Sam Smith, owner and general manager of Campus Stationery Store, is concerned about the sales behavior of a scanner at the store.  He understands that there may be many factors, which may help explain sales, but he believes that advertising and price are major determinants of sales.  Sam collects the data given below with Y = SALES (# of sales), X1 = ADS (# of ads), X2 = PRICE ($)

Regression Analysis: SALES versus ADS, PRICE 

The regression equation is

SALES = 157 + 4.33 ADS - 1.14 PRICE

Predictor        Coef                SE Coef          T         P

Constant         157.50              33.78            4.66     0.002

ADS                4.327                1.078            4.01     0.005

PRICE           -1.1428             0.2677          -4.27    0.004

S = 10.1422

R-Sq = 82.9%   

R-Sq(adj) = 78.1%

Analysis of Variance

Source          DF      SS      MS      F      P

Regression       2  3502.0  1751.0  17.02  0.002

Residual Error   7   720.1   102.9

Total            9  4222.1

Predicted Values for New Observations

New Obs    Fit  SE Fit      95% CI          95% PI

      1  52.20    4.67  (41.16, 63.25)  (25.80, 78.61)

 Values of Predictors for New Observations

New Obs   ADS  PRICE

      1  10.0    130

Correlations: SALES, ADS, PRICE 

        SALES     ADS

ADS     0.621

        0.055

PRICE -0.661   0.008

      0.037   0.982

Cell Contents: Pearson correlation

               P-Value

a. Analyze the above output to determine the multiple regression equation.

b. Find and interpret the multiple index of determination (R-Sq). 

c. Perform the t-tests on βˆ1and on βˆ2(use two tailed test with ( = .05). Interpret your results.

d. Predict the number of sales given that there were 10 ads and the price was $130. Use both a point estimate and the appropriate interval estimate.

Transcribed Image Text:

SALESADS PRICE Predict ADS Predict PRICE 125 115 113 130 145 140 120 116 110 108 10 130 61 70 82 17 24 40 48 56 72 10 13