The slope of price with OmniPower sales β 1 53217 indicates that for a given

The slope of price with omnipower sales β 1 53217

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The slope of price with OmniPower sales ( β ̂ 1 = -53.217) indicates that, for a given amount of monthly promotional expenditures, the mean sales of OmniPower are estimated to decrease by 53.217 bars per month for each 1-cent increase in the price. The slope of monthly promotional expenditures with OmniPower sales ( β ̂ 2 = 3.613) indicates that, for a given price, the mean sales of OmniPower are estimated to increase by 3.613 bars for each additional $1 spent on promotions. These estimates allow you to better understand the likely effect that price and promotion decisions will have in the marketplace. For example, a 10-cent decrease in price is estimated to increase mean sales by 532.17 bars, with a fixed amount of monthly promotional expenditures. A $100 increase in promotional expenditures is estimated to increase mean sales by 361.3 bars, for a given price. Predicting the Dependent Variable Y You can use the multiple regression equation to predict values of the dependent variable. For example, what is the predicted sales for a store charging 79 cents during a month in which promotional expenditures are $400? Using the multiple regression equation, ? ̂ = 5837.521 − 53.217(79) + 3.613(400) = 3078.57 Thus, your sales prediction for stores charging 79 cents and spending $400 in promotional expenditures is 3,078.57 OmniPower bars per month
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6 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 handling fee is added to each order, regardless of the amount of the order. Data collected over the past 24 months (stored in the file warecost.xls ) indicate the warehouse distribution costs (in thousands of dollars), the sales (in thousands of dollars), and the number of orders received. a) State the multiple regression equation b) Interpret the meaning of the slopes, β ̂ 1 and β ̂ 2 in this problem c) Explain why regression coefficient, β ̂ 0 has no practical meaning in the context of this problem. d) Predict the mean monthly warehouse distribution cost when sales are $400,000 and the number of orders is 4,500 Q2 A consumer products company wants to measure the effectiveness of different types of advertising media in the promotion of its products. Specifically, the company is interested in the effectiveness of radio advertising and newspaper advertising (including the cost of discount coupons). A sample of 22 cities with approximately equal populations is selected for study during a test period of one month. Each city is allocated a specific expenditure level both for radio advertising and for newspaper advertising. The sales of the product (in thousands of dollars) and also the levels of media expenditure (in thousands of dollars) during the test month are recorded, with the results stored in the file advertise .xls: a) State the multiple regression equation b) Interpret the meaning of the slopes, β ̂ 1 and β ̂ 2 in this problem c) Interpret the meaning of the regression coefficient, β 0 ̂ d) Predict the mean sales for a city in which radio advertising is $20,000 and newspaper advertising is $20,000
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