Deck 10: Correlation and Regression

Question 1

Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05.

- $$r = 0.845 , n = 5$$

A) Critical values: $r = 0.950$ , significant linear correlation
B) Critical values: $r = \pm 0.950$ , no significant linear correlation
C) Critical values: $r = \pm 0.878$ , no significant linear correlation
D) Critical values: $\mathrm { r } = \pm 0.878$ , significant linear correlation

Answer 1

Critical values: $r = \pm 0.878$ , no significant linear correlation

Question 2

Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05.

- $r = 0.981 , n = 25$

A) Critical values: $\mathrm { r } = \pm 0.487$ , no significant linear correlation
B) Critical values: $r = \pm 0.487$ , significant linear correlation
C) Critical values: $r = \pm 0.396$ , significant linear correlation
D) Critical values: $r = \pm 0.396$ , no significant linear correlation

Answer 2

Critical values: $r = \pm 0.396$ , significant linear correlation

Question 3

Provide an appropriate response.

-Explain why having a significant linear correlation does not imply causality. Give an example to support your answer.

Answer 3

Having a significant linear correlation does not imply causality because the relationships may coincide but not cause change in one another. Examples will vary.

Question 4

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?

Question 5

Construct a scatter diagram for the given data

- $\begin{array}{lr|r|r|r|r|r|r|r|r|r}\mathrm{x} & -4 & -3 & -5 & -7 & 4 & 3 & -6 & 9 & -4 & -1 \\\hline y & 2 & -7 & 2 & -7 & 2 & -2 & -4 & 4 & -10 & -2\end{array}$

A)

B)

C)

D)

Question 6

Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05.

- $\mathrm { r } = 0.168 , \mathrm { n } = 15$

A) Critical values: $r = \pm 0.514$ , significant linear correlation
B) Critical values: $\mathrm { r } = 0.514$ , no significant linear correlation
C) Critical values: $r = \pm 0.532$ , no significant linear correlation
D) Critical values: $\mathrm { r } = \pm 0.514$ , no significant linear correlation

Question 7

Provide an appropriate response.

Question 8

Provide an appropriate response.

-Discuss the guidelines under which the linear regression equation should be used for prediction. Refer to the correlation coefficient, the type of data used to create the linear regression, and the predicting value.

Question 9

Provide an appropriate response.

-Create a scatterplot that shows a perfect positive correlation between x and y. How would the scatterplot change if the correlation showed a)a strong positive correlation, b)a positive correlation, and c)no correlation?

Question 10

Provide an appropriate response.

-Describe what scatterplots are, and discuss the importance of creating scatterplots.

Question 11

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.

Question 12

Provide an appropriate response.

-Define the term independent, or predictor, variable and the term dependent, or response, variable. Give examples for each.

Question 13

Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05.

- $$\mathrm { r } = 0.803 , \mathrm { n } = 9$$

A) Critical values: $r = - 0.666$ , no significant linear correlation
B) Critical values: $\mathrm { r } = 0.666$ , no significant linear correlation
C) Critical values: $r = \pm 0.666$ , significant linear correlation
D) Critical values: $r = \pm 0.666$ , no significant linear correlation

Question 14

Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05.

- $$\mathrm { r } = 0.221 , \mathrm { n } = 90$$

A) Critical values: $r = \pm 0.217$ , no significant linear correlation
B) Critical values: $r = 0.217$ , significant linear correlation
C) Critical values: $r = \pm 0.207$ , no significant linear correlation
D) Critical values: $\mathrm { r } = \pm 0.207$ , significant linear correlation

Question 15

Provide an appropriate response.
What is the importance of correlation in terms of the linear regression equation?

Question 16

Provide an appropriate response.

-Suppose there is significant correlation between two variables. Describe two cases under which it might be inappropriate to use the linear regression equation for prediction. Give examples to support these cases.

Question 17

Provide an appropriate response.

Question 18

Construct a scatter diagram for the given data

- $\begin{array}{l|r|r|r|r|r|r}\mathrm{x} & 14 & -11 & -19 & 7 & -19 & -5 \\\hline \mathrm{y} & -76 & -5 & 17 & -70 & 72 & 15\end{array}$

A)

B)

C)

D)

Question 19

Provide an appropriate response.

-When testing to determine if correlation is significant, we use the hypotheses $\mathrm { H } _ { 0 } : \mathrm { Q } = 0 . \mathrm { H } _ { 1 } : \mathrm { Q } \neq 0$ . Suppose the conclusion is to reject the null hypothesis. What does that tell us about the linear regression equation?

Question 20

Provide an appropriate response.
Describe what correlation is, and explain the purpose of correlation.

Question 21

Find the best predicted value of y corresponding to the given value of x.

-Four pairs of data yield $\mathrm { r } = 0.942$ and the regression equation $\mathrm { y } = 3 \mathrm { x }$ . Also, $\overline { \mathrm { y } } = 12.75$ . What is the best predicted value of $y$ for $x = 2.8$ ?

A) $2.826$
B) $0.942$
C) $8.4$
D) $12.75$

Question 22

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): $\begin{array}{c|rrrrrrrr}\text { Cost } & 9 & 2 & 3 & 4 & 2 & 5 & 9 & 10 \\\hline \text { Number } & 85 & 52 & 55 & 68 & 67 & 86 & 83 & 73\end{array}$

A) $- 0.071$
B) $0.708$
C) $0.235$
D) $0.246$

Question 23

Find the value of the linear correlation coefficient r

-Two separate tests are designed to measure a student's ability to solve problems. Several students are randomly selected to take both tests and the results are shown below. $$\begin{array} { c | l | l | l | l | l | l | l | l | l } \text { Test A } & 48 & 52 & 58 & 44 & 43 & 43 & 40 & 51 & 59 \\\hline \text { Test B } & 73 & 67 & 73 & 59 & 58 & 56 & 58 & 64 & 74\end{array}$$

A)0.548
B)0.109
C)0.714
D)0.867

Question 24

Find the value of the linear correlation coefficient r

-The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test. $\begin{array}{l|rrrrrr}\text { Hours } & 5 & 10 & 4 & 6 & 10 & 9 \\\hline \text { Score } & 64 & 86 & 69 & 86 & 59 & 87\end{array}$

A) $- 0.678$
B) $- 0.224$
C) $0.678$
D) $0.224$

Question 25

Construct a scatter diagram for the given data

- $\begin{array}{r|r|r|r|r|r|r|r|r}\mathrm{x} & 0.17 & 0.07 & 0.16 & 0.34 & -0.16 & 0.3 & 0.51 & 0.08 \\\hline \mathrm{y} & 0.5 & 0.85 & 0.35 & 0.46 & 0.01 & 0.53 & 0.22 & -0.03\end{array}$

A)

B)

C)

D)

Question 26

Describe the error in the stated conclusion.

-Given: There is no significant linear correlation between scores on a math test and scores on a verbal test. Conclusion: There is no relationship between scores on the math test and scores on the verbal test.

Question 27

Find the best predicted value of y corresponding to the given value of x.

-Six pairs of data yield $\mathrm { r } = 0.444$ and the regression equation $\hat { \mathrm { y } } = 5 \mathrm { x } + 2$ . Also, $\overline { \mathrm { y } } = 18.3$ . What is the best predicted value of $y$ for $x = 5$ ?

A) $93.5$
B) $18.3$
C) $4.22$
D) 27

Question 28

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. $\begin{array}{cc|c|c|c|c|c|c|c|c|c}\text { Performance } & 59 & 63 & 65 & 69 & 58 & 77 & 76 & 69 & 70 & 64 \\\hline\text { Attitude } & 72 & 67 & 78 & 82 & 75 & 87 & 92 & 83 & 87 & 78\end{array}$

A)0.610
B)0.863
C)0.729
D)0.916

Question 29

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. $\begin{array}{cc|c|c|c|c|c|c|c|c|c}\text { Productivity } & 23 & 25 & 28 & 21 & 21 & 25 & 26 & 30 & 34 & 36 \\\hline \text { Dexterity } & 49 & 53 & 59 & 42 & 47 & 53 & 55 & 63 & 67 & 75\end{array}$

A) $0.471$
B) $0.115$
C) $- 0.280$
D) $0.986$

Question 30

Find the value of the linear correlation coefficient r

- $\begin{array}{l|rrrrr}\mathrm{x} & 21.5 & 10.8 & 34.9 & 48.6 & 45.3 \\\hline \mathrm{y} & 5 & 2 & 7 & 5 & 7\end{array}$

A) 0
B) $- 0.732$
C) $0.732$
D) $0.651$

Question 31

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.

Question 32

Find the value of the linear correlation coefficient r

-A study was conducted to compare the average time spent in the lab each week versus course grade for computer students. The results are recorded in the table below. $\begin{array}{cc}\text { Number of hours spent in lab } & \text { Grade (percent) } \\\hline 10 & 96 \\11 & 51 \\16 & 62 \\9 & 58 \\7 & 89 \\15 & 81 \\16 & 46 \\10 & 51\end{array}$

A) $- 0.335$
B) $- 0.284$
C) $0.462$
D) $0.017$

Question 33

Determine which plot shows the strongest linear correlation

A)


B)



C)

Question 34

Construct a scatter diagram for the given data

- $\begin{array}{r|r|r|r|r|r|r|r|r|r}\mathrm{x} & -4 & 3 & 7 & 5 & 11 & 10 & 6 & -1 & -1 \\\hline \mathrm{y} & 2 & 7 & 7 & 9 & 9 & 6 & 7 & 2 & 3\end{array}$

A)


B)


C)


D)

Question 35

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): $\begin{array}{c|rrrrrrrrr}\text { Temp } & 62 & 76 & 50 & 51 & 71 & 46 & 51 & 44 & 79 \\\hline \text { Growth } & 36 & 39 & 50 & 13 & 33 & 33 & 17 & 6 & 16\end{array}$

A) $- 0.210$
B) $0.256$
C) 0
D) $0.196$

Question 36

Determine which plot shows the strongest linear correlation

A)



B)


C)

Question 37

Describe the error in the stated conclusion.

-Given: The linear correlation coefficient between scores on a math test and scores on a test of athletic ability is negative and close to zero. Conclusion: People who score high on the math test tend to score lower on the test of athletic ability.

Question 38

Find the value of the linear correlation coefficient r

- $\begin{array}{r|rrrrrrr}\mathrm{x} & 62 & 53 & 64 & 52 & 52 & 54 & 58 \\\hline y & 158 & 176 & 151 & 164 & 164 & 174 & 162\end{array}$

A) 0.754
B) -0.081
C) -0.775
D) 0

Question 39

Describe the error in the stated conclusion.

-Given: Each school in a state reports the average SAT score of its students. There is a significant linear correlation between the average SAT score of a school and the average annual income in the district in which the school is located. Conclusion: There is a significant linear correlation between individual SAT scores and family income.

Question 40

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 $x = 9.1$ ?

A) $510.57$
B) $71.13$
C) $57.80$
D) $81.19$

Question 41

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 $x = 59$ ?

A) $64.7$
B) $57.8$
C) $79.6$
D) $74.3$

Question 42

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.

- $\begin{array}{r|rrrrr}\mathrm{x} & 3 & 5 & 7 & 15 & 16 \\\hline y & 8 & 11 & 7 & 14 & 20\end{array}$

A) $\hat { y } = 4.07 + 0.753 x$
B) $\hat { y } = 5.07 + 0.850 x$
C) $\hat { y } = 4.07 + 0.850 x$
D) $\hat { y } = 5.07 + 0.753 x$

Question 43

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.

- $\begin{array}{l|ccccc}\mathrm{x} & 24 & 26 & 28 & 30 & 32 \\\hline y & 15 & 13 & 20 & 16 & 24\end{array}$

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) $\hat { y } = - 11.8 + 0.950 x$

Question 44

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.

- $\begin{array}{l|lllll}\mathrm{x} & 0 & 3 & 4 & 5 & 12 \\\hline \mathrm{y} & 8 & 2 & 6 & 9 & 12\end{array}$

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) $\hat { y } = 4.88 + 0.625 x$

Question 45

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.

-Ten students in a graduate program were randomly selected. Their grade point averages (GPAs)when they entered the program were between 3.5 and 4.0. The following data were obtained regarding their GPAs on entering the program versus their current GPAs. $\begin{array}{cc}\text { Entering GPA } & \text { Current GPA } \\\hline 3.5 & 3.6 \\3.8 & 3.7 \\3.6 & 3.9 \\3.6 & 3.6 \\3.5 & 3.9 \\3.9 & 3.8 \\4.0 & 3.7 \\3.9 & 3.9 \\3.5 & 3.8 \\3.7 & 4.0\end{array}$

A) $\hat{y} = 4.91 + 0.0212 x$
B) $\hat{y} = 5.81 + 0.497 x$
C) $\hat { y } = 2.51 + 0.329 x$
D) $\hat { y } = 3.67 + 0.0313 x$

Question 46

Is the data point, P

-

A)Outlier
B)Neither
C)Both
D)Influential point

Question 47

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.

- $\begin{array}{r|rrrrr}\mathrm{x} & 1.2 & 1.4 & 1.6 & 1.8 & 2.0 \\\hline \mathrm{y} & 54 & 53 & 55 & 54 & 56\end{array}$

A) $\hat { y }= 50 + 3 x$
B) $\hat { y } = 55.3 + 2.40 \mathrm { x }$
C) $\hat { y } = 54$
D) $\hat { y } = 50.4 + 2.50 x$

Question 48

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.

-Managers rate employees according to job performance and attitude. The results for several randomly selected employees are given below. $\begin{array}{cc|c|c|c|c|c|c|c|c|c}\text { Performance } & 59 & 63 & 65 & 69 & 58 & 77 & 76 & 69 & 70 & 64 \\\hline \text { Attitude } & 72 & 67 & 78 & 82 & 75 & 87 & 92 & 83 & 87 & 78\end{array}$

A) $\hat { y } = - 47.3 + 2.02 x$
B) $\hat { y } = 92.3 - 0.669 \mathrm { x }$
C) $\hat { y } = 11.7 + 1.02 x$
D) $\hat { y } = 2.81 + 1.35 x$

Question 49

Is the data point, P

-

A)Influential point
B)Neither
C)Both
D)Outlier

Question 50

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.

- $\begin{array}{l|lllll}\mathrm{x} & 6 & 8 & 20 & 28 & 36 \\\hline \mathrm{y} & 2 & 4 & 13 & 20 & 30\end{array}$

A) $\hat { y } = - 3.79 + 0.897 x$
B) $\hat { y } = - 2.79 + 0.950 x$
C) $\hat { y } = - 2.79 + 0.897 x$
D) $\hat { y } = - 3.79 + 0.801 x$

Question 51

Find the best predicted value of y corresponding to the given value of x.

-The regression equation relating attitude rating $( \mathrm { x } )$ and job performance rating $( \mathrm { y } )$ for the employees of a company is $\hat{y} = 11.7 + 1.02 x$ . Ten pairs of data were used to obtain the equation. The same data yield $r = 0.863$ and $\bar { y } = 80.1$ . What is the best predicted job performance rating for a person whose attitude rating is 73 ?

A) $80.1$
B) $12.6$
C) $86.2$
D) $84.9$

Question 52

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.

-Two different tests are designed to measure employee productivity and dexterity. Several employees are randomly selected and tested with these results. $\begin{array}{cc|c|c|c|c|c|c|c|c|c}\text { Productivity } & 23 & 25 & 28 & 21 & 21 & 25 & 26 & 30 & 34 & 36 \\\hline\text { Dexterity } & 49 & 53 & 59 & 42 & 47 & 53 & 55 & 63 & 67 & 75\end{array}$

A) $\hat{y} = 10.7 + 1.53 x$
B) $\hat{y} = 5.05 + 1.91 \mathrm { x }$
C) $\hat { y } = 2.36 + 2.03 x$
D) $\hat { y } = 75.3 - 0.329 \mathrm { x }$

Question 53

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.

A)Neither
B)Outlier
C)Both
D)Influential point

Question 54

Find the best predicted value of y corresponding to the given value of x.

-Ten pairs of data yield $\mathrm { r } = 0.003$ and the regression equation $\hat { \mathrm { y } } = 2 + 3 \mathrm { x }$ . Also, $\overline { \mathrm { y } } = 5.0$ . What is the best predicted value of $y$ for $x = 2$ ?

A) $5.0$
B) $8.0$
C) $17.0$
D) $7.0$

Question 55

Is the data point, P

-

A)Neither
B)Outlier
C)Both
D)Influential point

Question 56

Find the best predicted value of y corresponding to the given value of x.

-The regression equation relating dexterity scores $( \mathrm { x } )$ and productivity scores ( $\mathrm { y } )$ for the employees of a company $\hat { y } = 5.50 + 1.91 \mathrm { x }$ . Ten pairs of data were used to obtain the equation. The same data yield $\mathrm { r } = 0.986$ and $\bar { y } = 56.3$ . What is the best predicted productivity score for a person whose dexterity score is 33 ?

A) $56.30$
B) $58.20$
C) $68.53$
D) $183.41$

Question 57

Find the value of the linear correlation coefficient r.

-Based on the data from six students, the regression equation relating number of hours of preparation (x)and test score $( \mathrm { y } )$ is $y = 67.3 + 1.07 x$ . The same data yield $r = 0.224$ and $\bar{y} = 75.2$ . What is the best predicted test score for a student who spent 2 hours preparing for the test?

A)69.4
B)78.1
C)75.2
D)59.7

Question 58

Find the best predicted value of y corresponding to the given value of x.

-Six pairs of data yield $\mathrm { r } = 0.789$ and the regression equation $\hat { \mathrm { y } } = 4 \mathrm { x } - 2$ . Also, $\overline { \mathrm { y } } = 19.0$ . What is the best predicted value of $y$ for $x = 5$ ?

A) $18.5$
B) $19.0$
C) $22.0$
D) $18.0$

Question 59

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.

- $\begin{array}{r|rrrrr}x & 1 & 3 & 5 & 7 & 9 \\\hline y & 143 & 116 & 100 & 98 & 90\end{array}$

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) $\hat { y } = 150.7 - 6.8 x$

Question 60

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.

- $\begin{array}{r|rrrr}x & 2 & 4 & 5 & 6 \\\hline y & 7 & 11 & 13 & 20\end{array}$

A) $\hat { y } = 0.15 + 3.0 x$
B) $\hat { y } = 2.8 x$
C) $\hat { y } = 0.15 + 2.8 x$
D) $\hat { y } = 3.0 x$

Question 61

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%

Question 62

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
$\begin{array}{lcccc}{\text { Score }=31.55+10.90 \text { Years. }} \\\text { Predictor } & \text { Coef } & \text { StDev } & \text { T } & \text { P } \\\text { Constant } & 31.55 & 6.360 & 4.96 & 0.000 \\\text { Years } & 10.90 & 1.744 & 6.25 & 0.000\end{array}$
$$\mathrm{S}=5.651 \quad \mathrm{R}-\mathrm{Sq}=83.0 \% \quad \mathrm{R}-\mathrm{Sq}(\mathrm{Adj})=82.7 \%$$
Predicted values
$\begin{array}{llcc}\text { Fit } & \text { StDev Fit } & 95.0 \% \text { CI } & 95.0 \% \text { PI } \\ 53.35 & 3.168 & (42.72,63.98) & (31.61,75.09)\end{array}$
For a person who studies for 2 years, obtain the $95 \%$ prediction interval and write a statement interpreting the in

A) $(42.72,63.98)$ ; We can be $95 \%$ confident that the mean test score of all individuals who study 2 years will lie in the interval $(42.72,63.98)$
B) $(31.61,75.09)$ ; We can be $95 \%$ confident that the test score of an individual who studies 2 years will lie in the interval $(31.61,75.09)$
C) $(31.61,75.09)$ ; We can be $95 \%$ confident that the mean test score of all individuals who study 2 years will lie in the interval $(31.61,75.09)$
D) $(42.72,63.98)$ ; We can be $95 \%$ confident that the test score of an individual who studies 2 years will lie in the interval $(42.72 .63 .98)$

Question 63

The equation of the regression line for the paired data below is $\hat { y } = 3 x$ . Find the unexplained variation. $$\begin{array} { r | r r r r } \mathrm { x } & 2 & 4 & 5 & 6 \\\hline \mathrm { y } & 7 & 11 & 13 & 20\end{array}$$

A)78.75
B)10.00
C)14.25
D)88.75

Question 64

A regression equation is obtained for a collection of paired data. It is found that the total variation is 114, the explained variation is 91.7, and the unexplained variation is 22.3. Find the coefficient of determination.

A)0.804
B)1.243
C)0.243
D)0.196

Question 65

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) $6,531.37$

Question 66

Is the data point, P

-The regression equation for a set of paired data is $y = - 21.1 + 1.3 x$ . The values of $x$ run from 100 to 400 . A new data point, $\mathrm { P } ( 175,206.4 )$ , is added to the set.

A)Both
B)Influential point
C)Neither
D)Outlier

Question 67

The test scores of 6 randomly picked students and the numbers of hours they prepared are as follows: $\begin{array} { c | r r r r r r } Hours & 5 & 10 & 4 & 6 & 10 & 9 \\\hline Score & 64 & 86 & 69 & 86 & 59 & 87\end{array}$
The equation of the regression line is $\hat { y } = 1.06604 \mathrm { x } + 67.3491$ . Find the coefficient of determination.

A) $0.2242$
B) $0.6781$
C) $0.0503$
D) $- 0.2242$

Question 68

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.

Question 69

The equation of the regression line for the paired data below is $\hat { y } = 3 x$ . Find the explained variation.
$\begin{array}{l|rrrr}\mathrm{x} & 2 & 4 & 5 & 6 \\\hline \mathrm{y} & 7 & 11 & 13 & 20\end{array}$

A) $88.75$
B) $10.00$
C) $72.45$
D) $78.75$

Question 70

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 unexplained variation.
$\begin{array}{c|rrrrr}\mathrm{x} \text { Hours of preparation } & 5 & 2 & 9 & 6 & 10 \\\hline \mathrm{y} \text { Test score } & 64 & 48 & 72 & 73 & 80\end{array}$

A) $96.103$
B) $599.2$
C) $511.724$
D) $87.4757$

Question 71

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.
$\begin{array}{c|rrrrr}x \text { Hours of preparation } & 5 & 2 & 9 & 6 & 10 \\\hline y \text { Test of score } & 64 & 48 & 72 & 73 & 80\end{array}$

A) $498.103$
B) $511.724$
C) $87.4757$
D) $599.2$

Question 72

For the data below, determine the logarithmic equation, $y = a + b \ln x$ that best fits the data. Hint: Begin by replacing each $x$ -value with $\ln x$ then use the usual methods to find the equation of the least squares regression 1
$\begin{array}{c|ccccc}\mathrm{x} & 1.2 & 2.7 & 4.4 & 6.6 & 9.5 \\\hline \mathrm{y} & 1.6 & 4.7 & 8.9 & 9.5 & 12.0\end{array}$

A) $\hat { y } = - 1.81 + 6.91 \ln x$
B) $\hat { y } = 0.881 + 4.86 \ln x$
C) $\hat { y } = 0.457 + 5.06 \ln x$
D) $\hat { y }= - 0.458 + 5.36 \ln x$

Question 73

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

Question 74

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. $$\begin{array} { l | l c c c l } \mathrm { x } & 1.2 & 2.7 & 4.4 & 6.6 & 9.5 \\\hline \mathrm { y } & 1.6 & 4.7 & 8.9 & 9.5 & 12.0\end{array}$$

Question 75

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. $$\begin{array}{l}\text { The regression equation is }\\\begin{array} { l } \text { Score } = 31.55 + 10.90 \text { Years. } \\\begin{array} { l c c c c } \text { Predictor } & \text { Coef } & \text { StDev } & \text { T } & \text { P } \\\text { Constant } & 31.55 & 6.360 & 4.96 & 0.000 \\\text { Years } & 10.90 & 1.744 & 6.25 & 0.000 \\\mathrm {~S} = 5.651 & \mathrm { R } - \mathrm { Sq } = 83.0 \% & \mathrm { R } - \mathrm { Sq } ( \mathrm { Adj } ) = 82.7 \% \\\text { Predicted values } \\\text { Fit } & \text { StDev Fit } & 95.0 \% \text { CI } & 95.0 \% \text { PI } \\53.35 & 3.168 & ( 42.72,63.98 ) & ( 31.61,75.09 )\end{array}\end{array}\end{array}$$ What percentage of the total variation in test scores is unexplained by the linear relationship between years of study and test scores?

A)82.7%
B)83.0%
C)17.0%
D)8.9%

Question 76

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. $$\text { The regression equation is }$$
$\begin{array}{l}\text { Score }=31.55+10.90 \text { Years. }\\\begin{array}{lllcc}\text { Predictor } & \text { Coef } & \text { StDev } & \text { T } & \text { P } \\\text { Constant } & 31.55 & 6.360 & 4.96 & 0.000 \\\text { Years } & 10.90 & 1.744 & 6.25 & 0.000\end{array}\end{array}$
$$S=5.651 \quad R-S q=83.0 \% \quad R-S q(\text { Adj })=82.7 \%$$
Predicted values
$\begin{array}{llcc}\text { Fit } & \text { StDev Fit } & 95.0 \% \text { CI } & 95.0 \% \text { PI } \\ 53.35 & 3.168 & (42.72,63.98) & (31.61,75.09)\end{array}$ If a person studies 4.5 years, what is the single value that is the best predicted test score? Assume that there is a significant linear correlation between years of study and test score.

A)53.35
B)80.6
C)83.0
D)49.1

Question 77

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

A)0.674
B)0.326
C)0.894
D)0.106

Question 78

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) $- 0.0707$

Question 79

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

A) $0.4839$
B) $0.8873$
C) $0.7265$
D) $0.9420$

Question 80

A regression equation is obtained for a collection of paired data. It is found that the total variation is 25.753, the explained variation is 18.658, and the unexplained variation is 7.095. Find the coefficient of determination.

A)0.724
B)1.380
C)0.380
D)0.276