Question 1

Based on the scatterplot, select the most likely value of the linear correlation coefficient r.

Accepted Answer

A)  1 
B)  -1 
C)  -0.5 
D)  0 
A)  1 
B)  -1 
C)  -0.5 
D)  0

Question 2

Find the indicated multiple regression equation.
-A fitness rating was obtained for 9 randomly selected adult women. Each person was also asked her age, weight, and the number of hours she spent exercising each week. The results are shown below.
$\begin{array}{r|rrrrrrrrr}
\text { Age } & 39 & 27 & 41 & 48 & 56 & 59 & 22 & 64 & 35 \
\hline \text { Weight } & 140 & 129 & 137 & 125 & 162 & 152 & 118 & 142 & 126 \
\hline \text { Hours of exercise per week } & 2 & 6 & 4 & 9 & 0 & 3 & 11 & 3 & 4 \
\hline \text { Fitness rating } & 72 & 88 & 63 & 84 & 47 & 52 & 90 & 31 & 64
\end{array}$

Identify the multiple regression equation that expresses fitness in terms of age, weight, and hours of exercise per week.

Accepted Answer

A)  $\hat { \mathrm { F } } = 45.12 - 0.918 \mathrm {~A} + 0.461 \mathrm {~W} + 2.34 \mathrm { E }$ 
B)  $\hat { \mathrm { F } } = 36.07 - 1.02 \mathrm {~A} + 0.429 \mathrm {~W} + 3.30 \mathrm { E }$ 
C)  $\hat { F } = 52.46 - 2.14 \mathrm {~A} + 1.39 \mathrm {~W} + 2.48 \mathrm { E }$ 
D)  $\hat { F } = 23.79 - 1.36 \mathrm {~A} + 0.241 \mathrm {~W} + 1.43 \mathrm { E }$ 
A)  $\hat { \mathrm { F } } = 45.12 - 0.918 \mathrm {~A} + 0.461 \mathrm {~W} + 2.34 \mathrm { E }$ 
B)  $\hat { \mathrm { F } } = 36.07 - 1.02 \mathrm {~A} + 0.429 \mathrm {~W} + 3.30 \mathrm { E }$ 
C)  $\hat { F } = 52.46 - 2.14 \mathrm {~A} + 1.39 \mathrm {~W} + 2.48 \mathrm { E }$ 
D)  $\hat { F } = 23.79 - 1.36 \mathrm {~A} + 0.241 \mathrm {~W} + 1.43 \mathrm { E }$

Question 3

The table below shows the population of a city (in millions) in each year during the period 2010-2015. Using the
number of years since 2010 as the independent variable, find the regression equation of the best model. Assume
that the model is to be used only for the scope of the given data, and consider only linear, quadratic,
logarithmic, exponential, and power models. Include the type of model and the equation for the model you find. $$\begin{array} { | | l | l | l | l | l | l | l | } 
\hline \text { Year } & 2010 & 2011 & 2012 & 2013 & 2014 & 2015 \
\hline \text { Population(millions) } & 1.08 & 1.37 & 1.68 & 2.19 & 2.73 & 3.34 \
\hline
\end{array}$$

Accepted Answer

The answer of The table below shows the population of...

Question 4

Solve the problem.
-A regression equation can be used to make predictions of the y value corresponding to a particular x value. Determine whether the following statement is true or false:
The 95% confidence interval for the mean of all values of y for whic $$x = x 0$$ will be wider than the 95%
Confidence interval for a single y for which $$x = x _ { 0 }$$

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

A quadratic regression model is fit to a set of sample data consisting of 6 pairs of data. Given that the sum of squares of residuals is 29.73 and that the y-values are 11, 14, 19, 22, 26, 27, find $R ^ { 2 } = 1 - \frac { \Sigma ( y - \hat { y } ) ^ { 2 } } { \Sigma ( y - y ) ^ { 2 } } .$

Accepted Answer

A)  0.144 
B)  0.88 
C)  0.856 
D)  0.844 
A)  0.144 
B)  0.88 
C)  0.856 
D)  0.844

Question 7

$$\mathrm { r } = 0.806 , \mathrm { n } = 9$$

Accepted Answer

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

Question 8

Use the given information to find the coefficient of determination. A regression equation is obtained for a collection of paired data. It is found that the total variation is 20.711, the explained variation is 18.592, and the
Unexplained variation is 2.119.

Accepted Answer

A)  0.114 
B)  1.114 
C)  0.898 
D)  0.102 
A)  0.114 
B)  1.114 
C)  0.898 
D)  0.102

Question 9

For each of 200 randomly selected cities, Pete recorded the number of churches in the city (x) and the number of
homicides in the past decade (y). He calculated the linear correlation coefficient and was surprised to find a
strong positive linear correlation for the two variables. Does this suggest that building new churches causes an
increase in the number of homicides? Why do you think that a strong positive linear correlation coefficient was
obtained? Explain your answer with reference to the term lurking variable.

Accepted Answer

The positive linear correlation coeffici

Question 10

Use computer software to find the multiple regression equation. Can the equation be used for prediction? 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. $\begin{array}{ccc}
\hline \text { CO } & \text { TAR } & \text { NIC } \
\hline 15 & 1.2 & 16 \
15 & 1.2 & 16 \
17 & 1.0 & 16 \
6 & 0.8 & 9 \
1 & 0.1 & 1 \
8 & 0.8 & 8 \
10 & 0.8 & 10 \
17 & 1.0 & 16 \
15 & 1.2 & 15 \
11 & 0.7 & 9 \
18 & 1.4 & 18 \
16 & 1.0 & 15 \
10 & 0.8 & 9 \
7 & 0.5 & 5 \
18 & 1.1 & 16 \
\hline
\end{array}$

Accepted Answer

A)  $\mathrm { CO } = 1.3 + 5.5 \mathrm { TAR } - 1.3 \mathrm { NIC }$; Yes, because the adjusted $R ^ { 2 }$ is high. 
B)  $\mathrm { CO } = 1.37 - 5.53 \mathrm { TAR } + 1.33 \mathrm { NIC }$; Yes, because the $R ^ { 2 }$ is high. 
C)  $\mathrm { CO } = 1.37 + 5.50 \mathrm { TAR } - 1.38 \mathrm { NIC }$; Yes, because the $P$-value is high. 
D)  $\mathrm { CO } = 1.25 + 1.55 \mathrm { TAR } - 5.79 \mathrm { NIC }$; Yes, because the $P$-value is too low. 
A)  $\mathrm { CO } = 1.3 + 5.5 \mathrm { TAR } - 1.3 \mathrm { NIC }$; Yes, because the adjusted $R ^ { 2 }$ is high. 
B)  $\mathrm { CO } = 1.37 - 5.53 \mathrm { TAR } + 1.33 \mathrm { NIC }$; Yes, because the $R ^ { 2 }$ is high. 
C)  $\mathrm { CO } = 1.37 + 5.50 \mathrm { TAR } - 1.38 \mathrm { NIC }$; Yes, because the $P$-value is high. 
D)  $\mathrm { CO } = 1.25 + 1.55 \mathrm { TAR } - 5.79 \mathrm { NIC }$; Yes, because the $P$-value is too low.

Question 11

Find the explained variation for the paired data.
-The paired data below consists of heights and weights of 6 randomly selected adults. The equation of the regression line is $\hat { y } = - 181.342 + 144.46 x$. Find the explained variation.
$\begin{array}{c|rrrrrr}
x \text { Height (meters) } & 1.61 & 1.72 & 1.78 & 1.80 & 1.67 & 1.88 \
\hline y \text { Weight }(\mathrm{kg}) & 54 & 62 & 70 & 84 & 61 & 92
\end{array}$

Accepted Answer

A)  $100.06$ 
B)  $979.44$ 
C)  $1149.2$ 
D)  $1079.5$ 
A)  $100.06$ 
B)  $979.44$ 
C)  $1149.2$ 
D)  $1079.5$

Question 12

Find the indicated multiple regression equation.
-A fitness rating was obtained for 9 randomly selected adult women. Each person was also asked her age, weight, and the number of hours she spent exercising each week. The results are shown below.
$\begin{array}{r|rrrrrrrrr}
\text { Age } & 39 & 27 & 41 & 48 & 56 & 59 & 22 & 64 & 35 \
\hline \text { Weight } & 140 & 129 & 137 & 125 & 162 & 152 & 118 & 142 & 126 \
\hline \text { Hours of exercise per week } & 2 & 6 & 4 & 9 & 0 & 3 & 11 & 3 & 4 \
\hline \text { Fitness rating } & 72 & 88 & 63 & 84 & 47 & 52 & 90 & 31 & 64
\end{array}$

Identify the multiple regression equation that expresses fitness in terms of age and hours of exercise per week.

Accepted Answer

A)  $\hat { \mathrm { F } } = 104.0 - 1.27 \mathrm {~A} + 4.08 \mathrm { E }$ 
B)  $\hat { \mathrm { F } } = 12.98 + 0.871 \mathrm {~A} + 3.71 \mathrm { E }$ 
C)  $\hat { \mathrm { F } } = 93.20 - 0.869 \mathrm {~A} + 2.19 \mathrm { E }$ 
D)  $\hat { \mathrm { F } } = 67.12 - 0.451 \mathrm {~A} + 7.29 \mathrm { E }$ 
A)  $\hat { \mathrm { F } } = 104.0 - 1.27 \mathrm {~A} + 4.08 \mathrm { E }$ 
B)  $\hat { \mathrm { F } } = 12.98 + 0.871 \mathrm {~A} + 3.71 \mathrm { E }$ 
C)  $\hat { \mathrm { F } } = 93.20 - 0.869 \mathrm {~A} + 2.19 \mathrm { E }$ 
D)  $\hat { \mathrm { F } } = 67.12 - 0.451 \mathrm {~A} + 7.29 \mathrm { E }$

Question 13

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

Accepted Answer

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

Question 14

Find the unexplained variation for the paired data.
-The paired data below consists of heights and weights of 6 randomly selected adults. The equation of the regression line is $\hat { \mathrm { y } } = - 181.342 + 144.46 \mathrm { x }$. Find the unexplained variation.
$\begin{array}{c|rrrrrr}
\text { x Height (meters) } & 1.61 & 1.72 & 1.78 & 1.80 & 1.67 & 1.88 \
\hline \text { y Weight }(\mathrm{kg}) & 54 & 62 & 70 & 84 & 61 & 92
\end{array}$

Accepted Answer

A)  $100.06$ 
B)  $119.3$ 
C)  $979.44$ 
D)  $1079.5$ 
A)  $100.06$ 
B)  $119.3$ 
C)  $979.44$ 
D)  $1079.5$

Question 15

A regression equation is obtained for a collection of paired data. It is found that the total variation is 20.711, the explained variation is 18.592, and the unexplained variation is 2.119. Find the coefficient of determination.

Accepted Answer

A)  1.114 
B)  0.114 
C)  0.898 
D)  0.102 
A)  1.114 
B)  0.114 
C)  0.898 
D)  0.102

Question 16

A regression equation is obtained for a set of data. After examining a scatter diagram, the researcher notices a
data point that is potentially an influential point. How could she confirm that this data point is indeed an
influential point?

Accepted Answer

The researcher should first graph the re

Question 17

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 $\alpha$
-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.

Accepted Answer

Averages suppress individual variation a

Question 18

Construct a scatterplot for the given data.
-$$\begin{array} { | l r | r | r | r | r | r | r | r | r | r | } 
\hline x & - 3 & - 2 & - 1 & - 4 & - 2 & 6 & 2 & 9 & - 5 & - 1 \
\hline y & - 7 & - 3 & - 2 & 1 & 2 & 1 & - 5 & 2 & - 4 & - 4 \
\hline
\end{array}$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 19

For the data below, determine the logarithmic equation, $$\hat { y } = a + b \ln x$$ 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
Line. $\begin{array}{c|ccccl}
\mathrm{x} & 1.2 & 2.7 & 4.4 & 6.6 & 9.5 \
\hline \mathrm{y} & 1.6 & 4.7 & 8.9 & 9.5 & 12.0
\end{array}$

Accepted Answer

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

Question 20

The following residual plot is obtained after a regression equation is determined for a set of data. Does the
residual plot suggest that the regression equation is a bad model? Why or why not?

Accepted Answer

No, the residual plot does not suggest t

Based on the scatterplot, select the most likely value of the linear correlation coefficient r.

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). Temperature 62 76 50 51 71 46 51 44 79 Growth 36 39 50 13 33 33 17 6 16

A quadratic regression model is fit to a set of sample data consisting of 6 pairs of data. Given that the sum of squares of residuals is 29.73 and that the y-values are 11, 14, 19, 22, 26, 27, find $R ^ { 2 } = 1 - \frac { \Sigma ( y - \hat { y } ) ^ { 2 } } { \Sigma ( y - y ) ^ { 2 } } .$

$\mathrm { r } = 0.806 , \mathrm { n } = 9$

Use the given information to find the coefficient of determination. A regression equation is obtained for a collection of paired data. It is found that the total variation is 20.711, the explained variation is 18.592, and the Unexplained variation is 2.119.

A regression equation is obtained for a collection of paired data. It is found that the total variation is 20.711, the explained variation is 18.592, and the unexplained variation is 2.119. Find the coefficient of determination.

A regression equation is obtained for a set of data. After examining a scatter diagram, the researcher notices a data point that is potentially an influential point. How could she confirm that this data point is indeed an influential point?

For the data below, determine the logarithmic equation, $\hat { y } = a + b \ln x$ 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 Line. 1.2 2.7 4.4 6.6 9.5 1.6 4.7 8.9 9.5 12.0

The following residual plot is obtained after a regression equation is determined for a set of data. Does the residual plot suggest that the regression equation is a bad model? Why or why not?

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

Based on the scatterplot, select the most likely value of the linear correlation coefficient r.

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). Temperature 62 76 50 51 71 46 51 44 79 Growth 36 39 50 13 33 33 17 6 16

r=0.806,n=9\mathrm { r } = 0.806 , \mathrm { n } = 9r=0.806,n=9

Use the given information to find the coefficient of determination. A regression equation is obtained for a collection of paired data. It is found that the total variation is 20.711, the explained variation is 18.592, and the Unexplained variation is 2.119.

A regression equation is obtained for a collection of paired data. It is found that the total variation is 20.711, the explained variation is 18.592, and the unexplained variation is 2.119. Find the coefficient of determination.

A regression equation is obtained for a set of data. After examining a scatter diagram, the researcher notices a data point that is potentially an influential point. How could she confirm that this data point is indeed an influential point?

Construct a scatterplot for the given data. - x -3 -2 -1 -4 -2 6 2 9 -5 -1 y -7 -3 -2 1 2 1 -5 2 -4 -4

The following residual plot is obtained after a regression equation is determined for a set of data. Does the residual plot suggest that the regression equation is a bad model? Why or why not?

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

$\mathrm { r } = 0.806 , \mathrm { n } = 9$