Question 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.

Accepted Answer

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

Question 2

The following table gives the US domestic oil production rates (excluding Alaska)from 1987
to 2002. A regression equation was fit to the data and the residual plot is shown below. $\begin{array}{c|c}
\text { Year } & \text { Millions of Barrels per Day } \
\hline 1987 & 6.39 \
1988 & 6.12 \
1989 & 5.74 \
1990 & 5.58 \
1991 & 5.62 \
1992 & 5.46 \
1993 & 5.26 \
1994 & 5.10
\end{array}$

$\begin{array}{c|c}
\text { Year } & \text { Millions of Barrels per Day } \
\hline 1995 & 5.08 \
1996 & 5.07 \
1997 & 5.16 \
1998 & 5.08 \
1999 & 4.83 \
2000 & 4.85 \
2001 & 4.84 \
2002 & 4.83
\end{array}$

$\text { Does the residual plot suggest that the regression equation is a bad model? Why or why not? }$

Accepted Answer

The answer of The following table gives the US domestic...

Question 3

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 value(s)of r given that $n = 10$ and $\alpha = 0.05$.

Accepted Answer

A)  $r = \pm 0.765$ 
B)  $r = \pm 0.632$ 
C)  $r = \pm 0.666$ 
D)  $r = 0.632$

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)   0.943,0.934,0.000 
C)   0.861,0.900,0.015 
D)   0.976,0.921,0.002

Question 5

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

Accepted Answer

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

Question 6

The table lists the value y (in dollars)of $100 deposited in a certificate of deposit (CD)at a
bank after y years. $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline \text { Year } & 1 & 2 & 3 & 4 & 5 & 20 \
\hline \text { Value } & 103 & 106.09 & 109.27 & 112.55 & 115.93 & 180.61 \
\hline
\end{array}$$ Construct a scatterplot and identify the mathematical model that best fits the given data.
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.

Accepted Answer

The answer of The table lists the value y (in...

Question 7

Determine which plot shows the strongest linear correlation._

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 8

Find the explained variation for the paired data. The equation of the regression line for the paired data below is $\hat { y } = 6.18286 + 4.33937 x$
$\begin{array} { r | r r r r r r r } 
\boldsymbol { x } & 9 & 7 & 2 & 3 & 4 & 22 & 17 \
\hline \boldsymbol { y } & 43 & 35 & 16 & 21 & 23 & 102 & 81
\end{array}$

Accepted Answer

A)   13.479 
B)   6,531.37 
C)   6,544.86 
D)   6,421.83

Question 9

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=12 , $\alpha _ { \mathrm { n } } = 0,01$

Accepted Answer

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

Question 10

The results for several randomly selected students for test 1 and test 2 grades are given
below. $$\begin{array} { | l | l | l | l | l | l | l | l | l | l | l | } 
\hline \text { Test 1 } & 59 & 63 & 65 & 69 & 58 & 77 & 76 & 69 & 70 & 64 \
\hline \text { Test 2 } & 72 & 67 & 78 & 82 & 75 & 87 & 92 & 83 & 87 & 78 \
\hline
\end{array}$$ 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 α
 = 0.05.

Accepted Answer

The answer of The results for several randomly selected students...

Question 11

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

Question 12

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)  $0.246$

Question 13

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. $\begin{array}{l|l|l|l|l|l|l|l|l|l|l}
\text { Productivity }(x) & 23 & 25 & 28 & 21 & 21 & 25 & 26 & 30 & 34 & 36 \
\hline \text { Dexterity (y) } & 49 & 53 & 59 & 42 & 47 & 53 & 55 & 63 & 67 & 75
\end{array}$

Accepted Answer

A)  $\hat { y } = 2.36 + 2.03 x$ 
B)  $\hat { y } = 10.7 + 1.53 x$ 
C)  $\hat { y } = 75.3 - 0329 x$ 
D)  $\hat { y } = 5.05 + 1.91 x$

Question 14

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

Question 15

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

Accepted Answer

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

Question 16

The table below lists weights (carats)and prices (dollars)for randomly selected diamonds.
Find the regression equation, letting the weight be the predictor variable. Find the best
predicted price for a diamond with a weight of 1.50 carats. What is wrong with predicting the
price of a 1.50-carat diamond? $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline \text { Weight } & 0.3 & 0.4 & 0.5 & 0.5 & 1.0 & 0.7 \
\hline \text { Price } & 510 & 1151 & 1343 & 1410 & 5669 & 2277 \
\hline
\end{array}$$

Accepted Answer

The answer of The table below lists weights (carats)and prices...

Question 17

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

Accepted Answer

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

Question 18

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

Question 19

Provide an appropriate response. For the data below, determine the logarithmic equation, ya=+b lnx 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. $\begin{array}{rrrrrr}
x & 1.2 & 2.7 & 4.4 & 6.6 & 9.5 \
\hline y & 1.6 & 4.7 & 8.9 & 9.5 & 12.0
\end{array}$

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

Accepted Answer

The answer of Provide an appropriate response. For the data...

Question 20

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 answer of For each of 200 randomly selected cities,...

Exam 10: Correlation and Regression

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.

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 value(s) of r given that $n = 10$ and $\alpha = 0.05$ .

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

Determine which plot shows the strongest linear correlation._

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=12 , $\alpha _ { \mathrm { n } } = 0,01$

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

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

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

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

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

Exam 10: Correlation and Regression

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.

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 value(s) of r given that n=10n = 10n=10 and α=0.05\alpha = 0.05α=0.05 .

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

Determine which plot shows the strongest linear correlation._

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

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

Use the given data to find the equation of the regression line. Round the final values to three_ significant digits, if necessary. x13579y1431161009890\begin{array}{l|lllll}x & 1 & 3 & 5 & 7 & 9 \\\hline y & 143 & 116 & 100 & 98 & 90\end{array}xy​1143​3116​5100​798​990​​

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. x68202836y24132030\begin{array}{l|lllll}x & 6 & 8 & 20 & 28 & 36 \\\hline y & 2 & 4 & 13 & 20 & 30\end{array}xy​62​84​2013​2820​3630​​

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 value(s) of r given that $n = 10$ and $\alpha = 0.05$ .

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

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