Question 1

A(n) ________ is a point that strongly affects the graph of the regression line.

Accepted Answer

A)  least squares point 
B)  residual point 
C)  influential point 
D)  marginal point 
A)  least squares point 
B)  residual point 
C)  influential point 
D)  marginal point

Question 2

Find the value of the linear correlation coefficient r.
-$$\begin{array} { r | r r r r r r r } 
\mathrm { x } & 62 & 53 & 64 & 52 & 52 & 54 & 58 \
\hline \mathrm { y } & 158 & 176 & 151 & 164 & 164 & 174 & 162
\end{array}$$

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

Use computer software to obtain the multiple regression equation and identify $R 2$, adjusted $R ^ { 2 }$, and the P-value. An anti-smoking group used data in the table to relate the carbon monoxide (CO) of various brands of cigarettes to their tar and nicotine (NIC) content. $$\begin{array} { | c c c | } 
\hline \text { CO } & \text { TAR } & \text { NIC } \
\hline 15 & 1.2 & 16 \
15 & 1.2 & 16 \
17 & 1.0 & 16 \
6 & 0.8 & 9 \
1 & 0.1 & 1 \
8 & 0.8 & 8 \
10 & 0.8 & 10 \
17 & 1.0 & 16 \
15 & 1.2 & 15 \
11 & 0.7 & 9 \
18 & 1.4 & 18 \
16 & 1.0 & 15 \
10 & 0.8 & 9 \
7 & 0.5 & 5 \
18 & 1.1 & 16 \
\hline
\end{array}$$

Accepted Answer

A)  0.931, 0.902, 0.000 
B)  0.976, 0.921, 0.002 
C)  0.861, 0.900, 0.015 
D)  0.943, 0.934, 0.000 
A)  0.931, 0.902, 0.000 
B)  0.976, 0.921, 0.002 
C)  0.861, 0.900, 0.015 
D)  0.943, 0.934, 0.000

Question 5

Use computer software to find the multiple regression equation. Can the equation be used for prediction?
-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. $$\begin{array} { | c c c c | } 
\hline \text { WEIGHT } & \text { CHEST } & \text { LENGTH } & \text { SEX } \
\hline 344 & 45.0 & 67.5 & 1 \
416 & 54.0 & 72.0 & 1 \
220 & 41.0 & 70.0 & 2 \
360 & 49.0 & 68.5 & 1 \
332 & 44.0 & 73.0 & 1 \
140 & 32.0 & 63.0 & 2 \
436 & 48.0 & 72.0 & 1 \
132 & 33.0 & 61.0 & 2 \
356 & 48.0 & 64.0 & 2 \
150 & 35.0 & 59.0 & 1 \
202 & 40.0 & 63.0 & 2 \
365 & 50.0 & 70.5 & 1 \
\hline
\end{array}$$

Accepted Answer

A)  WEIGHT $= 196 + 2.35$ CHEST $+ 3.40$ LENGTH $+ 25$ SEX; Yes, because the $\mathrm { R } ^ { 2 }$ is high 
B)  WEIGHT $= 442.6 + 12.1$ CHEST + 4.2LENGTH - 21SEX; Yes, because the P-value is low 
C)  WEIGHT $= - 320 + 10.6$ CHEST + 7.3LENGTH $- 10.7$ SEX; Yes, because the P-value is high 
D)  WEIGHT $= - 442.6 + 12.1$ CHEST + 3.6LENGTH $- 23.8$ SEX; Yes, because the adjusted $\mathrm { R } ^ { 2 }$ is high 
A)  WEIGHT $= 196 + 2.35$ CHEST $+ 3.40$ LENGTH $+ 25$ SEX; Yes, because the $\mathrm { R } ^ { 2 }$ is high 
B)  WEIGHT $= 442.6 + 12.1$ CHEST + 4.2LENGTH - 21SEX; Yes, because the P-value is low 
C)  WEIGHT $= - 320 + 10.6$ CHEST + 7.3LENGTH $- 10.7$ SEX; Yes, because the P-value is high 
D)  WEIGHT $= - 442.6 + 12.1$ CHEST + 3.6LENGTH $- 23.8$ SEX; Yes, because the adjusted $\mathrm { R } ^ { 2 }$ is high

Question 6

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

Accepted Answer

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

Question 7

Solve the problem.
-In the context of regression, determine whether the following statement is true or false: If there is no correlation between x and y, the best predicted value of y for a given value of x is $$\overline { \mathrm { y } }$$

Accepted Answer

A)  True 
B)  False 
A)  True 
B)  False

Question 8

Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear
correlation between two variables. Find the critical values of r given the number of pairs of data n and the significance
level $\alpha$
-$$\mathrm { n } = 12 , \alpha = 0.01$$

Accepted Answer

A)  $r = 0.708$ 
B)  $r = \pm 0.708$ 
C)  $\mathrm { r } = \pm 0.576$ 
D)  $r = 0.735$ 
A)  $r = 0.708$ 
B)  $r = \pm 0.708$ 
C)  $\mathrm { r } = \pm 0.576$ 
D)  $r = 0.735$

Question 9

A(n) ________ is a point lying far away from other data points on a scatterplot.

Accepted Answer

A)  residual point 
B)  least-squares point 
C)  outlier 
D)  marginal point 
A)  residual point 
B)  least-squares point 
C)  outlier 
D)  marginal point

Question 10

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.
-$\begin{array}{l|lllll}
\mathrm{x} & 6 & 8 & 20 & 28 & 36 \
\hline \mathrm{y} & 2 & 4 & 13 & 20 & 30
\end{array}$

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

Use the computer display to answer the question.
-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 $\text { Score }=31.55+10.90 \text { Years. }$

$\begin{array}{lcccc}
\text { Predictor } & \text { Coef } & \text { StDev } & \text { T } & \text { P } \
\text { Constant } & 31.55 & 6.360 & 4.96 & 0.000 \
\text { Years } & 10.90 & 1.744 & 6.25 & 0.000
\end{array}$

$\mathrm{S}=5.651 \quad \mathrm{R}-\mathrm{Sq}=83.0 \% \quad \mathrm{R}-\mathrm{Sq}(\mathrm{Adj})=82.7 \%$

$\text { Predicted values }$

What percentage of the total variation in test scores is unexplained by the linear relationship between years of
Study and test scores?

Accepted Answer

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

Question 13

A 0.05 significance level is being used to test a correlation between two variables. If the linear correlation coefficient r is found to be 0.591 and the critical values are $r = \pm 0.878$ 878, what can you conclude?

Accepted Answer

A)  There is sufficient evidence to support the claim of a linear correlation between the two variables. 
B)  There is not sufficient evidence to support the claim of a linear correlation between the two variables. 
A)  There is sufficient evidence to support the claim of a linear correlation between the two variables. 
B)  There is not sufficient evidence to support the claim of a linear correlation between the two variables.

Question 14

$$\begin{array}{l}
\text { For the data below, determine the value of the linear correlation coefficient } r \text { between } y \text { and } x ^ { 2 } \text {. }\
\begin{array} { r | r r r r r } 
\boldsymbol { x } & 1.2 & 2.7 & 4.4 & 6.6 & 9.5 \
\hline \boldsymbol { y } & 1.6 & 4.7 & 9.9 & 24.5 & 39.0
\end{array}
\end{array}$$

Accepted Answer

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

Question 15

Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear
correlation between two variables. Find the critical values of r given the number of pairs of data n and the significance
level $\alpha$
-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. $$\begin{array} { | c | c c c c l } 
\hline x & 1.2 & 2.7 & 4.4 & 6.6 & 9.5 \
\hline y & 1.6 & 4.7 & 8.9 & 9.5 & 12.0 \
\hline
\end{array}$$

Accepted Answer

\[\begin{array} { l } 
\mathrm { r } = 0

Question 16

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

Accepted Answer

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

Question 17

Use computer software to obtain the multiple 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 1 and whose smoking value was 1. $$\begin{array} { | c c c | } 
\hline \text { PULSE } & \text { EXERCISE } & \text { SMOKE } \
\hline 97 & 2 & 2 \
88 & 1 & 2 \
69 & 1 & 2 \
67 & 1 & 2 \
83 & 1 & 2 \
77 & 1 & 2 \
66 & 2 & 2 \
78 & 2 & 2 \
73 & 1 & 1 \
67 & 1 & 1 \
55 & 1 & 2 \
82 & 1 & 1 \
70 & 1 & 2 \
55 & 1 & 2 \
76 & 1 & 2 \
\hline
\end{array}$$

Accepted Answer

A)  77 beats/min 
B)  81 beats/min 
C)  74 beats/min 
D)  70 beats/min 
A)  77 beats/min 
B)  81 beats/min 
C)  74 beats/min 
D)  70 beats/min

Question 18

Use computer software to obtain the multiple regression equation and identify R $$\mathrm { R } ^ { 2 }$$ , adjusted R $$\mathrm { R } ^ { 2 }$$ , and the P-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.

Accepted Answer

A)  0.843, 0.799, 0.005 
B)  0.912, 0.901, 0.010 
C)  0.867, 0.852, 0.000 
D)  0.855, 0.844, 0.002 
A)  0.843, 0.799, 0.005 
B)  0.912, 0.901, 0.010 
C)  0.867, 0.852, 0.000 
D)  0.855, 0.844, 0.002

Question 19

Use computer software to obtain the multiple regression equation and identify R $$\mathrm { R } ^ { 2 }$$ , adjusted R $$\mathrm { R } ^ { 2 }$$ , and the P-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. $$\begin{array} { | c c c c | } 
\hline \text { WEIGHT } & \text { CHEST } & \text { LENGTH } & \text { SEX } \
\hline 344 & 45.0 & 67.5 & 1 \
416 & 54.0 & 72.0 & 1 \
220 & 41.0 & 70.0 & 2 \
360 & 49.0 & 68.5 & 1 \
332 & 44.0 & 73.0 & 1 \
140 & 32.0 & 63.0 & 2 \
436 & 48.0 & 72.0 & 1 \
132 & 33.0 & 61.0 & 2 \
356 & 48.0 & 64.0 & 2 \
150 & 35.0 & 59.0 & 1 \
202 & 40.0 & 63.0 & 2 \
365 & 50.0 & 70.5 & 1 \
\hline
\end{array}$$

Accepted Answer

A)  0.971, 0.723, 0.000 
B)  0.891, 0.926, 0.003 
C)  0.725, 0.961, 0.014 
D)  0.927, 0.900, 0.000 
A)  0.971, 0.723, 0.000 
B)  0.891, 0.926, 0.003 
C)  0.725, 0.961, 0.014 
D)  0.927, 0.900, 0.000

Question 20

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. $$\begin{array} { | c | c | c | c | c | c | c | c | c | c | } 
\hline \text { Test A } & 48 & 52 & 58 & 44 & 43 & 43 & 40 & 51 & 59 \
\hline \text { Test B } & 73 & 67 & 73 & 59 & 58 & 56 & 58 & 64 & 74 \
\hline
\end{array}$$

Accepted Answer

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

A(n) ________ is a point that strongly affects the graph of the regression line.

Find the value of the linear correlation coefficient r. - 62 53 64 52 52 54 58 158 176 151 164 164 174 162

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

Solve the problem. -In the context of regression, determine whether the following statement is true or false: If there is no correlation between x and y, the best predicted value of y for a given value of x is $\overline { \mathrm { y } }$

Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical values of r given the number of pairs of data n and the significance level $\alpha$ - $\mathrm { n } = 12 , \alpha = 0.01$

A(n) ________ is a point lying far away from other data points on a scatterplot.

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. - 6 8 20 28 36 2 4 13 20 30

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

A 0.05 significance level is being used to test a correlation between two variables. If the linear correlation coefficient r is found to be 0.591 and the critical values are $r = \pm 0.878$ 878, what can you conclude?

For the data below, determine the value of the linear correlation coefficient r between y and . 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. -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. Test A 48 52 58 44 43 43 40 51 59 Test B 73 67 73 59 58 56 58 64 74

Introduction to Statistics

Exploring Data With Tables and Graphs

Describing, Exploring, and Comparing Data

Probability

Discrete Probability Distributions

Normal Probability Distributions

Estimating Parameters and Determining Sample Sizes

Hypothesis Testing

Inferences From Two Samples

Goodness-Of-Fit and Contingency Tables

Analysis of Variance

Nonparametric Tests

Statistical Process Control

Filters

Exam 10: Correlation and Regression

A(n) ________ is a point that strongly affects the graph of the regression line.

Find the value of the linear correlation coefficient r. - 62 53 64 52 52 54 58 158 176 151 164 164 174 162

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

Solve the problem. -In the context of regression, determine whether the following statement is true or false: If there is no correlation between x and y, the best predicted value of y for a given value of x is y‾\overline { \mathrm { y } }y​

A(n) ________ is a point lying far away from other data points on a scatterplot.

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. - 6 8 20 28 36 2 4 13 20 30

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

A 0.05 significance level is being used to test a correlation between two variables. If the linear correlation coefficient r is found to be 0.591 and the critical values are r=±0.878r = \pm 0.878r=±0.878 878, what can you conclude?

For the data below, determine the value of the linear correlation coefficient r between y and . 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. -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. Test A 48 52 58 44 43 43 40 51 59 Test B 73 67 73 59 58 56 58 64 74

Introduction to Statistics

Exploring Data With Tables and Graphs

Describing, Exploring, and Comparing Data

Probability

Discrete Probability Distributions

Normal Probability Distributions

Estimating Parameters and Determining Sample Sizes

Hypothesis Testing

Inferences From Two Samples

Goodness-Of-Fit and Contingency Tables

Analysis of Variance

Nonparametric Tests

Statistical Process Control

Filters

Solve the problem. -In the context of regression, determine whether the following statement is true or false: If there is no correlation between x and y, the best predicted value of y for a given value of x is $\overline { \mathrm { y } }$

A 0.05 significance level is being used to test a correlation between two variables. If the linear correlation coefficient r is found to be 0.591 and the critical values are $r = \pm 0.878$ 878, what can you conclude?