0 and b1 in   this problem.  

 d. Predict the monthly rent for an   apartment that has 1,000 square feet.  

 e. Why would it not be appropriate to use   the model to predict the monthly rent for apartments that have 500 square   feet?  

 f. Your friends Jim and Jennifer are   considering signing a lease for an apartment in this residential   neighborhood. They are trying to decide between two apartments, one with   1,000 square feet for a monthly rent of $1,275 and the other with 1,200   square feet for a monthly rent of $1,425. Based on (a) through (d), which   apartment do you think is a better deal?      Rent Size   950 850   1600 1450   1200 1085   1500 1232   950 718   1700 1485   1650 1136   935 72 6   875 700   1150 956   1400 1100   1650 1285   2300 1985   1800 1369   1400 1175   1450 1225   1100 1245   1700 1259   1200 1150   1150 896   1600 1361   1650 1040   1200 755   800 1000   1750 1200    

     12.17

In Problem 12.5   on page 417, you used reported magazine newsstand sales to predict audited   sales (stored in the file Circulation). For that data, SSR = 130,301.41 and   SST = 144,538.64.      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. Determine the coefficient of   determination, r2, and interpret its meaning.   

b. Determine the standard error of the   estimate.   

c. How useful do you think this   regression model is for predicting audited sales?