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    Advertising and price as determinants of sales

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    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 ($)

    SALES ADS PRICE Predict ADS Predict PRICE
    33 3 125 10 130
    61 6 115
    70 10 113
    82 13 130
    17 9 145
    24 6 140
    40 5 120
    48 5 116
    56 7 110
    72 11 108

    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 ???? ? 1 and on ???? ? 2 (Use two tailed test with (??= 0.05). 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

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    Solution Summary

    Advertising and price as determinants of sales

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