# 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.

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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