A fitness rating was obtained for 9 randomly selected adult women. Each person was also asked her age, weight, and the number of hours she spent exercising each week. The results are shown below. $\begin{array}{c|rrrrrrrrr} \text { Age } & 39 & 27 & 41 & 48 & 56 & 59 & 22 & 64 & 35 \\ \hline \text { Weight } & 140 & 129 & 137 & 125 & 162 & 152 & 118 & 142 & 126 \\ \hline \text { Hours of exercise } & & & & & & & & & \\ \text { per week } & 2 & 6 & 4 & 9 & 0 & 3 & 11 & 3 & 4 \\ \hline \text { Fitness rating } & 72 & 88 & 63 & 84 & 47 & 52 & 90 & 31 & 64 \end{array}$ Identify the multiple regression equation that expresses fitness in terms of age and hours of exercise per week.

A) $\hat { \mathrm { F } } = 93.20 - 0.869 \mathrm {~A} + 2.19 \mathrm { E }$ B) $\hat { \mathrm { F } } = 12.98 + 0.871 \mathrm {~A} + 3.71 \mathrm { E }$ C) $\hat { F } = 104.0 - 1.27 \mathrm {~A} + 4.08 \mathrm { E }$ D) $\hat { \mathrm { F } } = 67.12 - 0.451 \mathrm {~A} + 7.29 \mathrm { E }$ A) $\hat { \mathrm { F } } = 93.20 - 0.869 \mathrm {~A} + 2.19 \mathrm { E }$ B) $\hat { \mathrm { F } } = 12.98 + 0.871 \mathrm {~A} + 3.71 \mathrm { E }$ C) $\hat { F } = 104.0 - 1.27 \mathrm {~A} + 4.08 \mathrm { E }$ D) $\hat { \mathrm { F } } = 67.12 - 0.451 \mathrm {~A} + 7.29 \mathrm { E }$

Find the value of the linear correlation coefficient r. -$\begin{array}{l|lllll} \mathrm{x} & 0 & 3 & 4 & 5 & 12 \\ \hline \mathrm{y} & 8 & 2 & 6 & 9 & 12 \end{array}$

A) $\hat { y } = 4.98 + 0.425 x$ B) $\hat { y } = 4.88 + 0.525 x$ C) $\hat { y } = 4.98 + 0.725 x$ D) $\hat { y } = 4.88 + 0.625 x$ A) $\hat { y } = 4.98 + 0.425 x$ B) $\hat { y } = 4.88 + 0.525 x$ C) $\hat { y } = 4.98 + 0.725 x$ D) $\hat { y } = 4.88 + 0.625 x$

The equation of the regression line for the paired data below is $\hat { y } = 6.18286 + 4.33937 x$. Find the explained variation. $\begin{array}{r|rrrrrrr} \mathrm{x} & 9 & 7 & 2 & 3 & 4 & 22 & 17 \\ \hline \mathrm{y} & 43 & 35 & 16 & 21 & 23 & 102 & 81 \end{array}$

A) $6,421.83$ B) $13.479$ C) $6,544.86$ D) $6,531.37$ A) $6,421.83$ B) $13.479$ C) $6,544.86$ D) $6,531.37$

Find the value of the linear correlation coefficient r. -$\begin{array}{r|rrrrr} x & 1 & 3 & 5 & 7 & 9 \\ \hline y & 143 & 116 & 100 & 98 & 90 \end{array}$

A) $\hat { y } = - 150.7 + 6.8 x$ B) $\hat { y } = 140.4 - 6.2 x$ C) $\hat { y } = - 140.4 + 6.2 x$ D) $\hat { y } = 150.7 - 6.8 x$ A) $\hat { y } = - 150.7 + 6.8 x$ B) $\hat { y } = 140.4 - 6.2 x$ C) $\hat { y } = - 140.4 + 6.2 x$ D) $\hat { y } = 150.7 - 6.8 x$

Construct a scatterplot and identify the mathematical model that best fits the data. Assume that the model is to be used only for the scope of the given data and consider only linear, quadratic, logarithmic, exponential, and power models. Use a calculator or computer to obtain the regression equation of the model that best fits the data. You may need to fit several models and compare the values of RS1U1P12S1S1P0 -$\begin{array} { c c c c } \mathrm { Y } & \mathrm { X } _ { 1 } & \mathrm { X } _ { 2 } & \\ 98.6 & 87.4 & 108.5 & \\ 101.2 & 97.6 & 110.1 & \\ 102.4 & 96.7 & 110.4 & \text { CORRELATION COEFFICIENTS } \\ 100.9 & 98.2 & 104.3 & \\ 102.3 & 99.8 & 107.2 & \mathrm { Y } / \mathrm { X } _ { 1 } = .850 \\ 101.5 & 100.5 & 105.8 & \mathrm { Y } / \mathrm { X } _ { 2 } = .742 \\ 101.6 & 103.2 & 107.8 & \\ 101.6 & 107.8 & 103.4 & \\ 99.8 & 96.6 & 102.7 & \text { COEFFICIENT OF DETERMINATION } \\ 100.3 & 88.9 & 104.1 & \\ 97.6 & 75.1 & 99.2 & \mathrm { Y } / \mathrm { X } _ { 1 } = .723 \\ 97.2 & 76.9 & 99.7 & \mathrm { Y } / \mathrm { X } _ { 2 } = .550 \\ 97.3 & 84.6 & 102.0 & \mathrm { Y } / \mathrm { X } _ { 1 } , \mathrm { X } _ { 2 } = .867 \\ 96.0 & 90.6 & 94.3 & \\ 99.2 & 103.1 & 97.7 & \\ 100.3 & 105.1 & 101.1 & \\ 100.3 & 96.4 & 102.3 & \\ 104.1 & 104.4 & 104.4 & \\ 105.3 & 110.7 & 108.5 & \\ 107.6 & 127.1 & 111.3 & \end{array}$

A) $\hat { Y } = 52.6 + .462 X _ { 2 }$ B) $\hat { Y } = 58.9 + .612 X _ { 1 }$ C) $\hat { \mathrm { Y } } = 48.0 + .398 \mathrm { X } _ { 1 } + .228 \mathrm { X } _ { 2 }$ D) $\hat { \mathrm { Y } } = 57.6 + .153 \mathrm { X } _ { 1 } + .270 \mathrm { X } _ { 2 }$ A) $\hat { Y } = 52.6 + .462 X _ { 2 }$ B) $\hat { Y } = 58.9 + .612 X _ { 1 }$ C) $\hat { \mathrm { Y } } = 48.0 + .398 \mathrm { X } _ { 1 } + .228 \mathrm { X } _ { 2 }$ D) $\hat { \mathrm { Y } } = 57.6 + .153 \mathrm { X } _ { 1 } + .270 \mathrm { X } _ { 2 }$

Exam 10: Correlation and Regression

The regression equation for the given paired data is $\hat { y } = 73.012 + 0.8859 \mathrm { x }$ and the standard error of estimate is $\mathrm { s } _ { \mathrm { e } } = 2.78807$ . Find the $95 \%$ prediction interval of $\mathrm { y }$ for $\mathrm { x } = 37$ . 25 26 36 36 40 48 95 95 102 109 110 114

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Question 61

A fitness rating was obtained for 9 randomly selected adult women. Each person was also asked her age, weight, and the number of hours she spent exercising each week. The results are shown below. Age 39 27 41 48 56 59 22 64 35 Weight 140 129 137 125 162 152 118 142 126 Hours of exercise per week 2 6 4 9 0 3 11 3 4 Fitness rating 72 88 63 84 47 52 90 31 64 Identify the multiple regression equation that expresses fitness in terms of age and hours of exercise per week.

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Question 62

Use computer software to find the best regression equation to explain the variation in the dependent variable, Y, in terms of the independent variables, X1, X2, X3 - 15 1.2 16 15 1.2 16 17 1.0 16 6 0.8 9 1 0.1 1 8 0.8 8 10 0.8 10 17 1.0 16 15 1.2 15 11 0.7 9 18 1.4 18 16 1.0 15 10 0.8 9 7 0.5 5 18 1.1 16 CORRELATION COEFFICIENT /=.886 /=.965 COEFFICIENTS OF DETERMINATION /=.932 Y/,=.943

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Question 63

Find the value of the linear correlation coefficient r. - 0 3 4 5 12 8 2 6 9 12

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Question 64

The equation of the regression line for the paired data below is $\hat { y } = 6.18286 + 4.33937 x$ . Find the explained variation. 9 7 2 3 4 22 17 43 35 16 21 23 102 81

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Question 65

The paired data below consists of heights and weights of 6 randomly selected adults. The equation of the regression line is $\hat { y } = - 181.342 + 144.46 x$ . Find the unexplained variation. x Height (meters) 1.61 1.72 1.78 1.80 1.67 1.88 Weight () 54 62 70 84 61 92

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Question 66

Find the coefficient of determination, given that the value of the linear correlation coefficient, r, is 0.326.

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Question 67

Find the value of the linear correlation coefficient r -The paired data below consist of the costs of advertising (in thousands of dollars)and the number of products sold (in thousands): Cost 9 2 3 4 2 5 9 10 Number 85 52 55 68 67 86 83 73

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Question 68

Use computer software to obtain the regression equation. Use the estimated equation to find the predicted value -A health specialist gathered the data in the table to see if pulse rates can be explained by exercise and smoking. For exercise, he assigns 1 for yes, 2 for no. For smoking, he assigns 1 for yes, 2 for no. He then used his results to predict the pulse rate of a person whose exercise value was 2 and whose smoking value was 2. PULSE EXERCISE SMOKE 97 2 2 88 1 2 69 1 2 67 1 2 83 1 2 77 1 2 66 2 2 78 2 2 73 1 1 67 1 1 55 1 2 82 1 1 70 1 2 55 1 2 76 1 2

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Question 69

The equation of the regression line for the paired data below is $\hat { y } = 3 \mathrm { x }$ . Find the coefficient of determination. 2 4 5 6 7 11 13 20

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Question 70

Is the data point, P -The regression equation for a set of paired data is $\hat { y } = 2 + 5 x$ . The correlation coefficient for the data is $0.93$ . A hew data point, $\mathrm { P } ( 15,97 )$ , is added to the set.

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Question 71

Find the value of the linear correlation coefficient r. - x 1 3 5 7 9 y 143 116 100 98 90

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Question 72

Find the best predicted value of y corresponding to the given value of x. -Nine pairs of data yield $\mathrm { r } = 0.867$ and the regression equation $\hat { \mathrm { y } } = 19.4 + 0.93 \mathrm { x }$ . Also, $\overline { \mathrm { y } } = 64.7$ . What is the best predicted value of $y$ for $x = 59$ ?

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Question 73

Find the best predicted value of y corresponding to the given value of x. -Eight pairs of data yield $\mathrm { r } = 0.708$ and the regression equation $\mathrm { y } = 55.8 + 2.79 x$ . Also, $\bar { y } = 71.125$ . What is the best oredicted value of $y$ for $x = 9.1$ ?

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Question 74

Construct a scatterplot and identify the mathematical model that best fits the data. Assume that the model is to be used only for the scope of the given data and consider only linear, quadratic, logarithmic, exponential, and power models. Use a calculator or computer to obtain the regression equation of the model that best fits the data. You may need to fit several models and compare the values of R² - 98.6 87.4 108.5 101.2 97.6 110.1 102.4 96.7 110.4 CORRELATION COEFFICIENTS 100.9 98.2 104.3 102.3 99.8 107.2 /=.850 101.5 100.5 105.8 /=.742 101.6 103.2 107.8 101.6 107.8 103.4 99.8 96.6 102.7 COEFFICIENT OF DETERMINATION 100.3 88.9 104.1 97.6 75.1 99.2 /=.723 97.2 76.9 99.7 /=.550 97.3 84.6 102.0 /,=.867 96.0 90.6 94.3 99.2 103.1 97.7 100.3 105.1 101.1 100.3 96.4 102.3 104.1 104.4 104.4 105.3 110.7 108.5 107.6 127.1 111.3

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Question 75

For the data below, determine the value of the linear correlation coefficient r between y and ln x and test whether the linear correlation is significant. Use a significance level of 0.05. 1.2 2.7 4.4 6.6 9.5 1.6 4.7 8.9 9.5 12.0

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Question 76

Use computer software to obtain the regression equation. Use the estimated equation to find the predicted value -A wildlife analyst gathered the data in the table to develop an equation to predict the weights of bears. He used WEIGHT as the dependent variable and CHEST, LENGTH, and SEX as the independent variables. For SEX, he used male = 1 and female = 2. He took his equation "to the forest" and found a male bear whose chest measured 40.3 inches and who was 64.0 inches long. WEIGHT CHEST LENGTH SEX 344 45.0 67.5 1 416 54.0 72.0 1 220 41.0 70.0 2 360 49.0 68.5 1 332 44.0 73.0 1 140 32.0 63.0 2 436 48.0 72.0 1 132 33.0 61.0 2 356 48.0 64.0 2 150 35.0 59.0 1 202 40.0 63.0 2 365 50.0 70.5 1

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Question 77

Find the value of the linear correlation coefficient r -Two different tests are designed to measure employee productivity and dexterity. Several employees are randomly selected and tested with these results. Productivity 23 25 28 21 21 25 26 30 34 36 Dexterity 49 53 59 42 47 53 55 63 67 75

(Multiple Choice)

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Question 78

Use computer software to obtain the regression equation. Use the estimated equation to find the predicted value -A visitor to Yellowstone National Park sat down one day and observed Old Faithful, which faithfully spurts throughout the day, day in and day out. He surmised that the height of a given spurt was caused by the pressure build-up during the interval between spurts and by the momentum build-up during the duration of the spurt. He wrote down the data to test his hypothesis. He then used the regression equation he obtained to predict the height of the geyser if the interval is 104 seconds and the duration is 241 seconds. HEIGHT INTERVAL DURATIC 150 86 240 154 86 237 140 62 122 140 104 267 160 62 113 140 95 258 150 79 232 150 62 105 160 94 276 155 79 248 125 86 243 136 85 241 140 86 214 155 58 114 130 89 272 125 79 227 125 83 237 139 82 238 125 84 203 140 82 270 140 82 270 140 78 218 135 87 270 140 70 241 100 56 102 105 81 271

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Question 79

Construct a scatter diagram for the given data - $r = 0.845 , n = 5$

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Question 80

Find the value of the linear correlation coefficient r. - 0 3 4 5 12 8 2 6 9 12

The equation of the regression line for the paired data below is $\hat { y } = 6.18286 + 4.33937 x$ . Find the explained variation. 9 7 2 3 4 22 17 43 35 16 21 23 102 81

The paired data below consists of heights and weights of 6 randomly selected adults. The equation of the regression line is $\hat { y } = - 181.342 + 144.46 x$ . Find the unexplained variation. x Height (meters) 1.61 1.72 1.78 1.80 1.67 1.88 Weight () 54 62 70 84 61 92

Find the coefficient of determination, given that the value of the linear correlation coefficient, r, is 0.326.

Find the value of the linear correlation coefficient r -The paired data below consist of the costs of advertising (in thousands of dollars)and the number of products sold (in thousands): Cost 9 2 3 4 2 5 9 10 Number 85 52 55 68 67 86 83 73

The equation of the regression line for the paired data below is $\hat { y } = 3 \mathrm { x }$ . Find the coefficient of determination. 2 4 5 6 7 11 13 20

Is the data point, P -The regression equation for a set of paired data is $\hat { y } = 2 + 5 x$ . The correlation coefficient for the data is $0.93$ . A hew data point, $\mathrm { P } ( 15,97 )$ , is added to the set.

Find the value of the linear correlation coefficient r. - x 1 3 5 7 9 y 143 116 100 98 90

Find the best predicted value of y corresponding to the given value of x. -Eight pairs of data yield $\mathrm { r } = 0.708$ and the regression equation $\mathrm { y } = 55.8 + 2.79 x$ . Also, $\bar { y } = 71.125$ . What is the best oredicted value of $y$ for $x = 9.1$ ?

For the data below, determine the value of the linear correlation coefficient r between y and ln x and test whether the linear correlation is significant. Use a significance level of 0.05. 1.2 2.7 4.4 6.6 9.5 1.6 4.7 8.9 9.5 12.0

Find the value of the linear correlation coefficient r -Two different tests are designed to measure employee productivity and dexterity. Several employees are randomly selected and tested with these results. Productivity 23 25 28 21 21 25 26 30 34 36 Dexterity 49 53 59 42 47 53 55 63 67 75

Construct a scatter diagram for the given data - $r = 0.845 , n = 5$

Introduction to Statistics

Summarizing and Graphing Data

Statistics for Describing, Exploring, and Comparing Data

Probability

Probability Distributions

Normal Probability Distributions

Estimates and Sample Sizes

Hypothesis Testing

Inferences From Two Samples

Multinomial Experiments and Contingency Tables

Analysis of Variance

Nonparametric Statistics

Statistical Process Control

Filters

Exam 10: Correlation and Regression

Find the value of the linear correlation coefficient r. - 0 3 4 5 12 8 2 6 9 12

The equation of the regression line for the paired data below is y^=6.18286+4.33937x\hat { y } = 6.18286 + 4.33937 xy^​=6.18286+4.33937x . Find the explained variation. 9 7 2 3 4 22 17 43 35 16 21 23 102 81

Find the coefficient of determination, given that the value of the linear correlation coefficient, r, is 0.326.

Find the value of the linear correlation coefficient r -The paired data below consist of the costs of advertising (in thousands of dollars)and the number of products sold (in thousands): Cost 9 2 3 4 2 5 9 10 Number 85 52 55 68 67 86 83 73

The equation of the regression line for the paired data below is y^=3x\hat { y } = 3 \mathrm { x }y^​=3x . Find the coefficient of determination. 2 4 5 6 7 11 13 20

Is the data point, P -The regression equation for a set of paired data is y^=2+5x\hat { y } = 2 + 5 xy^​=2+5x . The correlation coefficient for the data is 0.930.930.93 . A hew data point, P(15,97)\mathrm { P } ( 15,97 )P(15,97) , is added to the set.

Find the value of the linear correlation coefficient r. - x 1 3 5 7 9 y 143 116 100 98 90

For the data below, determine the value of the linear correlation coefficient r between y and ln x and test whether the linear correlation is significant. Use a significance level of 0.05. 1.2 2.7 4.4 6.6 9.5 1.6 4.7 8.9 9.5 12.0

Find the value of the linear correlation coefficient r -Two different tests are designed to measure employee productivity and dexterity. Several employees are randomly selected and tested with these results. Productivity 23 25 28 21 21 25 26 30 34 36 Dexterity 49 53 59 42 47 53 55 63 67 75

Construct a scatter diagram for the given data - r=0.845,n=5r = 0.845 , n = 5r=0.845,n=5

Introduction to Statistics

Summarizing and Graphing Data

Statistics for Describing, Exploring, and Comparing Data

Probability

Probability Distributions

Normal Probability Distributions

Estimates and Sample Sizes

Hypothesis Testing

Inferences From Two Samples

Multinomial Experiments and Contingency Tables

Analysis of Variance

Nonparametric Statistics

Statistical Process Control

Filters

The equation of the regression line for the paired data below is $\hat { y } = 6.18286 + 4.33937 x$ . Find the explained variation. 9 7 2 3 4 22 17 43 35 16 21 23 102 81

The equation of the regression line for the paired data below is $\hat { y } = 3 \mathrm { x }$ . Find the coefficient of determination. 2 4 5 6 7 11 13 20

Is the data point, P -The regression equation for a set of paired data is $\hat { y } = 2 + 5 x$ . The correlation coefficient for the data is $0.93$ . A hew data point, $\mathrm { P } ( 15,97 )$ , is added to the set.

Construct a scatter diagram for the given data - $r = 0.845 , n = 5$