Consider a logistic regression model for the probability of a "success",given a quantitative variable X. \[\begin{array} { | l | c | } \hline \text { Term } & \text { Estimate } \\ \hline \text { Intercept } & - 4.00 \\ \hline \mathrm { X } & 0.10 \\ \hline \end{array}\] Use the output above to estimate the odds in favour of a success when X = 25.

A) 0.1824 B) 0.8176 C) 0.2019 D) 0.7981 E) 0.2231 A) 0.1824 B) 0.8176 C) 0.2019 D) 0.7981 E) 0.2231

The sample data below are the index of exposure to radioactive waste for nine different geographic regions and cancer mortality rates (deaths per 100,000). \[\begin{array} { c | c } \text { Index of Exposure } & \text { Cancer Mortality Rate } \\ \hline 2.49 & 147.1 \\ 2.57 & 130.1 \\ 3.41 & 129.9 \\ 1.25 & 113.5 \\ 1.62 & 137.5 \\ 3.83 & 162.3 \\ 11.64 & 207.5 \\ 6.41 & 177.9 \\ 8.34 & 210.3 \end{array}\] Using a 1% level of significance,do the data below support the claim that a higher index of exposure is associated with a higher cancer mortality rate?

H0: No linear relationship between the i

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 following data consist of the students' GPAs on entering the program and their current GPAs. \[\begin{array} { c | c } \text { Entering GPA } & \text { Current GPA } \\ \hline 3.5 & 3.6 \\ 3.8 & 3.7 \\ 3.6 & 3.9 \\ 3.6 & 3.6 \\ 3.5 & 3.9 \\ 3.9 & 3.8 \\ 4.0 & 3.7 \\ 3.9 & 3.9 \\ 3.5 & 3.8 \\ 3.7 & 4.0 \end{array}\] Using a 10% level of significance,do the data below provide evidence of the conclusion that higher entering GPAs are associated with higher current GPAs?

H0: No linear relationship between enter

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. \[\begin{array} { c | c } \begin{array} { c } \text { Number } \\ \text { of years } \end{array} & \text { Score } \\ \hline 3 & 57 \\ 4 & 78 \\ 4 & 72 \\ 2 & 58 \\ 5 & 89 \\ 3 & 63 \\ 4 & 73 \\ 5 & 84 \\ 3 & 75 \\ 2 & 48 \end{array}\] Using a 1% level of significance,do the data provide sufficient evidence to conclude that the slope of the regression line is not 0 and hence that number of years of study is useful as a predictor of score on the test?

H0: No linear relationship between the n

The index of exposure to radioactive waste and the cancer mortality rates (deaths per 100,000)were recorded for nine different geographic regions.A 95% prediction interval for the cancer mortality rate of a region whose index of exposure is 5.79 is 133.0 to 203.4 deaths per 100,000. \[\begin{array} { l c l l c } \text { Variable } & \text { Count } & \text { Mean } & \text { StdDev } & \text { Range } \\ \text { Index of Exp } & 9 & 4.617778 & 1.163731 & 10.39 \\ \text { Cancer Mortality Rate } & 9 & 157.3444 & 11.59712 & 96.8 \end{array}\] Dependent variable is: Cancer Mortality Rate R-squared = 85.8% S = 14.00993 with 9 - 2 = 7 degrees of freedom \[\begin{array} { l l l l l } \text { Variable } & \text { Coefficient } & \text { SE(Coeff) } & \text { t-ratio } & \text { P-value } \\ \text { Constant } & 114.7156 & 8.045663 & 14.25807 & 0.00000198 \\ \text { Index of Exp } & 9.231456 & 1.418787 & 6.506584 & 0.000332 \end{array}\]

A) Based on this regression,we are 95% confident that the index of exposure will increase between 133.0 and 203.4 for each unit increase in the cancer mortality rate over 5.79. B) Based on this regression,we know that 95% of all random samples of regions will have a mean cancer mortality rate that is between 133.0 and 203.4 deaths per 100,000. C) Based on this regression,we are 95% confident that a region with an index of exposure of 5.79 will have a cancer mortality rate that is between 133.0 and 203.4 deaths per 100,000. D) Based on this regression,we are 95% confident that the mean cancer mortality rate will increase between 133.0 and 203.4 deaths per 100,000 for each unit increase in the index of exposure over 5.79. E) Based on this regression,we are 95% confident that the mean cancer mortality rate for regions with an index of exposure of 5.79 will be between 133.0 and 203.4 deaths per 100,000. A) Based on this regression,we are 95% confident that the index of exposure will increase between 133.0 and 203.4 for each unit increase in the cancer mortality rate over 5.79. B) Based on this regression,we know that 95% of all random samples of regions will have a mean cancer mortality rate that is between 133.0 and 203.4 deaths per 100,000. C) Based on this regression,we are 95% confident that a region with an index of exposure of 5.79 will have a cancer mortality rate that is between 133.0 and 203.4 deaths per 100,000. D) Based on this regression,we are 95% confident that the mean cancer mortality rate will increase between 133.0 and 203.4 deaths per 100,000 for each unit increase in the index of exposure over 5.79. E) Based on this regression,we are 95% confident that the mean cancer mortality rate for regions with an index of exposure of 5.79 will be between 133.0 and 203.4 deaths per 100,000.

The index of exposure to radioactive waste and the cancer mortality rates (deaths per 100,000)were recorded for nine different geographic regions.A 95% confidence interval for the mean cancer mortality rate of all regions whose index of exposure is 6.57 was determined to be (162.5,188.2). \[\begin{array} { l c l l c } \text { Variable } & \text { Count } & \text { Mean } & \text { StdDev } & \text { Range } \\ \text { Index of Exp } & 9 & 4.617778 & 1.163731 & 10.39 \\ \text { Cancer Mortality Rate } & 9 & 157.3444 & 11.59712 & 96.8 \end{array}\] Dependent variable is: Cancer Mortality Rate R-squared = 85.8% S = 14.00993 with 9 - 2 = 7 degrees of freedom \[\begin{array} { l l l l l } \text { Variable } & \text { Coefficient } & \text { SE(Coeff) } & \text { t-ratio } & \text { P-value } \\ \text { Constant } & 114.7156 & 8.045663 & 14.25807 & 0.00000198 \\ \text { Index of Exp } & 9.231456 & 1.418787 & 6.506584 & 0.000332 \end{array}\]

A) Based on this regression,we are 95% confident that the mean index of exposure will increase between 162.5 and 188.2 points for each one-unit increase in the cancer mortality rate. B) Based on this regression,95% of all random samples will have a mean cancer mortality rate between 162.5 and 188.2 deaths per 100,000. C) With 95% confidence,the cancer mortality rate for a region with an index of exposure of 6.57 is between 162.5 and 188.2 deaths per 100,000,based on this regression. D) Based on this regression,we are 95% confident that the mean cancer mortality rate will increase between 162.5 and 188.2 deaths per 100,000 for each one-unit increase in the index of exposure. E) With 95% confidence,the mean cancer mortality rate for regions with an index of exposure of 6.57 is between 162.5 and 188.2 deaths per 100,000,based on this regression. A) Based on this regression,we are 95% confident that the mean index of exposure will increase between 162.5 and 188.2 points for each one-unit increase in the cancer mortality rate. B) Based on this regression,95% of all random samples will have a mean cancer mortality rate between 162.5 and 188.2 deaths per 100,000. C) With 95% confidence,the cancer mortality rate for a region with an index of exposure of 6.57 is between 162.5 and 188.2 deaths per 100,000,based on this regression. D) Based on this regression,we are 95% confident that the mean cancer mortality rate will increase between 162.5 and 188.2 deaths per 100,000 for each one-unit increase in the index of exposure. E) With 95% confidence,the mean cancer mortality rate for regions with an index of exposure of 6.57 is between 162.5 and 188.2 deaths per 100,000,based on this regression.

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% confidence interval for the average cancer mortality rate of a county whose index of exposure is 6.81 \[\begin{array} { l c l l c } \text { Variable } & \text { Count } & \text { Mean } & \text { StdDev } & \text { Range } \\ \text { Index of Exp } & 9 & 4.617778 & 1.163731 & 10.39 \\ \text { Cancer Mortality Rate } & 9 & 157.3444 & 11.59712 & 96.8 \end{array}\] Dependent variable is: Cancer Mortality Rate R-squared = 85.8% S = 14.00993 with 9 - 2 = 7 degrees of freedom \[\begin{array} { l l l l l } \text { Variable } & \text { Coefficient } & \text { SE(Coeff) } & \text { t-ratio } & \text { P-value } \\ \text { Constant } & 114.7156 & 8.045663 & 14.25807 & 0.00000198 \\ \text { Index of Exp } & 9.231456 & 1.418787 & 6.506584 & 0.000332 \end{array}\]

A) 164.3 to 190.9 deaths per 100,000 B) 143.4 to 211.8 deaths per 100,000 C) 174.2 to 180.9 deaths per 100,000 D) 167.9 to 185.9 deaths per 100,000 E) 141.8 to 213.3 deaths per 100,000 A) 164.3 to 190.9 deaths per 100,000 B) 143.4 to 211.8 deaths per 100,000 C) 174.2 to 180.9 deaths per 100,000 D) 167.9 to 185.9 deaths per 100,000 E) 141.8 to 213.3 deaths per 100,000

Exam 24: Inferences for Regression

The index of exposure to radioactive waste and the cancer mortality rates (deaths per 100,000)were recorded for nine different geographic regions.A 99% confidence interval for the slope of the regression line was determined to be (4.27,14.20).Give an interpretation of this interval. 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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Question 41

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 odds in favour of a success when X = 25.

(Multiple Choice)

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Question 42

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 and summary statistics are given below.Determine a 99% prediction interval for the lawn quality of a lawn sown with a seed density of 1.3. Variable Count Mean StdDev Range Seed Density 8 2.75 0.49099 4 Lawn Quality 8 45.625 3.712611 35 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

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Question 43

In the context of regression analysis,explain what is meant by the term "residual".

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Question 44

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 provided below to find a 90% confidence interval for the slope of the regression line. 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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Question 45

The sample data below are the index of exposure to radioactive waste for nine different geographic regions and cancer mortality rates (deaths per 100,000). Index of Exposure Cancer Mortality Rate 2.49 147.1 2.57 130.1 3.41 129.9 1.25 113.5 1.62 137.5 3.83 162.3 11.64 207.5 6.41 177.9 8.34 210.3 Using a 1% level of significance,do the data below support the claim that a higher index of exposure is associated with a higher cancer mortality rate?

(Essay)

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Question 46

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 following data consist of the students' GPAs on entering the program and their current GPAs. Entering GPA Current GPA 3.5 3.6 3.8 3.7 3.6 3.9 3.6 3.6 3.5 3.9 3.9 3.8 4.0 3.7 3.9 3.9 3.5 3.8 3.7 4.0 Using a 10% level of significance,do the data below provide evidence of the conclusion that higher entering GPAs are associated with higher current GPAs?

(Essay)

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Question 47

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. Number of years Score 3 57 4 78 4 72 2 58 5 89 3 63 4 73 5 84 3 75 2 48 Using a 1% level of significance,do the data provide sufficient evidence to conclude that the slope of the regression line is not 0 and hence that number of years of study is useful as a predictor of score on the test?

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Question 48

Decide whether or not the conditions and assumptions for regression inference are satisfied. Explain your answer.

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Question 49

The index of exposure to radioactive waste and the cancer mortality rates (deaths per 100,000)were recorded for nine different geographic regions.A 95% prediction interval for the cancer mortality rate of a region whose index of exposure is 5.79 is 133.0 to 203.4 deaths per 100,000. 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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Question 50

The index of exposure to radioactive waste and the cancer mortality rates (deaths per 100,000)were recorded for nine different geographic regions.Using a 1% level of significance,use the regression analysis provided below to perform the hypothesis test to determine if the index of exposure is useful as a predictor or cancer mortality rate. 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

(Essay)

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Question 51

The typing speeds (in words per minute)and reading speeds (in words per minute)of nine randomly selected secretaries were recorded.Using a 10% level of significance,carry out a test to determine if the linear correlation is greater than 0.The regression analysis is given below. Dependent variable is: Reading speed R-squared = 12.385% s = 100.3348 with 9 - 2 = 7 degrees of freedom

(Essay)

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Question 52

A Regression Model Decide whether or not the conditions and assumptions for regression inference are satisfied. Explain your answer. -

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Question 53

Ten students in a graduate program 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.Using a 10% level of significance,do the data below provide evidence of the conclusion that higher entering GPAs are associated with higher current GPA? 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 0.4531

(Essay)

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Question 54

Decide whether or not the conditions and assumptions for regression inference are satisfied. Explain your answer. -

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Question 55

The index of exposure to radioactive waste and the cancer mortality rates (deaths per 100,000)were recorded for nine different geographic regions.A 95% confidence interval for the mean cancer mortality rate of all regions whose index of exposure is 6.57 was determined to be (162.5,188.2). 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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Question 56

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% confidence interval for the average cancer mortality rate of a county whose index of exposure is 6.81 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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Question 57

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 odds in favour of a success when X = 25.

In the context of regression analysis,explain what is meant by the term "residual".

Decide whether or not the conditions and assumptions for regression inference are satisfied. Explain your answer.

A Regression Model Decide whether or not the conditions and assumptions for regression inference are satisfied. Explain your answer. -

Decide whether or not the conditions and assumptions for regression inference are satisfied. Explain your answer. -

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