EBK BUSINESS STATISTICS
8th Edition
ISBN: 9780135179833
Author: STEPHAN
Publisher: VST
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The St. Lucian Government is interested in predicting the number of weekly riders on the public buses using the following variables:
• • • •
Price of bus trips per weekThe population in the cityThe monthly income of ridersAverage rate to park your personal vehicle
Determine the multiple regression equation for the data.
What is the predicted value of the number of weekly riders if: price of bus trips per week = $24; population = $2,000,000; the monthly income of riders = $13,500; and average rate to park your personal vehicle = $150.
Interpret the coefficient of determination.
Consider a linear regression model that relates school expenditures and family background to student performance in Massachusetts using 224 school districts. The response variable is the mean score on the MCAS (Massachusetts Comprehensive Assessment System) exam given in May 1998 to 10th-graders. Four explanatory variables are used: (1) STR is the student-to-teacher ratio, (2) TSAL is the average teacher’s salary, (3) INC is the median household income, and (4) SGL is the percentage of single family households. The Excel Regression output for the sample regression equation is given below.
(a) What proportion of the variation in MCAS score is explained by the explanatory variables?
(b) At the 5% level, are the explanatory variables jointly significant in explaining MCAS score? Explain briefly.
(c) At the 5% level, which variables are individually significant at predicting MCAS score? Explain briefly.
(d) Suppose a second regression model (Model 2) was generated using only…
Consider a linear regression model that relates school expenditures and family background to student performance in Massachusetts using 224 school districts. The response variable is the mean score on the MCAS (Massachusetts Comprehensive Assessment System) exam given in May 1998 to 10th-graders. Four explanatory variables are used: (1) STR is the student-to-teacher ratio, (2) TSAL is the average teacher’s salary, (3) INC is the median household income, and (4) SGL is the percentage of single family households. The Excel Regression output for the sample regression equation is given below.
(a) What proportion of the variation in MCAS score is explained by the explanatory variables?
(b) At the 5% level, are the explanatory variables jointly significant in explaining MCAS score? Explain briefly.
(c) At the 5% level, which variables are individually significant at predicting MCAS score? Explain briefly.
(d) Suppose a second regression model (Model 2) was generated using only…
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardOlympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forwardWhat does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forward
- Consider a linear regression model that relates school expenditures and family background to student performance in Massachusetts using 224 school districts. The response variable is the mean score on the MCAS (Massachusetts Comprehensive Assessment System) exam given in May 1998 to 10th-graders. Four explanatory variables are used: (1) STR is the student-to-teacher ratio, (2) TSAL is the average teacher’s salary, (3) INC is the median household income, and (4) SGL is the percentage of single family households. The Excel Regression output for the sample regression equation is given below. (a) What proportion of the variation in MCAS score is explained by the explanatory variables? (b) At the 5% level, are the explanatory variables jointly significant in explaining MCAS score? Explain briefly. (c) At the 5% level, which variables are individually significant at predicting MCAS score? Explain briefly. (d) Suppose a second regression model (Model 2) was generated using only…arrow_forwardD& T LTD marketing team needed more information about the effectiveness of their 3 main mode of advertising. To determine which type is the most effective, the manager collected one week’s data from 25 randomly selected stores. For each store, the following variables were recorded: Weekly gross sales Weekly expenditure on direct mailing (Direct) Weekly expenditure on newspaper advertising (Newspaper) Weekly expenditure on television commercials (Television) Following is the regression output based on the above-mentioned data. SUMMARY OUTPUT Regression Statistics Multiple R 0.442…arrow_forwardThe regional transit authority for a major metropolitan area wants to determine whetherthere is a relationship between the age of a bus and the annual maintenance cost. A sampleof ten buses resulted in the following data: a. Develop a scatter chart for these data. What does the scatter chart indicate about therelationship between age of a bus and the annual maintenance cost?b. Use the data to develop an estimated regression equation that could be used to predictthe annual maintenance cost given the age of the bus. What is the estimated regressionmodel?c. Test whether each of the regression parameters b0 and b1 is equal to zero at a 0.05level of significance. What are the correct interpretations of the estimated regressionparameters? Are these interpretations reasonable?d. How much of the variation in the sample values of annual maintenance cost does themodel you estimated in part b explain?e. What do you predict the annual maintenance cost to be for a 3.5-year-old bus?arrow_forward
- Suppose the athletic director at a university would like to develop a regression model to predict the point differential for games played by the men's basketball team. A point differential is the difference between the final points scored by two competing teams. A positive differential is a win, and a negative differential is a loss. For a random sample of games, the point differential was calculated, along with the number of assists, rebounds, turnovers, and personal fouls. Use the data in the accompanying table attached below to complete parts a through e below. Assume a = 0.05. a) Using technology, construct a regression model using all three independent variables. y = __ + (_)x1 + (_)x2 + (_)x3 + (_)x4 b) Test the significance of each independent variable using a= 0.10. c) interpret the p-value for each independent variable. d) Construxt a 90% confidence interval for the regression coefficients for each independent variable and interpret the meaning. e) Using the results from…arrow_forwardRestaurant Digest, a famous restaurant magazine writes that the amount of tips servers get in Florida is affected by several factors including the amount of bill, number of adult diners as well as kids and the income of the diners. Use the data below to answer the following questions: Find the multiple regression model. At a level of significance of 0.03, is there a significance relationship between the amount of tip and at least one of the independent variables? What is the likely amount of tip if a group of diners spend $40.33 and had an annual income of $81,000. The diners included 4 adults and 3 kids? What percent of the variation in amount of tip is accounted for by amount of bill, annual income, number of adults and kids? Customer Amount of Tip Amount of Bill Number of adult Diners Number of kids Annual Income 1 $ 7.00 $ 48.97 5 3 100000 2 $ 4.50 $ 28.23 4 3 80000 3…arrow_forwardThe Transactional Records Access Clearinghouse at Syracuse University reported data showing the odds of an Internal Revenue Service audit. The following table shows the average adjusted gross income reported and the percent of the returns that were audited for 20 selected IRS districts. Develop the estimated regression equation that could be used to predict the percent audited given the average adjusted gross income reported. At the .05 level of significance, determine whether the adjusted gross income and the percent audited are related. Did the estimated regression equation provide a good fit? District Adjusted Gross Income ($) Percent Audited Los Angeles 36,664 1.3 Sacramento 38,845 1.1 Atlanta 34,886 1.1 Boise 32,512 1.1 Dallas 34,531 1.0 Providence 35,995 1.0 San Jose 37,799 0.9 Cheyenne 33,876 0.9 Fargo 30,513 0.9 New Orleans 30,174 0.9 Oklahoma City 30,060 0.8 Houston 37,153…arrow_forward
- Five pairs of data are used in determining a regression line ŷ = -3 + 4x. If the five values of the explanatory variable are 28, 45, 16, 41, and 20, respectively, what is the mean of the five values of the response variable?arrow_forwardThe following table shows the starting salary and profile of a sample of 10 employees in a certain call center agency. Run a multiple regression analysis with starting salary as the dependent variable (pesos) and GPA, years of experience and civil service ratings as the independent variables. Use .05 level of significance. starting salary GPA Years of experience Civil Service Ratings 15000 80.1 1 79.5 15000 81.2 1 78.0 15500 81.3 2 79.0 16000 82.4 3 80.0 16200 83.4 3 85.0 17500 87.9 4 89.9 18000 90.3 5 89.1 16300 84.2 3 84.1 17000 87.0 4 89.0 17900 88.1 5 89.2 In the ANOVA F test output, what is the computed F and the conclusion of the test regarding the overall significance of the model?arrow_forwardThe following table shows the starting salary and profile of a sample of 10 employees in a certain call center agency. Run a multiple regression analysis with starting salary as the dependent variable (pesos) and GPA, years of experience and civil service ratings as the independent variables. Use .05 level of significance. starting salary GPA Years of experience Civil Service Ratings 15000 80.1 1 79.5 15000 81.2 1 78.0 15500 81.3 2 79.0 16000 82.4 3 80.0 16200 83.4 3 85.0 17500 87.9 4 89.9 18000 90.3 5 89.1 16300 84.2 3 84.1 17000 87.0 4 89.0 17900 88.1 5 89.2 Based on the multiple regression output, if GPA and civil service ratings are held fixed, how much is the expected increase in the starting salary (pesos) for every one year increase in the years of experience?arrow_forward
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