HW16

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School

Trine University *

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Course

6933

Subject

Statistics

Date

Feb 20, 2024

Type

docx

Pages

Uploaded by GeneralMetal248

1. A study was conducted to investigate browsing activity by shoppers. Shoppers were classified as nonbrowsers, light browsers, and heavy browsers. For each shopper in the study a measure was obtained to determine how comfortable the shopper was in the store. Higher scores indicated greater comfort . Assume that the following data are from this study. DATA i Nonbrowser Light Browser Heavy Browser 4 5 5 5 6 7 6 5 5 3 4 7 3 7 4 4 4 6 5 6 5 4 5 7 Use a 0.05 level of significance to test for differences in comfort levels among the three types of browsers. “ There are significant differences between comfort levels for the three types of browsers. V‘ @ 2. Consider the following data for two variables, and ¥. Excel File: data16-03.xls a. Choose the correct scatter diagram with and y. [y . F10 . -8 A. |6 ] [ ] . 4 L] L] L] -2 ps 4 ) g 10 X,

The correct scatter diagram is | A v @ Does there appear to be a linear relationship between & and Y? Explain. The scatter diagram | shows V\ @ some evidence of a possible linear relationship. b. Develop the estimated regression equation relating and ¥. Save "predicted” and "residuals” (to 4 decimals). ¥ = 2.3220 @+ 0.6366 @:c c. Choose the correct scatter diagram of the standardized residuals versus g for the estimated regression equation developed in part (b). ' Standard Residuals 4 3 2 3| 3 3 5 5 .7 S Predicted y ' Standard Residuals 4 -3 The correct scatter diagram is | B v/ @ Do the model assumptions appear to be satisfied? Explain. The standardized residual plot indicates that the constant variance assumption \ is not V\ 0 satisfied. d. Perform a logarithmic transformation (log;o under Data/Transform Data/Log10) on the dependent variable ¥. Develop an estimated regression equation using the transformed dependent variable (to 4 decimals). logyyy = 0.5134 @+ 0.0a11 Do 3. A study investigated the relationship between audit delay and variables that describe the client and the auditor. The file Audit contains data from a sample of 40 companies on the following set of variables: Delay The length of time from a company's fiscal year-end to the date of the auditor's report. Industry A dummy variable coded 1 if the firm was an industrial company or 0 if the firm was a bank, savings and loan, or insurance company. Public A dummy variable coded 1 if the company was traded on an organized exchange or over the counter; otherwise coded 0. Quality A measure of overall quality of internal controls, as judged by the auditor, on a five-point scale ranging from "virtually none" (1) to "excellent" (5). Finished A measure ranging from 1 to 4, as judged by the auditor, where 1 indicates "all work performed subsequent to year-end" and 4 indicates "most work performed prior to year-end.” Click on the datafile logo to reference the data. DATA I Consider a model in which only Industry is used to predict Delay. At a 0.05 level of significance, test for any positive autocorrelation in the data. Use Table 16.10. ‘ No significant positive autocorrelation vI 4.

The average monthly residential gas bill for Black Hills Energy customers in Cheyenne, Wyoming is $67.95 (Wyoming Public Service Commission website). How is the average monthly gas bill for a Cheyenne residence related to the square footage, number of rooms, and age of the residence? The following data show the average monthly gas bill for last year, square footage, number of rooms, and age for 20 typical Cheyenne residences. Average Monthly Gas Number of Bill for Last Year Age Square Footage Rooms $70.20 16 2537 6 $81.33 2 3437 8 $45.86 27 976 6 $59.21 1 1713 7 $117.88 16 3979 11 $57.78 2 1328 7 $47.01 27 1251 6 $52.89 4 827 5 $32.90 12 645 4 $67.04 29 2849 5 $76.76 1 2392 7 $60.40 26 900 5 $44.07 14 1386 5 $26.68 20 1299 4 $62.70 17 1441 6 $52.45 24 1568 5 $96.11 27 1140 10 a. Develop an estimated regression equation that can be used to predict a residence’s average monthly gas bill for last year given its age. Round your answers to four decimals. ¥ = 60.990 @_ 0.1243 oAge b. Develop an estimated regression equation that can be used to predict a residence’s average monthly gas bill for last year given its age, square footage, and number of rooms. Round your answers to four decimals. Enter negative value as negative number. §j = -5.393. @ + 0.1053 @ Age + 0.0067 @ Square Footage + 8.5267 @ Number of Rooms c. At the 0.05 level of significance, test whether the two independent variables added in part (b), the square footage and the number of rooms, contribute significantly to the estimated regression equation developed in part (a). If not stated otherwise, round your answers to four decimals. Use Table 4 from Appendix B. SSE (reduced) = 8996.3689 & SSE (full) = 1231.2755 [ MSE (full) = 760547 & I F = 33.74 0 (to 2 decimals) I 7 The p-value associated with F is | less than 0.01 <] . Therefore, the addition of the two independent variables @ statistically significant.

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HW16

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