Exam 26: Inferences for Regression

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

Determine which plot shows the strongest linear correlation.

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% confidence interval for the average reading speed of a secretary whose typing speed is 71. Dependent variable is: Reading speed R-squared = 12.385% S = 100.3348 with 9 - 2 = 7 degrees of freedom

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

The index of exposure to radioactive waste and the cancer mortality rates (deaths per 100,000)were recorded for nine different geographic regions.Explain what the R-squared in this regression means. Dependent variable is: Cancer Mortality Rate R-squared = 85.8% s = 14.00993 with 9 - 2 = 7 degrees of freedom

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.A 99% confidence interval for the mean lawn quality of all lawns sown with a seed density of 2.9 was found to be (32.3,56.3).Give an interpretation of this interval. Dependent variable is: Lawn Quality R-squared = 36.0% S = 9.073602 with 8 - 2 = 6 degrees of freedom

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. Dependent variable is: Lawn Quality R-squared = 36.0% S = 9.073602 with 8 - 2 = 6 degrees of freedom

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.

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 Dependent variable is: Cancer Mortality Rate R-squared = 85.8% S = 14.00993 with 9 - 2 = 7 degrees of freedom

In the context of regression analysis,the sum of the residuals is always zero.

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

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,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? The regression analysis is given below. Dependent variable is: Score R-squared = 83.0% s = 5.65138 with 10 - 2 = 8 degrees of freedom

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

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

When performing regression analysis,different samples will all yield the same sample regression line.

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?

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). Dependent variable is: Score R-squared = 83.0% S = 5.65138 with 10 - 2 = 8 degrees of freedom

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

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

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.Find a 95% confidence interval for the slope of the regression line. Dependent variable is: Lawn Quality R-squared = 36.0% S = 9.073602 with 8 - 2 = 6 degrees of freedom