Question

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 intervalestimate.


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  • CreatedJuly 29, 2013
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