Exam 24: Inferences for Regression
Exam 1: Stats Starts Here33 Questions
Exam 2: Displaying and Describing Categorical Data70 Questions
Exam 3: Displaying and Summarizing Quantitative Data148 Questions
Exam 4: Understanding and Comparing Distributions46 Questions
Exam 5: The Standard Deviation As a Ruler and the Normal Model111 Questions
Exam 6: Scatterplots, association, and Correlation78 Questions
Exam 7: Linear Regression71 Questions
Exam 8: Regression Wisdom32 Questions
Exam 9: Understanding Randomness26 Questions
Exam 10: Sample Surveys64 Questions
Exam 11: Experiments and Observational Studies80 Questions
Exam 12: From Randomness to Probability69 Questions
Exam 13: Probability Rules95 Questions
Exam 14: Random Variables215 Questions
Exam 15: Sampling Distribution Models51 Questions
Exam 16: Confidence Intervals for Proportions71 Questions
Exam 17: Testing Hypotheses About Proportions44 Questions
Exam 18: More About Tests67 Questions
Exam 19: Comparing Two Proportions53 Questions
Exam 20: Inferences About Means123 Questions
Exam 21: Comparing Means50 Questions
Exam 22: Paired Samples and Blocks35 Questions
Exam 23: Comparing Counts76 Questions
Exam 24: Inferences for Regression57 Questions
Exam 25: Analysis of Variance39 Questions
Exam 26: Multifactor Analysis of Variance22 Questions
Exam 27: Multiple Regression22 Questions
Exam 28: Multiple Regression Wisdom21 Questions
Exam 29: Rank-Based Nonparametric Tests29 Questions
Exam 30: The Bootstrap27 Questions
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Applicants for a particular job,which involves extensive travel in Spanish-speaking countries,must take a proficiency test in Spanish.The sample data below were obtained in a study of the relationship between the numbers of years applicants have studied Spanish and their score on the test.Use the regression analysis below to explain what the R-squared in this regression means.
Dependent variable is: Score
R-squared = 83.0%
s = 5.65138 with 10 - 2 = 8 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Constant 31.53333 6.360418 4.957745 0.00111 Number of years 10.90476 1.744054 6.252538 0.000245
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The index of exposure to radioactive waste and the cancer mortality rates (deaths per 100,000)were recorded for nine different geographic regions. Dependent variable is: Cancer Mortality Rate
R-squared = 85.8%
S = 14.00993 with 9 - 2 = 7 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Constant 114.7156 8.045663 14.25807 0.00000198 Index of Exp 9.231456 1.418787 6.506584 0.000332
(Multiple Choice)
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Consider a logistic regression model for the probability of a "success",given a quantitative variable X. Term Estimate Intercept -4.00 0.10 Use the output above to estimate the probability of a failure when X = 25.
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Applicants for a particular job,which involves extensive travel in Spanish-speaking countries,must take a proficiency test in Spanish.The sample data below were obtained in a study of the relationship between the numbers of years applicants have studied Spanish and their score on the test.Using a 1% level of significance,carry out a test to determine if the linear correlation is different from 0.The regression analysis is given below.
Dependent variable is: Score
R-squared = 83.0%
s = 5.65138 with 10 - 2 = 8 degrees of freedom
(Essay)
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A grass seed company conducts a study to determine the relationship between the density of seeds planted (in pounds per 500 sq ft)and the quality of the resulting lawn.Eight similar plots of land are selected and each is planted with a particular density of seed.One month later the quality of each lawn is rated on a scale of 0 to 100.The sample data are given below. Seed Density Lawn Quality 1 30 1 40 2 40 3 40 3 50 3 65 4 50 5 50 Using a 10% level of significance,is there evidence of an association between seed density and lawn quality?
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Ten students from a large lecture course were randomly sampled to see how many hours they studied for the final exam and their grade on the final exam.The professor wants to conduct a linear regression to determine if there is an association between the amount of time spent studying and the student's grade on the exam.Several plots are shown below.




(Essay)
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Applicants for a particular job,which involves extensive travel in Spanish-speaking countries,must take a proficiency test in Spanish.The sample data were obtained in a study of the relationship between the numbers of years applicants have studied Spanish and their score on the test.Use the regression analysis and summary statistics given below to find a 95% prediction interval for the score of an applicant who has studied Spanish for 2.2 years. Variable Count Mean StdDev Range Years 10 3.5 0.341565 3 Score 10 69.7 4.088058 41 Dependent variable is: Score R-squared = 83.0%
S = 5.65138 with 10 - 2 = 8 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Constant 31.53333 6.360418 4.957745 0.00111 Number of years 10.90476 1.744054 6.252538 0.000245
(Multiple Choice)
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Ten students in a graduate program at the University of Toronto were randomly selected.Their grade point averages (GPAs)when they entered the program were between 3.5 and 4.0.The students' GPAs on entering the program and their current GPAs were recorded.Use the regression analysis provided below to find a 95% confidence interval for the slope of the regression line. Dependent variable is: Current GPA
R-squared = 0.001849
S = 0.1452 with 10 - 2 = 8 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Constant 3.674375 0.95089 3.864144 0.004781 Entering GPA 0.03125 0.256697 0.121739 0.906108
(Multiple Choice)
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Determine which plot shows the strongest linear correlation.
(Multiple Choice)
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Applicants for a particular job,which involves extensive travel in Spanish-speaking countries,must take a proficiency test in Spanish.The sample data below were obtained in a study of the relationship between the numbers of years applicants have studied Spanish and their score on the test.A 95% confidence interval for the mean score of all applicants who have studied Spanish for 2.5 years was determined to be (53.0,64.6).Give an interpretation of this interval. Variable Count Mean StdDev Range Years 10 3.5 0.341565 3 Score 10 69.7 4.088058 41 Dependent variable is: Score R-squared = 83.0%
S = 5.65138 with 10 - 2 = 8 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Constant 31.53333 6.360418 4.957745 0.00111 Number of years 10.90476 1.744054 6.252538 0.000245
(Multiple Choice)
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Ten students in a graduate program at the University of Toronto were randomly selected.Their grade point averages (GPAs)when they entered the program were between 3.5 and 4.0.The data consist of the students' GPAs on entering the program and their current GPAs.Several graphs are shown below.




(Essay)
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The index of exposure to radioactive waste and the cancer mortality rates (deaths per 100,000)were recorded for nine different geographic regions.Use the regression analysis and summary statistics provided below to determine a 95% prediction interval for the cancer mortality rate of a county whose index of exposure is 5.93. Variable Count Mean StdDev Range Index of Exp 9 4.617778 1.163731 10.39 Cancer Mortality Rate 9 157.3444 11.59712 96.8 Dependent variable is: Cancer Mortality Rate R-squared = 85.8%
S = 14.00993 with 9 - 2 = 7 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Constant 114.7156 8.045663 14.25807 0.00000198 Index of Exp 9.231456 1.418787 6.506584 0.000332
(Multiple Choice)
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Determine which plot shows the strongest linear correlation.
(Multiple Choice)
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The typing speeds (in words per minute)and reading speeds (in words per minute)of nine randomly selected secretaries were recorded.Use the regression analysis and summary statistics provided below to determine a 90% prediction interval for the reading speed of a secretary whose typing speed is 50. Variable Count Mean StdDev Range Typing speed 9 60.44444 3.3587 35 Reading speed 9 501.8889 33.42298 297 Dependent variable is: Reading speed R-squared = 12.385%
S = 100.3348 with 9 - 2 = 7 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Constant 290.2093 215.4116 1.347231 0.219884 Typing speed 3.502052 3.520579 0.994737 0.352998
(Multiple Choice)
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Applicants for a particular job,which involves extensive travel in Spanish-speaking countries,must take a proficiency test in Spanish.The sample data were obtained in a study of the relationship between the numbers of years applicants have studied Spanish and their score on the test.Use the regression analysis given below to find a 99% confidence interval for the slope of the regression line. Dependent variable is: Score
R-squared = 83.0%
S = 5.65138 with 10 - 2 = 8 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Constant 31.53333 6.360418 4.957745 0.00111 Number of years 10.90476 1.744054 6.252538 0.000245
(Multiple Choice)
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A grass seed company conducts a study to determine the relationship between the density of seeds planted (in pounds per 500 sq ft)and the quality of the resulting lawn.Eight similar plots of land are selected and each is planted with a particular density of seed.One month later the quality of each lawn is rated on a scale of 0 to 100.The regression analysis is given below. Dependent variable is: Lawn Quality
R-squared = 36.0%
S = 9.073602 with 8 - 2 = 6 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Constant 33.14815 7.510757 4.413423 0.004503 Seed Density 4.537037 2.469522 1.837213 0.115825
(Multiple Choice)
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Applicants for a particular job,which involves extensive travel in Spanish-speaking countries,must take a proficiency test in Spanish.The sample data below were obtained in a study of the relationship between the numbers of years applicants have studied Spanish and their score on the test.A 95% prediction interval for the score of an applicant who has studied Spanish for 2.6 years was determined to be (45.7,74.0). Variable Count Mean StdDev Range Years 10 3.5 0.341565 3 Score 10 69.7 4.088058 41 Dependent variable is: Score R-squared = 83.0%
S = 5.65138 with 10 - 2 = 8 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Constant 31.53333 6.360418 4.957745 0.00111 Number of years 10.90476 1.744054 6.252538 0.000245
(Multiple Choice)
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The reading speeds (in tens of words per minute)and typing speeds (in words per minute)of nine randomly selected secretaries were recorded. Dependent variable is: Reading speed
R-squared = 97.9521%
S = 2.094847 with 9 - 2 = 7 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Constant -40.738 5.820749 -6.99876 0.000212 Typing Speed 2.260433 0.123535 18.29785 3.61\times1
(Multiple Choice)
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Ten students in a graduate program at the University of Toronto were randomly selected.Their grade point averages (GPAs)when they entered the program were between 3.5 and 4.0.The students' GPAs on entering the program and their current GPAs were recorded. Dependent variable is: Current GPA
R-squared = 0.677968
S =0.024768 with 10 - 2 = 8 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Constant 3.584756 0.078183 45.85075 5.66\times1 Entering GPA 0.090953 0.022162 4.103932 0.003419
(Multiple Choice)
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If the assumptions for regression inferences are met,what would you expect to see when constructing a residual plot and a normal probability plot for the residuals?
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