Explanation The given information is that, a stepwise regression model is fitted to predict car theft based on the predictors ‘Income (per capita income), Unem (unemployment percent), Pupil/Tea (pupil-to-teacher ratio), and Divorce (divorces per 1,000 population) for the 50 U.S. states’. From the reported results, the models with values of s , R adj 2 and R 2 is, Number of variables in model Names of variables in the model s R adj 2 R 2 1 Pupil/Tea 167.482 0.218 0.234 2 Pupil/Tea, Income 152.362 0.353 0.379 3 Pupil/Tea, Income, Unem 144.451 0.418 0.454 4 Pupil/Tea, Income, Unem, divorce 143.362 0.427 0.474 Table 1 Identifying the model that best balances fit: The value of s for the model with four variables ‘Pupil/Tea, Income, Unem, divorce’ is 143.362, which is small when compared to all the other models. Also, the value of R adj 2 = 0.427 and R 2 = 0.474 for 3 variables model is large when compared to other models But the variable divorce has the highest p -value 0.1987 and it is not significant. Hence the 4 variables model is ignored. The value of s for the model with three variables ‘Pupil/Tea, Income, Unem’ is ‘144.351’ which is small when compared to all the other models. Also, the value of R adj 2 = 0.418 and R 2 = 0.454 for 3 variables model is large when compared to other models. That is the 3 variables model is good fit when compared to other variable models. Improvement in model by adding variable: The value of R adj 2 with three variables model is 0.418. When the variable ‘Divorce’ is added to the model the value of R adj 2 has increased to 0.427. By adding the variables ‘divorce’ the value of R adj 2 has increased making the model morefit. The larger value of R adj 2 indicates that model is good fit. Hence, by adding the variable ‘divorce’ has improved the model with respect to R adj 2 . Significant variables: From the reported results, the p -values each predictor variable in all the variable models is, Number of variables in model Income Unemployment Pupil/Tea Divorce 1 0.0004 2 0.0018 0.0000 3 0.0013 0.0157 0.0001 4 0.0007 0.0323 0.0003 0.1987 Table 2 The p -values are said to be most significant, it they are significant at α = 0.01 significant level. Since model with 3 variables is significant the p -value for model with 3 variables are to be considered

Applied Statistics in Business and Economics

5th Edition

ISBN: 9781259329050

Author: DOANE

Publisher: MCG

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Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

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Applied Statistics in Business and Economics

Ch. 13.1 - Observations are taken on net revenue from sales...Ch. 13.1 - Observations are taken on sales of a certain...Ch. 13.1 - Prob. 3SE Ch. 13.1 - A regression model to predict Y, the...Ch. 13.2 - Refer to the ANOVA table below. (a) State the...Ch. 13.2 - Refer to the ANOVA table below. (a) State the...Ch. 13.2 - Prob. 7SE Ch. 13.2 - Refer to the ANOVA table below. (a) State the...Ch. 13.3 - Observations are taken on net revenue from sales...Ch. 13.3 - Observations are taken on sales of a certain...

Ch. 13.3 - Prob. 11SE Ch. 13.3 - A regression model to predict Y, the state...Ch. 13.4 - A regression of accountants starting salaries in a...Ch. 13.4 - An agribusiness performed a regression of wheat...Ch. 13.5 - Prob. 15SE Ch. 13.5 - A regression model to predict the price of...Ch. 13.5 - Prob. 17SE Ch. 13.5 - Prob. 18SE Ch. 13.6 - Prob. 19SE Ch. 13.6 - Prob. 20SE Ch. 13.7 - Prob. 21SE Ch. 13.7 - Using the Metals data, construct a correlation...Ch. 13.8 - Prob. 23SE Ch. 13.8 - Which violations of regression assumptions, if...Ch. 13 - (a) List two limitations of simple regression. (b)...Ch. 13 - (a) What does represent in the regression model?...Ch. 13 - Prob. 3CR Ch. 13 - Prob. 4CR Ch. 13 - Prob. 5CR Ch. 13 - Prob. 6CR Ch. 13 - Prob. 7CR Ch. 13 - Prob. 8CR Ch. 13 - Prob. 9CR Ch. 13 - (a) State the formula for the standard error of...Ch. 13 - (a) What is a categorical predictor? (b) Why is a...Ch. 13 - Prob. 12CR Ch. 13 - Prob. 13CR Ch. 13 - (a) What is multicollinearity? (b) What are its...Ch. 13 - Prob. 15CR Ch. 13 - (a) State the formula for a variance inflation...Ch. 13 - Prob. 17CR Ch. 13 - Prob. 18CR Ch. 13 - Prob. 19CR Ch. 13 - Prob. 20CR Ch. 13 - (a) Name two ways to detect autocorrelated...Ch. 13 - (a) What is a lurking variable? How might it be...Ch. 13 - Instructions for Data Sets: Choose one of the data...Ch. 13 - Note: Exercises marked are based on optional...Ch. 13 - Prob. 27CE Ch. 13 - Note: Exercises marked are based on optional...Ch. 13 - Note: Exercises marked are based on optional...Ch. 13 - Prob. 30CE Ch. 13 - Prob. 31CE Ch. 13 - Prob. 32CE Ch. 13 - Prob. 33CE Ch. 13 - Prob. 34CE Ch. 13 - Prob. 35CE Ch. 13 - Note: Exercises marked are based on optional...Ch. 13 - Note: Exercises marked are based on optional...Ch. 13 - Note: Exercises marked are based on optional...Ch. 13 - Prob. 39CE Ch. 13 - Prob. 40CE Ch. 13 - Prob. 41CE Ch. 13 - In a model of Fords quarterly revenue TotalRevenue...Ch. 13 - In a study of paint peel problems, a regression...Ch. 13 - A hospital emergency room analyzed n = 17,664...Ch. 13 - Prob. 45CE Ch. 13 - A researcher used stepwise regression to create...Ch. 13 - A sports enthusiast created an equation to predict...Ch. 13 - An expert witness in a case of alleged racial...Ch. 13 - Prob. 50CE Ch. 13 - Prob. 51CE Ch. 13 - Prob. 52CE Ch. 13 - Which statement is correct concerning one-factor...Ch. 13 - Prob. 2ERQ Ch. 13 - Prob. 3ERQ Ch. 13 - Prob. 4ERQ Ch. 13 - Prob. 5ERQ Ch. 13 - Prob. 6ERQ Ch. 13 - Prob. 7ERQ Ch. 13 - Prob. 8ERQ Ch. 13 - Prob. 9ERQ Ch. 13 - Prob. 10ERQ Ch. 13 - Prob. 11ERQ Ch. 13 - Prob. 12ERQ Ch. 13 - Prob. 13ERQ Ch. 13 - Prob. 14ERQ Ch. 13 - Prob. 15ERQ

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