Statistics: The Art and Science of Learning from Data (4th Edition)
4th Edition
ISBN: 9780321997838
Author: Alan Agresti, Christine A. Franklin, Bernhard Klingenberg
Publisher: PEARSON
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Chapter 13, Problem 93CP
To determine
Prove that the logistic regression equation,
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Log(Wagei) = α + β1Educationi + β2Femalei + β3Non Whitei + β4Educationi × Femalei + εi For males, and holding other variables constant, the regression output from the linear regression model above implies that an extra year of education is associated with what percent change in wages?
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Determine whether -log (1-
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Chapter 13 Solutions
Statistics: The Art and Science of Learning from Data (4th Edition)
Ch. 13.1 - Predicting weight For a study of female college...Ch. 13.1 - Prob. 2PBCh. 13.1 - Predicting college GPA For all students at Walden...Ch. 13.1 - Prob. 4PBCh. 13.1 - Does more education cause more crime? The FL Crime...Ch. 13.1 - Crime rate and income Refer to the previous...Ch. 13.1 - The economics of golf The earnings of a PGA Tour...Ch. 13.1 - Prob. 8PBCh. 13.1 - Controlling can have no effect Suppose that the...Ch. 13.1 - House selling prices Using software with the House...
Ch. 13.1 - Used cars The following data (also available from...Ch. 13.2 - Predicting sports attendance Keeneland Racetrack...Ch. 13.2 - Predicting weight Lets use multiple regression to...Ch. 13.2 - Prob. 14PBCh. 13.2 - Price of used cars For the 19 used cars listed in...Ch. 13.2 - Prob. 16PBCh. 13.2 - Softball data For the Softball data set on the...Ch. 13.2 - Slopes, correlations, and units In Example 2 on y...Ch. 13.2 - Predicting college GPA Using software with the...Ch. 13.3 - Predicting GPA For the 59 observations in the...Ch. 13.3 - Study time help GPA? Refer to the previous...Ch. 13.3 - Variability in college GPA Refer to the previous...Ch. 13.3 - Does leg press help predict body strength? Chapter...Ch. 13.3 - Prob. 24PBCh. 13.3 - Interpret strength variability Refer to the...Ch. 13.3 - Any predictive power? Refer to the previous three...Ch. 13.3 - Predicting pizza revenue Aunt Ermas Pizza...Ch. 13.3 - Prob. 28PBCh. 13.3 - Mental health again Refer to the previous...Ch. 13.3 - Prob. 30PBCh. 13.3 - House prices Use software to do further analyses...Ch. 13.4 - Body weight residuals Examples 47 used multiple...Ch. 13.4 - Strength residuals In Chapter 12, we analyzed...Ch. 13.4 - Prob. 34PBCh. 13.4 - Nonlinear effects of age Suppose you fit a...Ch. 13.4 - Prob. 36PBCh. 13.4 - Why inspect residuals? When we use multiple...Ch. 13.4 - College athletes The College Athletes data set on...Ch. 13.4 - House prices Use software with the House Selling...Ch. 13.4 - Prob. 40PBCh. 13.5 - U.S. and foreign used cars Refer to the used car...Ch. 13.5 - Prob. 42PBCh. 13.5 - Predict using house size and condition For the...Ch. 13.5 - Quality and productivity The table shows data from...Ch. 13.5 - Predicting hamburger sales A chain restaurant that...Ch. 13.5 - Prob. 46PBCh. 13.5 - House size and garage interact? Refer to the...Ch. 13.5 - Prob. 48PBCh. 13.5 - Comparing sales You own a gift shop that has a...Ch. 13.6 - Prob. 50PBCh. 13.6 - Prob. 51PBCh. 13.6 - Prob. 52PBCh. 13.6 - Prob. 53PBCh. 13.6 - Prob. 54PBCh. 13.6 - Prob. 55PBCh. 13.6 - Prob. 56PBCh. 13.6 - Prob. 57PBCh. 13.6 - Prob. 58PBCh. 13.6 - Prob. 59PBCh. 13 - House prices This chapter has considered many...Ch. 13 - Prob. 61CPCh. 13 - Prob. 62CPCh. 13 - Prob. 63CPCh. 13 - Prob. 64CPCh. 13 - Prob. 65CPCh. 13 - Prob. 66CPCh. 13 - Prob. 67CPCh. 13 - Prob. 68CPCh. 13 - Prob. 69CPCh. 13 - AIDS and AZT In a study (reported in the New York...Ch. 13 - Factors affecting first home purchase The table...Ch. 13 - Unemployment and GDP Refer to Exercise 13.67. When...Ch. 13 - Prob. 75CPCh. 13 - Prob. 76CPCh. 13 - Prob. 77CPCh. 13 - Prob. 78CPCh. 13 - Prob. 79CPCh. 13 - True or false: Slopes For data on y = college GPA,...Ch. 13 - Prob. 81CPCh. 13 - Lurking variable Give an example of three...Ch. 13 - Prob. 83CPCh. 13 - Prob. 84CPCh. 13 - Prob. 85CPCh. 13 - Logistic versus linear For binary response...Ch. 13 - Prob. 87CPCh. 13 - Prob. 88CPCh. 13 - Prob. 89CPCh. 13 - Prob. 90CPCh. 13 - Prob. 91CPCh. 13 - Prob. 92CPCh. 13 - Prob. 93CP
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- Run a simple linear regression in SPSS to know if previous experience (‘prevexp’: Previous Experience-months) significantly predicts current salary(‘salary’: Current Salary) in the work force . Use α =.05 Does Previous Experience significantly predict Current Salary? Report Beta(β), and the p-value (p).arrow_forwardConstruct an example of a regression model that satisfies the assumptionE(ui | Xi) = 0 but for which E(U | X ) ≠0n.arrow_forwardRun a simple linear regression in SPSS to know if previous experience (‘prevexp’: Previous Experience-months) significantly predicts current salary(‘salary’: Current Salary) in the work force . Use α =.05 Is the regression equation significant? That is, does Previous Experience explains (or predicts) a significant amount of variability in Current Salary? Report the F, df (of numerator, and df of the denominator) and p-value.arrow_forward
- Assume a simple logistic regression model for X and Y. We know: bo= -1.1 and b₁ = 0.4 Estimate P(Y= 1) when X = 1.arrow_forwardThe regression equation is calculated to be y' = 5.333 + 0.777x. After conducting a hypothesis test, your decision is to fail to reject the null hypothesis. Predict the value of y' when x=11. A researcher wants to determine if the number of years of education for a parent correlates with the number of years of education for their child. The table shows the number of years of education of the parent and the number of years of education of their child for a random sample of 7. Years of Education of Parent 13 9 12 10 12 10 12 Years of Education of their Child 15 11 10 16 17 12 17 The regression equation is calculated to be y' = 5.333 + 0.777x. After conducting a hypothesis test, your decision is to fail to reject the null hypothesis. Predict the value of y' when x=11. 5.333 13 14 13.88arrow_forwardAssume it is possible to estimate a person's score on Test B from the person's score on Test A. The regression equation is: B' = 2.3A + 9.5. What is a person's predicted score on Test B assuming this person got a 40 on Test A?arrow_forward
- also compute the regression equation in which you predict Y using X as the predictor variablearrow_forwardThe estimated regression equation for a model involving two independent variables and 10 observations follows. ý = 29.1370 + 0.5103x, + 0.4980x2 (a) Interpret b, in this estimated regression equation. O b, = 0.5103 is an estimate of the change in y corresponding to a 1 unit change in x, when x, is held constant. O b, = 29.1370 is an estimate of the change in y corresponding to a 1 unit change in x, when x., is held constant. O b, = 0.4980 is an estimate of the change in y corresponding to a 1 unit change in x, when x, is held constant. O b, = 0.4980 is an estimate of the change in y corresponding to a 1 unit change in x, when x, is held constant. O b, = 0.5103 is an estimate of the change in y corresponding to a 1 unit change in x, when x, is held constant. Interpret b, in this estimated regression equation. O b, = 0.4980 is an estimate of the change in y corresponding to a 1 unit change in x, when x, is held constant. O b, = 0.4980 is an estimate of the change in y corresponding to a…arrow_forwardA regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).The results of the regression were: y=a+bxa=-0.797b=0.181 (c) If a country increases its life expectancy, the happiness index will increase decrease (d) If the life expectancy is increased by 1 years in a certain country, how much will the happiness index change? Round to two decimal places.arrow_forward
- Data was gathered from a random sample of young mothers between the ages of 15 and 19 years, and the relationship between the mother's age (measured in years) and the baby's birth weight (measured in grams) was observed to be linear, with r= 0.88. Further, the regression equation to predict a baby's birth welght based on the mother's age was found to be: Predicted birth weight = -1163.45 + 245.15(age). Based on this information, which one of the following statements is incorrect? O The predicted birth weight for a baby whose mother is 15 years old is 4840.7 grams. O If weight was measured in pounds instead of grams, the value of rwould still be 0.88. O If we switch the variables so that age is the response variable and birth weight is the explanatory variable, r would still be 0,88. O If a mother's age is 25 years, we would not want to use the regression equation to predict the baby's birth weight since this would be considered extrapolation. O Becauseris 0.88, we would consider the…arrow_forwardA virus, due to human error, escaped a research facility in an isolated island. A day after the breach, 7 test subjects were found to be infected. On the sixth day, the count increased to 21 infected. The number increased to 63 infected on the 11th day, 189 on the 16th day, and 567 on the 21st day. If no intervention happened, create a regression model to quantify the infected test subjects after "t" days, graph the function, and, determine the number of infected after 60 days. Use exponential regression model.arrow_forwardUse the linear regression model yˆ=−21.9x+927.93 to predict the y-value for x=37.arrow_forward
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