Question 1

An environmentalist wants to determine the relationship between the number (in thousands) of forest fires over the year and the number (in hundreds of thousands) burned. The data for 8 recent years are shown.
a. Draw the scatter plot for the variables.
b. Give a brief explanation of the type of relationship.
$\begin{array} { c c } \text { Number of fires } x & \text { Number of acres burned } \ 72 & 62 \ 69 & 42 \ 58 & 19 \ 47 & 26 \ 84 & 51 \ 62 & 15 \ 57 & 30 \ 45 & 15 \end{array}$

Accepted Answer

The answer of An environmentalist wants to determine the relationship...

Question 2

$$\begin{array}{l}
\text { Find the equation of the regression line. }\
\begin{array} { c | c c c c c c } 
x & 50 & 58 & 43 & 52 & 47 & 42 \
\hline y & 184 & 187 & 163 & 171 & 171 & 144
\end{array}
\end{array}$$

Accepted Answer

The answer of \[\begin{array}{l}
\text { Find the equation of the...

Question 3

In a study of reaction times, the time to respond to a visual stimulus $( x )$ and the time to respond to an auditory stimulus $( y )$ were recorded for each of 6 subjects. Times were measured in thousandths of a second. The results are presented in the following table.
The following MINITAB output describes the fit of a linear model to these data. Assume assumptions of the linear model are satisfied.
The regression equation is
Auditory $= 193.269291 + 0.354955$ Visual
$\begin{array} { l l l l l } \text { Predictor } & \text { Coef } & \text { SE Coef } & \mathrm { T } & \mathrm { P } \ \text { Constant } & 193.269291 & 16.307408 & 11.851625 & 0.000291 \ \text { Visual } & 0.354955 & 0.086702 & 4.093976 & 0.014927 \end{array}$
What is the slope of the least-squares regression line?

Accepted Answer

A)  0.354955 
B)  11.851625 
C)  0.086702 
D)  193.269291

Question 4

If the equation for the regression line is $y ^ { \prime } = 9 x + 2$, then a value of $x = - 3$ will result in a predicted value for $y$ of

Accepted Answer

A)  3 
B)  9 
C)  2 
D)  -25

Question 5

$$\text { The equation of a regression line is } y ^ { \prime } = 4.6 + 3.2 x \text {. What is the intercept of this line? }$$

Accepted Answer

A)  3.2 
B)  0 
C)  4.6 
D)  -4.6

Question 6

$$\text { The formula for the coefficient of nondetermination is } 1.00 - r ^ { 2 } \text {. }$$

Accepted Answer

A) True 
 B)False

Question 7

Two researchers run identical experiments except researcher A collects twice as many points as researcher B. For a specific value $x$, researcher A estimates a $y$ value of $y _ { A } ^ { \prime }$ and researcher B estimates a $y$ value of $y _ { B ^ { \prime } }$. We would expect that researcher $\mathrm { A } ^ { \prime } \mathrm { s } 95 \%$ prediction interval around $y _ { A } ^ { \prime }$ to be, in general,

Accepted Answer

A)  wider than researcher B's $95 \%$ prediction interval around $y _ { B } ^ { \prime }$ or narrower than researcher B's $95 \%$ prediction interval around $y _ { B } ^ { \prime }$, with equal probability. 
B)  the same as researcher B's $95 \%$ prediction interval around $y _ { B } ^ { \prime }$. 
C)  narrower than researcher B's $95 \%$ prediction interval around $y _ { B } ^ { \prime } { } _ { B }$. 
D)  wider than researcher B's $95 \%$ prediction interval around $y _ { B } ^ { \prime }$.

Question 8

If the correlation coefficient $r$ is equal to $0.547$, find the coefficient of determination and the coefficient of nondetermination.

Accepted Answer

A)  The coefficient of determination is 0.299 and the coefficient of nondetermination is 0.701 
B)  The coefficient of determination is 0.701 and the coefficient of nondetermination is 0.299 
C)  The coefficient of determination is 0.260 and the coefficient of nondetermination is 0.740 
D)  The coefficient of determination is 0.740 and the coefficient of nondetermination is 0.260

Question 9

The variation due to chance, found by the formula , is called the
unexplained variation.

Accepted Answer

The answer of The variation due to chance, found by...

Question 10

In a multiple regression model $y ^ { \prime } = - 9 + 3 x _ { 1 } + 21 x _ { 2 } + 13 x _ { 3 } + 4 x _ { 4 }$, if the $x _ { 1 }$ value changes by 2 , then the predicted value for $y$ will change by

Accepted Answer

A)  32 
B)  6 
C)  -3 
D)  42

Question 11

$$\begin{array}{l}
\text { Compute the value of the correlation coefficient. }\
\begin{array} { c | c c c c c } 
x & 40 & 43 & 46 & 41 & 44 \
\hline y & 182 & 214 & 210 & 194 & 218
\end{array}
\end{array}$$

Accepted Answer

A)  0.644 
B)  0.826 
C)  0.814 
D)  0.774

Question 12

With enough variables, it is possible to get an $R ^ { 2 }$ value close to 1 , even if the variables have no particular meaning in the model

Accepted Answer

A) True 
 B)False

Question 13

$$\text { If the equation for the regression line is } y ^ { \prime } = - 8 x + 3 \text {, then the slope of this line is }$$

Accepted Answer

A)  3 
B)  6 
C)  -8 
D)  -5

Question 14

When $r$ is not significantly different from 0 , the best predictor of $y$ is the___________ of the data values of $y$.

Accepted Answer

The answer of When $r$ is not significantly different from...

Question 15

A psychologist wants to determine if there is a linear relationship between the nun hours a person goes without sleep and the number of mistakes he/she makes on a : test. The following data is recorded.
a. Draw a scatter plot.
b. Determine the regression line equation and plot the regression line on the scatter plot.
$\begin{array} { c c } \text { Hours without Sleep, } \boldsymbol { x } & \text { Number of Mistakes, } y \ 32 & 6 \ 38 & 8 \ 48 & 13 \ 24 & 5 \ 46 & 7 \ 35 & 6 \ 30 & 5 \ 34 & 8 \ 42 & 12 \end{array}$

Accepted Answer

The answer of A psychologist wants to determine if there...

Question 16

A regression line can be used to show trends in data.

Accepted Answer

A) True 
 B)False

Question 17

$$\text { If the equation for the regression line is } y ^ { \prime } = - 8 x + 6 \text {, then the intercept of this line is }$$

Accepted Answer

A)  12 
B)  6 
C)  -8 
D)  -2

Question 18

$$\begin{array} { l } 
\text { Compute the standard error of the estimate for the data below. } \
\begin{array} { l c c c c c } 
\text { X values } & 54 & 63 & 70 & 84 & 97 \
\text { Y values } & 94 & 122 & 146 & 167 & 191
\end{array}
\end{array}$$

Accepted Answer

A)  7.47 
B)  4.26 
C)  6.20 
D)  2.76

Question 19

An experiment is carried out to determine the relationship between the average speed (rpm) and power (hp) of a mixer. Draw the scatter plot for the variables.
$\begin{array} { c c } \text { Average Speed } & \text { Power } \ 325.0 & 1.10 \ 348.9 & 1.40 \ 312.9 & 1.07 \ 230.0 & 0.25 \ 269.2 & 0.64 \ 305.0 & 0.93 \end{array}$

Accepted Answer

The answer of An experiment is carried out to determine...

Question 20

As a researcher collects more and more data, the 95% prediction intervals in general

Accepted Answer

A)  become narrower and narrower, but the widths are always more than approximately 4 times the slope. 
B)  become narrower and narrower, but the widths are always more than approximately 2 times the standard error of the estimate. 
C)  become narrower and narrower, with the widths getting closer and closer to 0. 
D)  become narrower and narrower, but the widths are always more than approximately 4 times the standard error of the estimate.

Exam 10: Correlation and Regression

$\begin{array}{l}\text { Find the equation of the regression line. }\\\begin{array} { c | c c c c c c } x & 50 & 58 & 43 & 52 & 47 & 42 \\\hline y & 184 & 187 & 163 & 171 & 171 & 144\end{array}\end{array}$

If the equation for the regression line is $y ^ { \prime } = 9 x + 2$ , then a value of $x = - 3$ will result in a predicted value for $y$ of

$\text { The equation of a regression line is } y ^ { \prime } = 4.6 + 3.2 x \text {. What is the intercept of this line? }$

$\text { The formula for the coefficient of nondetermination is } 1.00 - r ^ { 2 } \text {. }$

If the correlation coefficient $r$ is equal to $0.547$ , find the coefficient of determination and the coefficient of nondetermination.

The variation due to chance, found by the formula , is called the unexplained variation.

In a multiple regression model $y ^ { \prime } = - 9 + 3 x _ { 1 } + 21 x _ { 2 } + 13 x _ { 3 } + 4 x _ { 4 }$ , if the $x _ { 1 }$ value changes by 2 , then the predicted value for $y$ will change by

$\begin{array}{l}\text { Compute the value of the correlation coefficient. }\\\begin{array} { c | c c c c c } x & 40 & 43 & 46 & 41 & 44 \\\hline y & 182 & 214 & 210 & 194 & 218\end{array}\end{array}$

With enough variables, it is possible to get an $R ^ { 2 }$ value close to 1 , even if the variables have no particular meaning in the model

$\text { If the equation for the regression line is } y ^ { \prime } = - 8 x + 3 \text {, then the slope of this line is }$

When $r$ is not significantly different from 0 , the best predictor of $y$ is the___________ of the data values of $y$ .

A regression line can be used to show trends in data.

$\text { If the equation for the regression line is } y ^ { \prime } = - 8 x + 6 \text {, then the intercept of this line is }$

$\begin{array} { l } \text { Compute the standard error of the estimate for the data below. } \\\begin{array} { l c c c c c } \text { X values } & 54 & 63 & 70 & 84 & 97 \\\text { Y values } & 94 & 122 & 146 & 167 & 191\end{array}\end{array}$

As a researcher collects more and more data, the 95% prediction intervals in general

Exam 10: Correlation and Regression

If the equation for the regression line is y′=9x+2y ^ { \prime } = 9 x + 2y′=9x+2 , then a value of x=−3x = - 3x=−3 will result in a predicted value for yyy of

The equation of a regression line is y′=4.6+3.2x. What is the intercept of this line? \text { The equation of a regression line is } y ^ { \prime } = 4.6 + 3.2 x \text {. What is the intercept of this line? } The equation of a regression line is y′=4.6+3.2x. What is the intercept of this line?

The formula for the coefficient of nondetermination is 1.00−r2. \text { The formula for the coefficient of nondetermination is } 1.00 - r ^ { 2 } \text {. } The formula for the coefficient of nondetermination is 1.00−r2.

If the correlation coefficient rrr is equal to 0.5470.5470.547 , find the coefficient of determination and the coefficient of nondetermination.

The variation due to chance, found by the formula , is called the unexplained variation.

In a multiple regression model y′=−9+3x1+21x2+13x3+4x4y ^ { \prime } = - 9 + 3 x _ { 1 } + 21 x _ { 2 } + 13 x _ { 3 } + 4 x _ { 4 }y′=−9+3x1​+21x2​+13x3​+4x4​ , if the x1x _ { 1 }x1​ value changes by 2 , then the predicted value for yyy will change by

With enough variables, it is possible to get an R2R ^ { 2 }R2 value close to 1 , even if the variables have no particular meaning in the model

If the equation for the regression line is y′=−8x+3, then the slope of this line is \text { If the equation for the regression line is } y ^ { \prime } = - 8 x + 3 \text {, then the slope of this line is } If the equation for the regression line is y′=−8x+3, then the slope of this line is

When rrr is not significantly different from 0 , the best predictor of yyy is the___________ of the data values of yyy .

A regression line can be used to show trends in data.

As a researcher collects more and more data, the 95% prediction intervals in general

If the equation for the regression line is $y ^ { \prime } = 9 x + 2$ , then a value of $x = - 3$ will result in a predicted value for $y$ of

$\text { The equation of a regression line is } y ^ { \prime } = 4.6 + 3.2 x \text {. What is the intercept of this line? }$

$\text { The formula for the coefficient of nondetermination is } 1.00 - r ^ { 2 } \text {. }$

If the correlation coefficient $r$ is equal to $0.547$ , find the coefficient of determination and the coefficient of nondetermination.

In a multiple regression model $y ^ { \prime } = - 9 + 3 x _ { 1 } + 21 x _ { 2 } + 13 x _ { 3 } + 4 x _ { 4 }$ , if the $x _ { 1 }$ value changes by 2 , then the predicted value for $y$ will change by

With enough variables, it is possible to get an $R ^ { 2 }$ value close to 1 , even if the variables have no particular meaning in the model

$\text { If the equation for the regression line is } y ^ { \prime } = - 8 x + 3 \text {, then the slope of this line is }$

When $r$ is not significantly different from 0 , the best predictor of $y$ is the___________ of the data values of $y$ .