The district manager of Jasons, a large discount electronics chain, is investigating why certain stores in her region are performing better than others. She believes that three factors are related to total sales: the number of competitors in the region, the population in the surrounding area, and the amount spent on advertising. From her district consisting of several hundred stores, she selects a random sample of 30 stores. For each store, she gathered the following information. y = total sales last year (in $ thousands) x1 = number of competitors in the region x2 = population of the region (in millions) x3 = advertising expense (in $ thousands) The results of a multiple regression analysis, using Minitab, follow. Analysis of variance Source DF SS MS Regression 3 3050 1016.67 Residual Error 26 2200 84.62 Total 29 5250 Predictor Coefficient SE Coefficient t Constant 14.00 7.00 2.00 x1 −1.00 0.70 −1.43 x2 30.00 5.20 5.77 x3 0.20 0.08 2.50 What are the estimated sales for the Bryne store, which has four competitors, a regional population of 0.4 (400,000), and an advertising expense of 30 ($30,000)? Compute the R2 value. (Round your answer to 3 decimal places.) Compute the multiple standard error of estimate. (Round your answer to 3 decimal places.) d-1. State the decision rule. H0: β1 = β2 = β3 = 0; H1: Not all β's are 0. Use the 0.05 level of significance. (Round your answer to 2 decimal places.) d-2. Compute the F-value. (Round your answer to 2 decimal places.) d-3. What is your decision regarding the null hypothesis?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
The district manager of Jasons, a large discount electronics chain, is investigating why certain stores in her region are performing better than others. She believes that three factors are related to total sales: the number of competitors in the region, the population in the surrounding area, and the amount spent on advertising. From her district consisting of several hundred stores, she selects a random sample of 30 stores. For each store, she gathered the following information.
y = total sales last year (in $ thousands)
x1 = number of competitors in the region
x2 = population of the region (in millions)
x3 = advertising expense (in $ thousands)
The results of a multiple
| Analysis of variance | |||||
| Source | DF | SS | MS | ||
| Regression | 3 | 3050 | 1016.67 | ||
| Residual Error | 26 | 2200 | 84.62 | ||
| Total | 29 | 5250 | |||
| Predictor | Coefficient | SE Coefficient | t | |||
| Constant | 14.00 | 7.00 | 2.00 | |||
| x1 | −1.00 | 0.70 | −1.43 | |||
| x2 | 30.00 | 5.20 | 5.77 | |||
| x3 | 0.20 | 0.08 | 2.50 | |||
- What are the estimated sales for the Bryne store, which has four competitors, a regional population of 0.4 (400,000), and an advertising expense of 30 ($30,000)?
- Compute the R2 value. (Round your answer to 3 decimal places.)
- Compute the multiple standard error of estimate. (Round your answer to 3 decimal places.)
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d-1. State the decision rule. H0: β1 = β2 = β3 = 0; H1: Not all β's are 0. Use the 0.05 level of significance. (Round your answer to 2 decimal places.)
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d-2. Compute the F-value. (Round your answer to 2 decimal places.)
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d-3. What is your decision regarding the null hypothesis?
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e-1. If we test the significance of the individual regression coefficients, H0: βi = 0, state the decision rule using the 0.05 significance level. (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.)
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e-2. Should any variable be dropped?
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