Exam 9: Correlation and Regression

A medical researcher wishes to see whether there is a relationship between a personʹs age, cholesterol level, and systolic blood pressure. Eight people are randomly selected. The data are listed below. Person Age Cholesterol level Blood Pressure 1 38 220 116 2 41 225 120 3 45 200 123 4 48 190 131 5 51 250 142 6 53 215 145 7 57 200 148 8 61 170 150 a)Find a multiple regression equation for the data. b)What is the standard error of estimate? c)What is the coefficient of determination? d)Interpret the results in (c). e)If a person 50 years old with a cholesterol reading of 220 is selected, what is that personʹs predicted blood pressure reading?

In order for applicants to work for the foreign-service department, they must take a test in the language of the country where they plan to work. The data below shows the relationship between the number of years that Applicants have studied a particular language and the grades they received on the proficiency exam. Construct A 95% prediction interval for y given x = 2.5, $\hat{\hat { y }}$ = 6.91x + 46.26, and $\mathrm { s } _ { \mathrm { e } }$ = 4.578. Round interval to two decimal Places. Number of years, x 3 4 4 5 3 6 2 7 3 Grades on test, y 61 68 75 82 73 90 58 93 72

In an area of the Midwest, records were kept on the relationship between the rainfall (in inches)and the yield of wheat (bushels per acre). Construct a scatter plot for the data. Rain fall (in inches), 10.5 8.8 13.4 12.5 18.8 10.3 7.0 15.6 16.0 Yield (bushels per acre), y 50.5 46.2 58.8 59.0 82.4 49.2 31.9 76.0 78.8

A manager wishes to determine the relationship between the number of miles (in hundreds of miles)the managerʹs sales representatives travel per month and the amount of sales (in thousands of dollars)per month. Test the significance of the correlation coefficient using α $\alpha$ = 0.01 and the claim ρ $\mathrm { Q } = 0$ Miles traveled, x 5 6 13 10 11 18 6 4 14 Sales, y 33 35 80 64 67 63 50 57 122

The data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for the exam. Calculate the correlation coefficient r. Hours, 2 4 1 7 1 3 3 4 5 2 Scores, y 68 83 63 91 69 81 88 93 93 74

Given the equation of a regression line is y = -1.04x + 50.3, determine whether there is a positive linear correlation or a negative linear correlation.

Calculate the coefficient of correlation, r, letting Row 1 represent the x-values and Row 2 represent the y-values. Now calculate the coefficient of correlation, r, letting Row 2 represent the x-values and Row 1 represent the y-values. What effect does switching the explanatory and response variables have on the correlation coefficient? Row 1 1 3 10 7 5 4 6 8 9 2 Row 2 -7 11 12 4 1 -3 2 6 9 11

A medical researcher wishes to see whether there is a relationship between a personʹs age, cholesterol level, and systolic blood pressure. Eight people are randomly selected. The data are listed below. Person Age Cholesterol level Blood Pressure 1 38 220 116 2 41 225 120 3 45 200 123 4 48 190 131 5 51 250 142 6 53 215 145 7 57 200 148 8 61 170 150 Calculate the adjusted coefficient of determination, $r ^ { 2 } \text { adj. }$

A researcher at a local law university wishes to see whether a studentʹs grade point average and age are related to a studentʹs score on the state bar exam. Six students are randomly selected. The data are given below. Student GPA Age Score 1 3.5 23 530 2 2.8 28 550 3 3.9 22 690 4 3.4 27 620 5 2.3 21 430 6 3.3 26 580 Calculate the adjusted coefficient of determination, $\mathrm { r } ^ { 2 } \text { adj. }$

A researcher at a local law university wishes to see whether a studentʹs grade point average and age are related to a studentʹs score on the state bar exam. Six students are randomly selected. The data are given below. Student GPA Age Score 1 3.5 23 530 2 2.8 28 550 3 3.9 22 690 4 3.4 27 620 5 2.3 21 430 6 3.3 26 580 a)Find a multiple regression equation for the data. b)What is the standard error of estimate? c)What is the coefficient of determination? d)Interpret the results in (c). e)Predict the state bar exam score for a 25-year-old student with a grade point average of 3.0.

The data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for the exam. Find the equation of the regression line for the given data. Hours, 3 5 2 8 2 4 4 5 6 3 Scores, 65 80 60 88 66 78 85 90 90 71

Construct a 95% prediction interval for y given x = -3.5, ? = 2.097x - 0.552 and $\mathrm { Se }$ = 0.976. Round interval to two decimal places. -5 -3 4 1 -1 -2 0 2 3 -4 -10 -8 9 1 -2 -6 -1 3 6 -8

The data below are the temperatures on randomly chosen days during a summer class and the number of absences on those days. Construct a scatter plot for the data. Temperature, 72 85 91 90 88 98 75 100 80 Number of absences, 3 7 10 10 8 15 4 15 5

In an area of the Midwest, records were kept on the relationship between the rainfall (in inches)and the yield of wheat (bushels per acre). Test the significance of the correlation coefficient using α $\alpha$ = 0.01 and the claim ρ $\varrho = 0 .$ Rain fall (in inches), x 11 9.3 13.9 13 19.3 10.8 7.5 16.1 16.5 Yield (bushels per acre), y 51.5 47.2 59.8 60 83.4 50.2 32.9 77 79.8

The data below are the gestation periods, in months, of randomly selected animals and their corresponding life spans, in years. Construct a scatter plot for the data. Determine whether there is a positive linear correlation, a negative linear correlation, or no linear correlation. Gestation, 8 2.1 1.3 1 11.5 5.3 3.8 24.3 Life span, 30 12 6 3 25 12 10 40

Given a sample with r = -0.541, n = 20, test the significance of the correlation r using α $\alpha$ = 0.01 and the claim $Q$ ρ = 0.

A manager wishes to determine the relationship between the number of miles (in hundreds of miles)the manager?s sales representatives travel per month and the amount of sales (in thousands of dollars)per month. Find the equation of the regression line for the given data. Miles traveled, 2 3 10 7 8 15 3 1 11 Sales, 31 33 78 62 65 61 48 55 120

Find the equation of the regression line by letting Row 1 represent the x-values and Row 2 represent the y-values. Now find the equation of the regression line letting Row 2 represent the x-values and Row 1 represent the y-values. What effect does switching the explanatory and response variables have on the regression line? Row 1 -5 -3 4 1 -1 -2 0 2 3 -4 Row 2 -10 -8 9 1 -2 -6 -1 3 6 -8

Find the standard error of estimate, $\text { Se }$ for the data below, given that y = 2.097x - 0.552. -5 -3 4 1 -1 -2 0 2 3 -4 -10 -8 9 1 -2 -6 -1 3 6 -8

The data below are the temperatures on randomly chosen days during a summer class and the number of absences on those days. Calculate the correlation coefficient, r. Temperature, 76 89 95 94 92 102 79 104 84 Number of absences, y 12 16 19 19 17 24 13 24 14