Question 1

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

Accepted Answer

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

Question 2

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 $\alpha$. $n = 14 , \alpha = 0.01$

Accepted Answer

A)  $r = 0.661$ 
B)  $r = 0.684$ 
C)  $r = \pm 0.532$ 
D)  $r = \pm 0.661$ 
A)  $r = 0.661$ 
B)  $r = 0.684$ 
C)  $r = \pm 0.532$ 
D)  $r = \pm 0.661$

Question 3

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

Accepted Answer

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

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 $r = \pm 0.590$ what can you conclude?

Accepted Answer

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

Question 5

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
$R ^ { 2 } = 1 - \frac { ( y - \hat { y } ) ^ { 2 } } { ( y - \bar { y } ) ^ { 2 } } .$

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

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 9

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

Accepted Answer

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

Question 10

Use computer software to find the best multiple regression equation to explain the variation in the dependent variable, Y, in terms of the independent variables, $X _ { 1 } , X _ { 2 } , X _ { 3 }$\(\begin{array} { c c c c l } Y & X _ { 1 } & X _ { 2 } & X _ { 3 } & \ 456 & 9896 & 29.1 & 1 & \ 421 & 9680 & 42.3 & 2 & \ 653 & 10449 & 29.8 & 3 & \ 573 & 10811 & 26.0 & 4 & \text { CORRELATION COEFFICIENTS } \ 546 & 10014 & 34.3 & 5 & \ 499 & 10293 & 22.7 & 6 & Y / X _ { 1 } = 0.509 \ 504 & 9413 & 24.2 & 7 & Y / X _ { 2 } = 0.280 \ 611 & 9860 & 31.6 & 8 & Y / X _ { 3 } = 0.930 \ 646 & 9782 & 25.6 & 9 & \ 789 & 12139 & 37.9 & 10 & \text { COEFFICIENTS OF DETERMINATION } \ 773 & 12166 & 33.9 & 11 & \ 753 & 9976 & 37.4 & 12 & \text { YI } X _ { 1 } = 0.259 \ 852 & 10645 & 27.0 & 13 & Y / X _ { 2 } = 0.079 \ 755 & 9738 & 31.5 & 14 & Y / X _ { 3 } = 0.864 \ 815 & 9933 & 39.9 & 15 & Y / X _ { 1 } , X _ { 3 } = 0.880 \ 902 & 10132 & 25.3 & 16 & Y / X _ { 1 } , X _ { 2 } , X _ { 3 } = 0.884 \ 986 & 11145 & 30.4 & 17 & \ 909 & 9775 & 32.7 & 18 & \ 945 & 9549 & 35.0 & 19 & \ 866 & 10077 & 33.8 & 20 & \ 1178 & 11550 & 29.4 & 21 & \ 1230 & 10600 & 37.1 & 22 & \ 1207 & 11280 & 42.9 & 23 & \ 968 & 12100 & 32.2 & 24 & \ 1118 & 12420 & 30.5 & 25 & \end{array}\)

Accepted Answer

A)  $\hat { Y } = 57.8 + 0.036 X _ { 1 } + 28.1 X _ { 3 }$ 
B)  $\hat { Y } = - 21.1 + 0.36 X _ { 1 } + 2.62 X _ { 2 } + 27.6 X _ { 3 }$ 
C)  $\hat { Y } = 201.7 + 0.40 X _ { 1 } + 22.3 X _ { 3 }$ 
D)  $\hat { Y } = 308.6 + 29.9 X _ { 3 }$ 
A)  $\hat { Y } = 57.8 + 0.036 X _ { 1 } + 28.1 X _ { 3 }$ 
B)  $\hat { Y } = - 21.1 + 0.36 X _ { 1 } + 2.62 X _ { 2 } + 27.6 X _ { 3 }$ 
C)  $\hat { Y } = 201.7 + 0.40 X _ { 1 } + 22.3 X _ { 3 }$ 
D)  $\hat { Y } = 308.6 + 29.9 X _ { 3 }$

Question 11

Sketch a sample scatterplot of at least 5 points that would have a linear correlation coefficient
equal to −1.

Accepted Answer

Answers wi

Question 12

The results for several randomly selected students for test 1 and test 2 grades are given
below. $\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline \text { Test 1 } & 59 & 63 & 65 & 69 & 58 & 77 & 76 & 69 & 70 & 64 \
\hline \text { Test 2 } & 72 & 67 & 78 & 82 & 75 & 87 & 92 & 83 & 87 & 78 \
\hline
\end{array}$

Is there sufficient evidence to suggest that there is a linear correlation between test 1 and test 2 grades? Construct a scatterplot, and find the value of the linear correlation coefficient $r$. Also, find the $P$-value or the critical value(s) of $r$ using $\alpha = 0.05$.

Accepted Answer

There is sufficient evidence t

Question 13

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

Question 14

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

Accepted Answer

Scatterplots are graphs in which paired

Question 15

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

Accepted Answer

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

Question 16

The residual is the difference between the ____________________ and the ___________________.

Accepted Answer

A)  predicted value of y; observed value of y 
B)  observed value of y; predicted value of y 
C)  predicted value of x; observed value of x 
D)  observed value of x; predicted value of y 
A)  predicted value of y; observed value of y 
B)  observed value of y; predicted value of y 
C)  predicted value of x; observed value of x 
D)  observed value of x; predicted value of y

Question 17

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 18

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

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

Provide an appropriate response. 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 line.
$\begin{array}{rrrrrr}
x & 1.2 & 2.7 & 4.4 & 6.6 & 9.5 \
\hline y & 1.6 & 4.7 & 8.9 & 9.5 & 12.0
\end{array}$

Accepted Answer

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

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

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 $\alpha$ . $n = 14 , \alpha = 0.01$

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

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 $r = \pm 0.590$ what can you conclude?

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 $R ^ { 2 } = 1 - \frac { ( y - \hat { y } ) ^ { 2 } } { ( y - \bar { y } ) ^ { 2 } } .$

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

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 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?

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

Sketch a sample scatterplot of at least 5 points that would have a linear correlation coefficient equal to −1.

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.

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

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

The residual is the difference between the __ and the _.

For the data below, determine the value of the linear correlation coefficient $r$ between $y$ and $x ^ { 2 }$ . 1.2 2.7 4.4 6.6 9.5 1.6 4.7 9.9 24.5 39.0

Find the unexplained variation for the paired data. The equation of the regression line for the paired data below is $y = 3 x$ . x 2 4 5 6 y 7 11 13 20

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

Chi-Square and Analysis of Variance

Control Charts and Process Monitoring

Filters

Exam 10: Correlation and Regression

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

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

A 0.010.010.01 significance level is being used to test a correlation between two variables. If the linear correlation coefficient rrr is found to be 0.5910.5910.591 and the critical values are r=±0.590r = \pm 0.590r=±0.590 what can you conclude?

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

Find the value of the linear correlation coefficient rrr . 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 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?

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

Sketch a sample scatterplot of at least 5 points that would have a linear correlation coefficient equal to −1.

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.

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

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

The residual is the difference between the ____________________ and the ___________________.

For the data below, determine the value of the linear correlation coefficient rrr between yyy and x2x ^ { 2 }x2 . 1.2 2.7 4.4 6.6 9.5 1.6 4.7 9.9 24.5 39.0

Find the unexplained variation for the paired data. The equation of the regression line for the paired data below is y=3xy = 3 xy=3x . x 2 4 5 6 y 7 11 13 20

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

Chi-Square and Analysis of Variance

Control Charts and Process Monitoring

Filters

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 $r = \pm 0.590$ what can you conclude?

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

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

The residual is the difference between the __ and the _.

For the data below, determine the value of the linear correlation coefficient $r$ between $y$ and $x ^ { 2 }$ . 1.2 2.7 4.4 6.6 9.5 1.6 4.7 9.9 24.5 39.0

Find the unexplained variation for the paired data. The equation of the regression line for the paired data below is $y = 3 x$ . x 2 4 5 6 y 7 11 13 20