The district manager of Jasons, large discount electronics chain, is investigating why certain stores in her region are executing better than others. She believes that three factors are related to total sales: the number of competitors in region, the population in surrounding area, and the amount spent on advertising. From her district, consisting of many hundred stores, she selects a random sample of 30 stores. For each store she gathered the following information.
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Y =
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total sales last year (in $ thousands).
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X1 =
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number of competitors in the region.
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X2 =
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population of the region (in millions).
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X3 =
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advertising expense (in $ thousands).
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The sample data were run on MINITAB, with following results.
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Analysis of variance
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SOURCE
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DF
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SS
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MS
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Regression
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3
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3050.00
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1016.67
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Error
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26
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2200.00
|
84.62
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Total
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29
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5250.00
|
Â
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Predictor
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Coef
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StDev
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t-ratio
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Constant
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14.00
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7.00
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2.00
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X 1
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-1.00
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0.70
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-1.43
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X 2
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30.00
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5.20
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5.77
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X 3
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0.20
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0.08
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a) Conduct global test of hypothesis to determine whether any of regression coefficients aren't equal to zero. Use the .05 level of significance.
b) Conduct tests of hypotheses to find out which of independent variables have significant regression coefficients. Which variables would you consider eliminating? Employ the .05 significance level.