Use computer software to obtain the regression equation. Use the estimated equation to find the predicted value -A study of food consumption in the country related the level of food consumed to an index of food prices and an index of personal disposable income. $\begin{array}{ccc} \hline\text { FOODCONS } & \text { INCOME } & \text { PRICE } \\ \hline 98.6 & 87.4 & 108.5 \\ 101.2 & 97.6 & 110.1 \\ 102.4 & 96.7 & 110.4 \\ 100.9 & 98.2 & 104.3 \\ 102.3 & 99.8 & 107.2 \\ 101.5 & 100.5 & 105.8 \\ 101.6 & 103.2 & 107.8 \\ 101.6 & 107.8 & 103.4 \\ 99.8 & 96.6 & 102.7 \\ 100.3 & 88.9 & 104.1 \\ 97.6 & 75.1 & 99.2 \\ 97.2 & 76.9 & 99.7 \\ 97.3 & 84.6 & 102.0 \\ 96.0 & 90.6 & 94.3 \\ 99.2 & 103.1 & 97.7 \\ 100.3 & 105.1 & 101.1 \\ 100.3 & 96.4 & 102.3 \\ 104.1 & 104.4 & 104.4 \\ 105.3 & 110.7 & 108.5 \\ 107.6 & 127.1 & 111.3\\\hline \end{array}$

A) $ .912, .901, .010 $ B) $ .867, .852, .000 $ C) $ .843, .799, .005 $ D) $ .855, .844, .002 $ A) $ .912, .901, .010 $ B) $ .867, .852, .000 $ C) $ .843, .799, .005 $ D) $ .855, .844, .002 $

A collection of paired data consists of the number of years that students have studied Spanish and their scores on a Spanish language proficiency test. A computer program was used to obtain the least squares linear regression line and the computer output is shown below. Along with the paired sample data, the program was also given an x value of 2 (years of study)to be used for predicting test score. The regression equation is $\text { Score }=31.55+10.90 \text { Years. }$ $\begin{array}{lclcc} \text { Predictor } & \text { Coef } & \text { StDev } & \text { T } & \text { P } \\ \text { Constant } & 31.55 & 6.360 & 4.96 & 0.000 \\ \text { Years } & 10.90 & 1.744 & 6.25 & 0.000 \end{array}$ \[ \mathrm{S}=5.651 \quad \mathrm{R}-\mathrm{Sq}=83.0 \% \quad \mathrm{R}-\mathrm{Sq}(\text { Adj })=82.7 \% \] Predicted values $ \begin{array}{llcc}\text { Fit } & \text { StDev Fit } & 95.0 \% \text { CI } & 95.0 \% \text { PI } \\ 53.35 & 3.168 & (42.72,63.98) & (31.61,75.09)\end{array} $ Use the information in the display to find the value of the linear correlation coefficient r. Determine whether the significant linear correlation between years of study and test scores. Use a significance level of $0.05$. There are 16 data.

A) $r = 0.91$; There is significant linear correlation. B) $\mathrm { r } = 0.83$; There is no significant linear correlation. C) $\mathrm { r } = 0.91$; There is no significant linear correlation D) $r = 0.83$; There is significant linear correlation. A) $r = 0.91$; There is significant linear correlation. B) $\mathrm { r } = 0.83$; There is no significant linear correlation. C) $\mathrm { r } = 0.91$; There is no significant linear correlation D) $r = 0.83$; There is significant linear correlation.

Solve the problem. -For the data below, determine the value of the linear correlation coefficient r between y and x2. \[\begin{array} { c | c c c c c } \mathrm { x } & 1.2 & 2.7 & 4.4 & 6.6 & 9.5 \\ \hline \mathrm { y } & 1.6 & 4.7 & 9.9 & 24.5 & 39.0 \end{array}\]

A) 0.913 B) 0.990 C) 0.985 D) 0.873 A) 0.913 B) 0.990 C) 0.985 D) 0.873

The following are costs of advertising (in thousands of dollars)and the numbers of products sold (in thousands): $\begin{array} { c | r r r r r r r r } Cost & 9 & 2 & 3 & 4 & 2 & 5 & 9 & 10 \\ \hline Number & 85 & 52 & 55 & 68 & 67 & 86 & 83 & 73 \end{array}$ The equation of the regression line is $y = 2.78846 x + 55.7885$. Find the coefficient of determination.

A) $0.2353$ B) $0.5009$ C) $0.7077$ D) $- 0.0707$ A) $0.2353$ B) $0.5009$ C) $0.7077$ D) $- 0.0707$

A confidence interval for the slope $\beta _ { 1 }$ for a regression line $\mathrm { y } = \beta _ { 0 } + \beta _ { 1 } \mathrm { x }$ can be found by evaluating the limits in $\mathrm { t }$ interval below: \[\begin{array} { l } \mathrm { b } _ { 1 } - \mathrm { E } < \beta _ { 1 } < \mathrm { b } _ { 1 } + \mathrm { E } _ { g } \\ \text { where } \mathrm { E } = \frac { \left( \mathrm { t } _ { \alpha / 2 } \right) \mathrm { se } _ { \mathrm { e } } } { \sqrt { \sum \mathrm { x } ^ { 2 } - \left( \sum \mathrm { x } \right) ^ { 2 } / \mathrm { n } } } . \end{array}\] The critical value $t _ { \alpha / 2 }$ is found from the t-table using $\mathrm { n } - 2$ degrees of freedom and $\mathrm { b } _ { 1 }$ is calculated in the usual v from the sample data. Use the data below to obtain a $95 \%$ confidence interval estimate of $\beta _ { 1 }$. $\begin{array}{c|ccccc} \mathrm{x} \text { (hours studied) } & 2.5 & 4.5 & 5.1 & 7.9 & 11.6 \\ \hline \mathrm{y} \text { (score on test) } & 66 & 70 & 60 & 83 & 93 \end{array}$

A) $0.322 < \beta _ { 1 } < 6.488$ B) $1.936 < \beta _ { 1 } < 4.874$ C) $0.134 < \beta _ { 1 } < 6.676$ D) $0.686 < \beta _ { 1 } < 6.124$ A) $0.322 < \beta _ { 1 } < 6.488$ B) $1.936 < \beta _ { 1 } < 4.874$ C) $0.134 < \beta _ { 1 } < 6.676$ D) $0.686 < \beta _ { 1 } < 6.124$

A collection of paired data consists of the number of years that students have studied Spanish and their scores on a Spanish language proficiency test. A computer program was used to obtain the least squares linear regression line and the computer output is shown below. Along with the paired sample data, the program was also given an x value of 2 (years of study)to be used for predicting test score. The regression equation is \[\text { Score } = 31.55 + 10.90 \text { Years }\] \[\begin{array} { c c c c c c } \text { Predictor } & \text { Coef } & \text { StDev } & \text { T } & \text { P } \\ \text { Constant } & 31.55 & 6.360 & 4.96 & 0.000 \\ \text { Years } & 10.90 & 1.744 & 6.25 & 0.000 \\ \mathrm {~S} = 5.651 \quad \mathrm { R } - \mathrm { Sq } = 83.0 \% & \mathrm { R } - \mathrm { Sq } & \text { (Adj) } = 82.7 \% \end{array}\] Predicted values \[\begin{array} { l l c c } \text { Fit } & \text { StDev Fit } & 95.0 \% \text { CI } & 95.0 \% \text { PI } \\ 53.35 & 3.168 & ( 42.72,63.98 ) & ( 31.61,75.09 ) \end{array}\] What percentage of the total variation in test scores can be explained by the linear relationship between years of study and test scores?

A) 82.7% B) 17.0% C) 91.1% D) 83.0% A) 82.7% B) 17.0% C) 91.1% D) 83.0%

Find the value of the linear correlation coefficient r. -$\begin{array}{l|ccccc} \mathrm{x} & 24 & 26 & 28 & 30 & 32 \\ \hline y & 15 & 13 & 20 & 16 & 24 \end{array}$

A) $\hat { y } = 11.8 + 0.950 \mathrm { x }$ B) $\hat { y } = 11.8 + 1.05 x$ C) $\hat { y } = - 11.8 + 1.05 x$ D) $\hat { y } = - 11.8 + 0.950 x$ A) $\hat { y } = 11.8 + 0.950 \mathrm { x }$ B) $\hat { y } = 11.8 + 1.05 x$ C) $\hat { y } = - 11.8 + 1.05 x$ D) $\hat { y } = - 11.8 + 0.950 x$

Exam 10: Correlation and Regression

Use computer software to obtain the regression equation. Use the estimated equation to find the predicted value -A study of food consumption in the country related the level of food consumed to an index of food prices and an index of personal disposable income. FOODCONS INCOME PRICE 98.6 87.4 108.5 101.2 97.6 110.1 102.4 96.7 110.4 100.9 98.2 104.3 102.3 99.8 107.2 101.5 100.5 105.8 101.6 103.2 107.8 101.6 107.8 103.4 99.8 96.6 102.7 100.3 88.9 104.1 97.6 75.1 99.2 97.2 76.9 99.7 97.3 84.6 102.0 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

(Multiple Choice)

4.8/5

(33)

Question 41

A collection of paired data consists of the number of years that students have studied Spanish and their scores on a Spanish language proficiency test. A computer program was used to obtain the least squares linear regression line and the computer output is shown below. Along with the paired sample data, the program was also given an x value of 2 (years of study)to be used for predicting test score. The regression equation is $\text { Score }=31.55+10.90 \text { Years. }$ Predictor Coef StDev T P Constant 31.55 6.360 4.96 0.000 Years 10.90 1.744 6.25 0.000 $\mathrm{S}=5.651 \quad \mathrm{R}-\mathrm{Sq}=83.0 \% \quad \mathrm{R}-\mathrm{Sq}(\text { Adj })=82.7 \%$ Predicted values Fit StDev Fit 95.0\% CI 95.0\% PI 53.35 3.168 (42.72,63.98) (31.61,75.09) Use the information in the display to find the value of the linear correlation coefficient r. Determine whether the significant linear correlation between years of study and test scores. Use a significance level of $0.05$ . There are 16 data.

(Multiple Choice)

4.8/5

(37)

Question 42

Provide an appropriate response. -Describe the standard error of estimate, $\mathrm { s } _ { \mathrm { e } }$ . How do smaller values of $\mathrm { s } _ { \mathrm { e } }$ relate to the dispersion of data points about the line determined by the linear regression equation? What does it mean when $\mathrm { s } _ { \mathrm { e } }$ is 0 ?

(Essay)

4.8/5

(42)

Question 43

Solve the problem. -For the data below, determine the value of the linear correlation coefficient r between y and x2. 1.2 2.7 4.4 6.6 9.5 1.6 4.7 9.9 24.5 39.0

(Multiple Choice)

4.8/5

(31)

Question 44

Provide an appropriate response. -Suppose that statisticians determine that there is a significant positive correlation between the grade earned in the class College Reading Skills and the grade earned in Statistics. Does achieving a high grade in reading cause an individual to earn a high grade in Statistics? Explain your answer with reference to the term lurking variable.

(Essay)

4.9/5

(37)

Question 45

Find the value of the linear correlation coefficient r -The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters): Temp 62 76 50 51 71 46 51 44 79 Growth 36 39 50 13 33 33 17 6 16

(Multiple Choice)

4.8/5

(30)

Question 46

Find the value of the linear correlation coefficient r -Managers rate employees according to job performance and attitude. The results for several randomly selected employees are given below. Performance 59 63 65 69 58 77 76 69 70 64 Attitude 72 67 78 82 75 87 92 83 87 78

(Multiple Choice)

4.7/5

(36)

Question 47

Describe the error in the stated conclusion. -Given: There is a significant linear correlation between the number of homicides in a town and the number of movie theaters in a town. Conclusion: Building more movie theaters will cause the homicide rate to rise.

(Essay)

4.8/5

(25)

Question 48

Construct a scatter diagram for the given data - 14 -11 -19 7 -19 -5 -76 -5 17 -70 72 15 $Construct a scatter diagram for the given data - \begin{array}{l|r|r|r|r|r|r} \mathrm{x} & 14 & -11 & -19 & 7 & -19 & -5 \\ \hline \mathrm{y} & -76 & -5 & 17 & -70 & 72 & 15 \end{array}$

(Multiple Choice)

4.9/5

(29)

Question 49

The following are costs of advertising (in thousands of dollars)and the numbers 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 is $y = 2.78846 x + 55.7885$ . Find the coefficient of determination.

(Multiple Choice)

4.9/5

(38)

Question 50

A confidence interval for the slope $\beta _ { 1 }$ for a regression line $\mathrm { y } = \beta _ { 0 } + \beta _ { 1 } \mathrm { x }$ can be found by evaluating the limits in $\mathrm { t }$ interval below: -<<+ where =. The critical value $t _ { \alpha / 2 }$ is found from the t-table using $\mathrm { n } - 2$ degrees of freedom and $\mathrm { b } _ { 1 }$ is calculated in the usual v from the sample data. Use the data below to obtain a $95 \%$ confidence interval estimate of $\beta _ { 1 }$ . (hours studied) 2.5 4.5 5.1 7.9 11.6 (score on test) 66 70 60 83 93

(Multiple Choice)

4.9/5

(25)

Question 51

A collection of paired data consists of the number of years that students have studied Spanish and their scores on a Spanish language proficiency test. A computer program was used to obtain the least squares linear regression line and the computer output is shown below. Along with the paired sample data, the program was also given an x value of 2 (years of study)to be used for predicting test score. The regression equation is $\text { Score } = 31.55 + 10.90 \text { Years }$ Predictor Coef StDev T P Constant 31.55 6.360 4.96 0.000 Years 10.90 1.744 6.25 0.000 =5.651-=83.0\% - (Adj) =82.7\% Predicted values Fit StDev Fit 95.0\% CI 95.0\% PI 53.35 3.168 (42.72,63.98) (31.61,75.09) What percentage of the total variation in test scores can be explained by the linear relationship between years of study and test scores?

(Multiple Choice)

4.8/5

(35)

Question 52

Provide an appropriate response. -Describe what scatterplots are, and discuss the importance of creating scatterplots.

(Essay)

4.8/5

(33)

Question 53

Find the value of the linear correlation coefficient r. - 24 26 28 30 32 y 15 13 20 16 24

(Multiple Choice)

4.7/5

(52)

Question 54

Use computer software to find the regression equation. Can the equation be used for prediction? -An anti-smoking group used data in the table to relate the carbon monoxide of various brands of cigarettes to their tar and nicotine content. CO TAR NICOTINE 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

(Multiple Choice)

4.8/5

(27)

Question 55

Solve the problem. -The sum of squares of residuals $\sum ( y - \hat { y } ) ^ { 2 }$ can be used to assess the quality of a regression model. A residual is the difference between an observed y value and the value of y predicted from the model, $\hat { y }$ . The better the model, the smaller the sum of squares of residuals. For the data below find the sum of squares of residuals which results from fitting a linear model, and the sum of squares of residuals which results from fitting a power model. Which model fits better? How can you tell? 1 2 3 4 5 3 9 17 30 40

(Essay)

4.9/5

(36)

Question 56

The paired data below consists of test scores and hours of preparation for 5 randomly selected students. The equation of the regression line is $\mathrm { y } = 44.8447 + 3.52427 \mathrm { x }$ . Find the explained variation. x Hours of preparation 5 2 9 6 10 y Test of score 64 48 72 73 80

(Multiple Choice)

4.8/5

(26)

Question 57

The paired data below consists of test scores and hours of preparation for 5 randomly selected students. The equation of the regression line is $\hat { y } = 44.8447 + 3.52427 x$ . Find the total variation. Hours of preparation 5 2 9 6 10 Test score 64 48 72 73 80

(Multiple Choice)

4.7/5

(31)

Question 58

Provide an appropriate response. -Suppose data are collected concerning the weight of a person in pounds and the number of calories burned in 30 minutes of walking on a treadmill at 3.5 mph. How would the value of the correlation coefficient, r, change if all of the weights were converted to kilograms?

(Essay)

4.9/5

(39)

Question 59

Is the data point, P -

(Multiple Choice)

4.8/5

(37)

Question 60

Solve the problem. -For the data below, determine the value of the linear correlation coefficient r between y and x2. 1.2 2.7 4.4 6.6 9.5 1.6 4.7 9.9 24.5 39.0

Find the value of the linear correlation coefficient r -The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters): Temp 62 76 50 51 71 46 51 44 79 Growth 36 39 50 13 33 33 17 6 16

Find the value of the linear correlation coefficient r -Managers rate employees according to job performance and attitude. The results for several randomly selected employees are given below. Performance 59 63 65 69 58 77 76 69 70 64 Attitude 72 67 78 82 75 87 92 83 87 78

Describe the error in the stated conclusion. -Given: There is a significant linear correlation between the number of homicides in a town and the number of movie theaters in a town. Conclusion: Building more movie theaters will cause the homicide rate to rise.

Construct a scatter diagram for the given data - 14 -11 -19 7 -19 -5 -76 -5 17 -70 72 15 $Construct a scatter diagram for the given data - \begin{array}{l|r|r|r|r|r|r} \mathrm{x} & 14 & -11 & -19 & 7 & -19 & -5 \\ \hline \mathrm{y} & -76 & -5 & 17 & -70 & 72 & 15 \end{array}$

The following are costs of advertising (in thousands of dollars)and the numbers 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 is $y = 2.78846 x + 55.7885$ . Find the coefficient of determination.

Provide an appropriate response. -Describe what scatterplots are, and discuss the importance of creating scatterplots.

Find the value of the linear correlation coefficient r. - 24 26 28 30 32 y 15 13 20 16 24

The paired data below consists of test scores and hours of preparation for 5 randomly selected students. The equation of the regression line is $\mathrm { y } = 44.8447 + 3.52427 \mathrm { x }$ . Find the explained variation. x Hours of preparation 5 2 9 6 10 y Test of score 64 48 72 73 80

The paired data below consists of test scores and hours of preparation for 5 randomly selected students. The equation of the regression line is $\hat { y } = 44.8447 + 3.52427 x$ . Find the total variation. Hours of preparation 5 2 9 6 10 Test score 64 48 72 73 80

Is the data point, P -

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