Exam 9: Correlation and Regression

The data below are the gestation periods, in months, of randomly selected animals and their corresponding life spans, in years. Use the regression equation to predict the life span, y, for a gestation period of 6 months, x. Assume the variables x and y have a significant 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 the size of a humanʹs brain, x, and their score on an IQ test, y, would you expect a positive correlation, a negative correlation, or no correlation?

The data below are the temperatures on randomly chosen days during a summer class and the number of absences on those days. Test the significance of the correlation coefficient using α $\alpha$ = 0.02, and the claim ρ $Q = 0$ Temperature, x 71 84 90 89 87 97 74 99 79 Number of absences, y 12 16 19 19 17 24 13 24 14

For the data below, test the significance of the correlation coefficient using α $\alpha$ = 0.01 and the claim ρ $Q = 0$ -13 -11 -4 -7 -9 -10 -8 -6 -5 -12 5 0 -12 -7 -3 -2 -5 -10 -11 2

A multiple regression equation is $\hat { \mathrm { y } } = - 35,000 + 130 \mathrm { x } _ { 1 } + 20,000 \mathrm { x } _ { 2 } , \text { where } \mathrm { x } _ { 1 }$ is a person?s age, x $x _ { 2 }$ is the person?s grade point average in college, and y is the person?s income. Predict the income for a person who is 26 years Old and had a college grade point average of 3.8.

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 standard error of estimate, $\mathrm { s } _ { \mathrm { e } }$ given that ? = 3.53x + 37.92. Miles traveled, 2 3 10 7 8 15 3 1 11 Sales, y 31 33 78 62 65 61 48 55 120

The data below are the gestation periods, in months, of randomly selected animals and their corresponding life spans, in years. Test the significance of the correlation coefficient using α $\alpha$ = 0.01 and the claim ρ $Q > 0$ 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 40

Given the equation of a regression line is y = 3.5x - 5.4, what is the best predicted value for y given x = -1.2? Assume that the variables x and y have a significant correlation.

Calculate the correlation coefficient, r, for the data below. 5 7 14 11 9 8 10 12 13 6 7 -10 4 -7 -6 -3 1 -9 2 3

Use the regression equation to predict the value of y for x = -2.8. Assume that the variables x and y have a significant correlation. -5 -3 4 1 -1 -2 0 2 3 -4 -10 -8 9 1 -2 -6 -1 3 6 -8

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). Find the equation of the regression line for the given 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

Given a sample with r = 0.321, n = 30, and ? $\alpha$ = 0.10, determine the standardized test statistic t necessary to test the claim ? $Q$ = 0. Round answers to three decimal places.

The data below are the average monthly temperatures, in ${ } ^ { \circ } \mathrm { F } \text {, }$ and the monthly natural gas consumption, in ccf, for a household in northwestern Pennsylvania. Test the significance of the correlation coefficient using α $\alpha = 0.05$ and the claim ρ $\varrho < 0 .$ 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 number of absences and the final grades of 9 randomly selected students from a statistics class. Test the significance of the correlation coefficient using α $\alpha = 0.05$ and the claim ρ $\varrho = 0 .$ Number of absences, x 1 4 7 5 10 3 16 9 6 Final Grade, y 89 77 71 73 62 83 46 67 73

Given the supply of a commodity, x, and the price of a commodity, y, would you expect a positive correlation, a negative correlation, or no correlation?

The data below are the number of absences and the final grades of 9 randomly selected students from a statistics class. What is the best predicted value for y given x = 10? Assume that the variables x and y have a Significant correlation. Number of absences, x 0 3 6 4 9 2 15 8 5 Final grade, y 98 86 80 82 71 92 55 76 82

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 95% prediction interval for y, the yield, given x = 11 inches, ? = 4.379x + 4.267 and $\mathrm { Se }$ = 3.529. Round interval to two decimal places. Rainfall (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

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 standard error of estimate, $\mathrm { Se }$ given that ? = 5.044x + 56.11. Hours, 3 5 2 8 2 4 4 5 6 3 Scores, y 65 80 60 88 66 78 85 90 90 71