Question 1

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. $\begin{array}{|l|lllll|}
\hline x & 1 & 3 & 5 & 7 & 9 \
\hline y & 143 & 116 & 100 & 98 & 90 \
\hline
\end{array}$

Accepted Answer

A)  $y = 140.4 - 6.2 x$ 
B)  $y = - 150.7 + 6.8 x$ 
C)  $y = 150.7 - 6.8 x$ 
D)  $y = - 140.4 + 6.2 x$ 
A)  $y = 140.4 - 6.2 x$ 
B)  $y = - 150.7 + 6.8 x$ 
C)  $y = 150.7 - 6.8 x$ 
D)  $y = - 140.4 + 6.2 x$

Question 2

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

Accepted Answer

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

Question 3

Find the coefficient of determination, given that the value of the linear correlation coefficient, r, is 0.738.

Accepted Answer

A)  0.262 
B)  0.738 
C)  0.455 
D)  0.545 
A)  0.262 
B)  0.738 
C)  0.455 
D)  0.545

Question 4

A 0.01 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 = ±0.590 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 5

Find the value of the linear correlation coefficient r.
-$$\begin{array} { r | r r r r r r r } 
\mathrm { x } & 57 & 53 & 59 & 61 & 53 & 56 & 60 \
\hline \mathrm { y } & 156 & 164 & 163 & 177 & 159 & 175 & 151
\end{array}$$

Accepted Answer

A)  0.214 
B)  -0.078 
C)  0.109 
D)  -0.054 
A)  0.214 
B)  -0.078 
C)  0.109 
D)  -0.054

Question 6

Solve the problem.
-After obtaining a regression line $y = \beta _ { 0 } + \beta _ { 1 } x$, a confidence interval for the mean of all values $y$ for which $x = x 0$ can be obtained as follows:
$( \hat { y } - \mathrm { E } , \hat { \mathrm { y } } + \mathrm { E } )$ where $E = \left( t _ { \alpha / 2 } \right) \operatorname { se } \sqrt { \frac { 1 } { n } + \frac { n \left( x _ { 0 } - \bar { x } \right) ^ { 2 } } { n \sum x ^ { 2 } - \left( \sum x \right) ^ { 2 } } }$
The critical value $t _ { \alpha / 2 }$ is found from the t-table using $n - 2$ degrees of freedom.
Use the data below to obtain a $95 \%$ confidence interval estimate of the mean test score of all students who study $10.5$ hours. Note that the equation of the regression line is $\hat { y } = 52.8804 + 3.405 \mathrm { x }$ and that $\mathrm { s } = 6.8359$.
$\begin{array}{l|lllll}
x \text { (hours studied) } & 2.5 & 4.5 & 5.1 & 7.9 & 11.6 \
\hline \mathrm{y} \text { (score on test) } & 66 & 70 & 60 & 83 & 93
\end{array}$

Accepted Answer

A)  $( 80.48,96.78 )$ 
B)  $( 77.11,100.15 )$ 
C)  $( 72.49,104.78 )$ 
D)  $( 61.55,115.71 )$ 
A)  $( 80.48,96.78 )$ 
B)  $( 77.11,100.15 )$ 
C)  $( 72.49,104.78 )$ 
D)  $( 61.55,115.71 )$

Question 7

The residual is the ________ the observed value of y and the predicted value of y.

Accepted Answer

A)  quotient of 
B)  product of 
C)  sum of 
D)  difference between 
A)  quotient of 
B)  product of 
C)  sum of 
D)  difference between

Question 8

Is the data point, P, an outlier, an influential point, both, or neither?
-

Accepted Answer

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

Question 9

Is the data point, P, an outlier, an influential point, both, or neither?
-The regression equation for a set of paired data is $\hat { y } = 8 + 5 x$. The correlation coefficient for the data is $0.9$. A new data point, $\mathrm { P } ( 11,76 )$, is added to the set.

Accepted Answer

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

Question 10

A regression equation is obtained for a collection of paired data. It is found that the total variation is 110.7, the explained variation is 93.3, and the unexplained variation is 17.4. Find the coefficient of determination.

Accepted Answer

A)  0.843 
B)  0.186 
C)  1.186 
D)  0.157 
A)  0.843 
B)  0.186 
C)  1.186 
D)  0.157

Question 11

The sample data below are the typing speeds (in words per minute) and reading speeds (in words per minute)
of nine randomly selected secretaries. Here, x denotes typing speed, and y denotes reading speed. $$\begin{array} { l l l l l l l l l l | } 
\hline x & 60 & 56 & 52 & 63 & 70 & 58 & 44 & 79 & 62 \
\hline \mathrm { y } & 370 & 551 & 528 & 348 & 645 & 454 & 503 & 618 & 500 \
\hline
\end{array}$$ The regression equation $$\hat { \mathrm { y } } = 290.2 + 3.502 \mathrm { x }$$ was obtained. Construct a residual plot for the data.

Accepted Answer

The answer of The sample data below are the typing...

Question 12

Solve the problem.
-In the context of regression, determine whether the following statement is true or false: If there is a very strong correlation between x and y, the amount of unexplained variation should be relatively
Large.

Accepted Answer

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

Question 13

Use the given data to find the best predicted value of the response variable. Ten pairs of data yield r = 0.003 and the regression equation $\hat { y } = 2 + 3 x . \mathrm { Also } , \bar { y } = 5.0$ . What is the best predicted value of y for x = 2?

Accepted Answer

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

Question 14

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.
-$\begin{array}{|l|lllll}
\mathrm{x} & 0 & 3 & 4 & 5 & 12 \
\hline \mathrm{y} & 8 & 2 & 6 & 9 & 12
\end{array}$

Accepted Answer

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

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. x 1 3 5 7 9 y 143 116 100 98 90

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 coefficient of determination, given that the value of the linear correlation coefficient, r, is 0.738.

A 0.01 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 = ±0.590 what can you conclude?

Find the value of the linear correlation coefficient r. - 57 53 59 61 53 56 60 156 164 163 177 159 175 151

The residual is the ________ the observed value of y and the predicted value of y.

Is the data point, P, an outlier, an influential point, both, or neither? -

Is the data point, P, an outlier, an influential point, both, or neither? -The regression equation for a set of paired data is $\hat { y } = 8 + 5 x$ . The correlation coefficient for the data is $0.9$ . A new data point, $\mathrm { P } ( 11,76 )$ , is added to the set.

A regression equation is obtained for a collection of paired data. It is found that the total variation is 110.7, the explained variation is 93.3, and the unexplained variation is 17.4. Find the coefficient of determination.

Solve the problem. -In the context of regression, determine whether the following statement is true or false: If there is a very strong correlation between x and y, the amount of unexplained variation should be relatively Large.

Use the given data to find the best predicted value of the response variable. Ten pairs of data yield r = 0.003 and the regression equation $\hat { y } = 2 + 3 x . \mathrm { Also } , \bar { y } = 5.0$ . What is the best predicted value of y for x = 2?

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. - 0 3 4 5 12 8 2 6 9 12

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

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. x 1 3 5 7 9 y 143 116 100 98 90

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 coefficient of determination, given that the value of the linear correlation coefficient, r, is 0.738.

A 0.01 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 = ±0.590 what can you conclude?

Find the value of the linear correlation coefficient r. - 57 53 59 61 53 56 60 156 164 163 177 159 175 151

The residual is the ________ the observed value of y and the predicted value of y.

Is the data point, P, an outlier, an influential point, both, or neither? -

A regression equation is obtained for a collection of paired data. It is found that the total variation is 110.7, the explained variation is 93.3, and the unexplained variation is 17.4. Find the coefficient of determination.

Solve the problem. -In the context of regression, determine whether the following statement is true or false: If there is a very strong correlation between x and y, the amount of unexplained variation should be relatively Large.

Use the given data to find the best predicted value of the response variable. Ten pairs of data yield r = 0.003 and the regression equation y^=2+3x.Also,yˉ=5.0\hat { y } = 2 + 3 x . \mathrm { Also } , \bar { y } = 5.0y^​=2+3x.Also,yˉ​=5.0 . What is the best predicted value of y for x = 2?

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. - 0 3 4 5 12 8 2 6 9 12

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

Use the given data to find the best predicted value of the response variable. Ten pairs of data yield r = 0.003 and the regression equation $\hat { y } = 2 + 3 x . \mathrm { Also } , \bar { y } = 5.0$ . What is the best predicted value of y for x = 2?