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Question
NARRBEGIN: SA_82_87An internet-based retail company that specializes in audio and visual equipment is interested in creating a model to determine the amount of money, in dollars, its customers will spend purchasing products from them in the coming year. In order to create a reliable model, this company has tracked a number of variables on its customers. Below you will find the Excel output related to several of these variables. This company has tried using the customer's annual salary for entire household
, the number of children in the household
, and if the customer purchased merchandise from them in the previous year (
in 2004).| Summary measures | |
| Multiple R | 0.7825 |
| R-Square | 0.6122 |
| Adj R-Square | 0.5852 |
| StErr of Estimate | 541.70 |
| ANOVA Table | |||||
| Source | df | SS | MS | F | p-value |
| Explained | 3 | 19921803 | 6640601 | 22.6303 | 0.0000 |
| Unexplained | 43 | 12617877 | 293439 | ||
| Regression coefficients | |||||
| Coefficient | Std Err | t-value | p-value | ||
| Constant | 291.243 | 193.840 | 1.5025 | 0.1403 | |
| Salary | 0.026 | 0.003 | 8.0182 | 0.0000 | |
| Number of children | -331.972 | 79.725 | -4.1640 | 0.0001 | |
| Purchase in 2004 | 281.80 | 133.82 | 2.1058 | 0.0411 | |
(A) Estimate the regression model. How well does this model fit the data?
(B) Is there a linear relationship between the explanatory variables and the dependent variable? Explain how you arrived at your answer at the 5% significance level.
(C) Use the estimated regression model to predict the amount of money a customer will spend if their annual salary is $45,000, they have 1 child and they were a customer that purchased merchandise in the previous year (2004).
(D) Find a 95% prediction interval for the point prediction calculated in (C). Use a t-multiple = 2.02.
(E) Find a 95% confidence interval for the amount of money spent by all customers sharing the characteristics described in (C). Use a t-multiple = 2.02.
(F) How do you explain the differences between the widths of the intervals in (D) and (E)?
Answer
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