Exam 9: Correlation and Regression

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 show 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 scatter plot for the data. Number of years, 3 4 4 5 3 6 2 7 3 Grades on test, 61 68 75 82 73 90 58 93 72

A researcher found a significant relationship between a person?s age, $\mathrm { x } _ { 1 } ,$ the number of hours a person works per weekweek, $\mathrm { x } _ { 2 }$ and the number of accidents, y, the person has per year. The relationship can be represented by The multiple regression equation ? = - $3.2 + 0.012 \mathrm { x } _ { 1 } + 0.23 \mathrm { x } _ { 2 }$ Predict the number of accidents per year (to the Nearest whole number)for a person whose age is 50 and who works 38 hours per week.

Given a sample with r = -0.765 and n = 22, test the significance of the correlation r using α $\alpha$ = 0.02 and the claim $Q$ ρ = 0.

For the data below, test the significance of the correlation coefficient using α $a$ = 0.05 and the claim ρ $Q$ = 0. -10 -8 -1 -4 -6 -7 -5 -3 -2 -9 -2 0 17 9 6 2 7 11 14 0

Given a sample with r = 0.321 and n = 30, test the significance of the correlation r using α $\alpha$ = 0.10 and the claim $\varrho$ ρ = 0.

The data below are the temperatures on randomly chosen days during a summer class and the number of absences on those days. Find the standard error of estimate, $\mathrm { Se }$ given that ? = 0.449x - 30.27. Temperature, 72 85 91 90 88 98 75 100 80 Number of absences, y 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). Calculate the correlation coefficient, r. Rain fall (in inches), x 9.5 7.8 12.4 11.5 17.8 9.3 6 14.6 15 Yield (bushels per acre), y 45.5 41.2 53.8 54 77.4 44.2 26.9 71 73.8

The data below are the temperatures on randomly chosen days during a summer class and the number of absences on those days. Construct a 95% prediction interval for y, the number of days absent, given x = 95 Degrees,? = 0.449x - 30.27 and $\mathrm { s } _ { \mathrm { e } }$ = 0.934. Round interval to three decimal places. Temperature, 72 85 91 90 88 98 75 100 80 Number of absences, 3 7 10 10 8 15 4 15 5

The data below are the ages and systolic blood pressures (measured in millimeters of mercury)of 9 randomly selected adults. Find the standard error of estimate, $\mathrm { Se } ,$ given that ? = 1.488x + 60.46. Age, 38 41 45 48 51 53 57 61 65 Pressure, 116 120 123 131 142 145 148 150 152

The data below are the ages and systolic blood pressures (measured in millimeters of mercury)of 9 randomly selected adults. Construct a scatter plot for the data. Age, x 38 41 45 48 51 53 57 61 65 Pressure, y 116 120 123 131 142 145 148 150 152

Find the standard error of estimate, se, for the data below, given that y = 2x + 1. 1 2 3 4 3 5 7 9

The data below are the number of absences and the final grades of 9 randomly selected students from a statistics class. Find the equation of the regression line for the given data. Number of absences, 0 3 6 4 9 2 15 8 5 Final grade, 98 86 80 82 71 92 55 76 82

The data below are the average monthly temperatures, in ${ } ^ { \circ } \mathrm { F }$ and the monthly natural gas consumption, in ccf, for a household in northwestern Pennsylvania. What is the best-predicted value for the gas consumption, y, given x = 50°F? Assume that the variables x and y have a significant correlation. Temperature 47 35 21 27 39 48 61 65 70 Consumption 34 169 248 134 137 100 19 34 12

The data below are the gestation periods, in months, of randomly selected animals and their corresponding life spans, in years. Construct a 95% prediction interval for y, the life span, given x = 10 months, ŷ = 1.523x + 6.343, and $\mathrm { S } \mathrm { e }$ = 5.618. Round interval to two decimal places. 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 = 0.823 and n = 10, test the significance of the correlation r using α $\alpha$ = 0.05 and the claim $Q$ ρ ρ= 0.

Find the equation of the regression line for the given data. -5 -3 4 1 -1 -2 0 2 3 -4 11 -6 8 -3 -2 1 5 -5 6 7

Given the equation of a regression line is y = 3x - 1, what is the best predicted value for y given x = 4? Assume that the variables x and y have a significant correlation.

Calculate the coefficient of determination, given that the linear correlation coefficient, r, is -0.625. What does this tell you about the explained variation and the unexplained variation of the data about the regression line?

The data below are the number of absences and the final grades of 9 randomly selected students from a statistics class. Find the standard error of estimate, $\mathrm { s } _ { \mathrm { e } }$ given that ? = -2.75X + 96.14. Number of absences, 0 3 6 4 9 2 15 8 5 Final grade, 98 86 80 82 71 92 55 76 82

Find the standard error of estimate, $\mathrm { s } \mathrm { e }$ for the data below, given that $\hat { y } = - 1.885 x + 0.758$ -5 -3 4 1 -1 -2 0 2 3 -4 11 6 -6 -1 3 4 1 -4 -5 8