1 Regression 39472730773 2 19736365387 48477 000 b Residual 12620946668 31

1 regression 39472730773 2 19736365387 48477 000 b

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1 Regression 39472730.773 2 19736365.387 48.477 .000 b Residual 12620946.668 31 407127.312 Total 52093677.441 33 a. Dependent Variable: Bars b. Predictors: (Constant), Promotion, Price p-value = 0.000 Since the p-value =0.000 < 0.05, we rejected the null hypothesis. We have enough evidence to conclude that at least one of the independent variables (price and/or promotional expenditures) is related to sales.
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9 Tests of Hypothesis To determine whether variable X 2 (amount of promotional expenditures) has a significant effect on sales, taking into account the price of OmniPower bars, the null and alternative hypotheses are H 0 : β 2 = 0 H 1 : β 2 ≠ 0 Coefficients a Model Unstandardized Coefficients Standardized Coefficients t Sig. 95.0% Confidence Interval for B Collinearity Statistics B Std. Error Beta Lower Bound Upper Bound Tolerance VIF 1 (Constant) 5837.521 628.150 9.293 .000 4556.400 7118.642 Price -53.217 6.852 -.690 -7.766 .000 -67.193 -39.242 .991 1.009 Promotion 3.613 .685 .468 5.273 .000 2.216 5.011 .991 1.009 a. Dependent Variable: Bars The p-value = 0.000 Since the p-value =0.000 < 0.05, we rejected the null hypothesis. We have enough evidence to conclude that there is a significant relationship between the variable X 2 (promotional expenditures) and sales, taking into account the price, X 1 At the 0.05 level of significance, is there evidence that the slope of sales with price is different from zero? H 0 : β 1 = 0 H 1 : β 1 ≠ 0 The p-value = 0.000 Since the p-value =0.000 < 0.05, we rejected the null hypothesis. We have enough evidence to conclude that there is a significant relationship between the variable X 1 (price) and sales, taking into account the promotional expenditures, X 2
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10 Confidence Interval Estimation Instead of testing the significance of a population slope, you may want to estimate the value of a population slope. To construct a 95% confidence interval estimate of the population slope, β 1 (the effect of price, X 1 , on sales, Y, holding constant the effect of promotional expenditures, X 2 ), Coefficients a Model Unstandardized Coefficients Standardized Coefficients t Sig. 95.0% Confidence Interval for B Collinearity Statistics B Std. Error Beta Lower Bound Upper Bound Tolerance VIF 1 (Constant) 5837.521 628.150 9.293 .000 4556.400 7118.642 Price -53.217 6.852 -.690 -7.766 .000 -67.193 -39.242 .991 1.009 Promotion 3.613 .685 .468 5.273 .000 2.216 5.011 .991 1.009 a. Dependent Variable: Bars Taking into account the effect of promotional expenditures, the estimated effect of a 1-cent increase in price is to reduce mean sales by approximately 39.242 to 67.193 bars. −67.193 ≤ β 1 ≤ −39.242 You have 95% confidence that this interval correctly estimates the relationship between these variables. More example Construct a 95% confidence interval estimate of the population slope of sales with promotional expenditures. 2.216 ≤ β 1 ≤ 5.011 Thus, taking into account the effect of price, the estimated effect of each additional dollar of promotional expenditures is to increase mean sales by approximately 2.2 to 5.0 bars. You have 95% confidence that this interval correctly estimates the relationship between these variables.
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11 Exercises Q1 A mail-order catalog business selling personal computer supplies, software, and hardware maintains a centralized warehouse. Management is currently examining the process of distribution from the warehouse and wants to study the factors that affect warehouse distribution costs. Currently, a small
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