(d) Fit a multiple linear regression model with an interaction term to these data. (e) Estimate o and se(ß,) for this new model. How did these quantities change. Does this tell you anything about the value of adding the interaction term to the model?
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Applied Statistics for Engineers.
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- The owner of a restaurant in Bloomington, Indiana, has recorded sales data for the past 19 years. He has also recorded data on potentially relevant variables. The data are listed in the file P13_17.xlsx. a. Estimate a simple regression equation involving annual sales (the dependent variable) and the size of the population residing within 10 miles of the restaurant (the explanatory variable). Interpret R-square for this regression. b. Add another explanatory variableannual advertising expendituresto the regression equation in part a. Estimate and interpret this expanded equation. How does the R-square value for this multiple regression equation compare to that of the simple regression equation estimated in part a? Explain any difference between the two R-square values. How can you use the adjusted R-squares for a comparison of the two equations? c. Add one more explanatory variable to the multiple regression equation estimated in part b. In particular, estimate and interpret the coefficients of a multiple regression equation that includes the previous years advertising expenditure. How does the inclusion of this third explanatory variable affect the R-square, compared to the corresponding values for the equation of part b? Explain any changes in this value. What does the adjusted R-square for the new equation tell you?The Baker Company wants to develop a budget to predict how overhead costs vary with activity levels. Management is trying to decide whether direct labor hours (DLH) or units produced is the better measure of activity for the firm. Monthly data for the preceding 24 months appear in the file P13_40.xlsx. Use regression analysis to determine which measure, DLH or Units (or both), should be used for the budget. How would the regression equation be used to obtain the budget for the firms overhead costs?Do the sales prices of houses in a given community vary systematically with their sizes (as measured in square feet)? Answer this question by estimating a simple regression equation where the sales price of the house is the dependent variable, and the size of the house is the explanatory variable. Use the sample data given in P13_06.xlsx. Interpret your estimated equation, the associated R-square value, and the associated standard error of estimate.
- Accountants at the Tucson firm, Larry Youdelman,CPAs, believed that several traveling executives were submittingunusually high travel vouchers when they returned from businesstrips. First, they took a sample of 200 vo uchers submitted fromthe past year. Then they developed the following multiple regressionequation relating expected travel cost to number of days onthe road (x1) and distance traveled (x2) in miles:y = $90.00 + $48.50x1 + $.40x2The coefficient of correlation computed was .68.a) If Barba ra Downey returns from a 300-miJe trip that took herout of town for 5 days, what is the expected amount she shouldclaim as expenses?b) Downey submitted a reimbursement request for $685. Whatshould the accountant do?c) Should any other variables be included? Which ones? Why?I obtained a ridge regression model by k-fold cross-validation using cv_glmnet in R. I need to calculate adjusted R^2 and VIFs for it but I don't know howbex Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 3.136512 0.964065 0.985521 0.971252 0971252 Given the above regression statistics, what is the value of the coefficient of determination? 0.964065 3.136512
- A study to determine the correlation between bankdeposits and consumer price indices in Birmingham, Alabama,revealed the following (which was based on n = 5 years of da ta):• LX = 15• Lx2 = 55• Lxy = 70• Ly = 20• L/ = 130a) What is the equation of the least-squares regression line?b) Find the coefficient of correlation. What does it imply to you?c) What is the standard error of the estimate?Bo Using data from 50 workers, a researcher estimates Wage = ẞe + B₁Education + B2Experience + B3Age + ε, where Wage is the hourly wage rate and Education, Experience, and Age are the years of higher education, the years of experience, and the age of the worker, respectively. A portion of the regression results is shown in the following table. Intercept Education Experience Age Coefficients Standard Error t Stat p-Value 7.17 4.26 1.68 0.0991 1.81 0.35 5.17 0.0000 0.45 0.10 4.50 0.0000 -0.01 0.06 -0.17 0.8684 a-1. Interpret the point estimate for ẞ1. As Education increases by 1 year, Wage is predicted to increase by 1.81/hour. As Education increases by 1 year, Wage is predicted to increase by 0.45/hour. As Education increases by 1 year, Wage is predicted to increase by 1.81/hour, holding Age and Experience constant. As Education increases by 1 year, Wage is predicted to increase by 0.45/hour, holding Age and Experience constant. a-2. Interpret the point estimate for $2. As Experience…High-Low; Analysis of Regression Results Regression analysis is commonly used to estimatecosts. However, the usefulness of the results depends upon the quality of the data.Fletcher Inc. is a local delivery company. The employees handle deliveries for a variety of companies that have developed apps that allow customers to place orders for food, beverages, packages, etc.The controller of Fletcher would like to come up with an estimate of the cost behavior for the deliverycosts. Fifteen months of data were collected, and the data appear below.Using the high-low method, the controller did a quick calculation and estimated the variable andfixed portions of the delivery costs. A new employee in the accounting department, however, suggested that regression would give a much better estimate of the costs.Observation Delivery Costs Number of Deliveries1 $148,620 11,5402 150,980 12,1803 199,200 16,5604 143,100 11,6855 203,695 16,6856 183,065 14,8757 156,390 13,0108 193,440 13,0109 189,330…
- Based on the following regression ANOVA table, what is R2? Source df SS MS F Regression 4 1793.2356 448.3089 7.4854 Residual 45 2695.0996 59.8911 Total 49 4488.3352 0.6005 0.3995 0.8807 0.7230In multiple regression analysis, testing the significance of individual regression coefficients is based on A t statistic A z statistic An F statisticThe following multiple regression printout can be used to predict a person's height (in inches) given his or her shoe size and gender, where gender = 1 for males and 0 for females. Regression Analysis: Height Versus Shoe Size, Gender Coefficients Term Coef Constant 55.28 SE Coef 1.04 T-Value P-Value Shoe Size 0.105 Gender 0.268 0.12 0.489 53.1 0.875 0.000 0.000 0.548 0.000 (a) The dependent variable in this regression is which of the following? height gender shoe size constant (b) What is the regression coefficient of shoe size? (c) What is the regression coefficient of gender?