Question 1

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 B

Question 2

Given the linear correlation coefficient r and the sample size n, determine the critical values of r_ and use your finding to state whether or not the given r represents a significant linear
Correlation. Use a significance level of 0.05. $$r = 0.543 , n = 25$$

Accepted Answer

A)  Critical values: $r = \pm 0.487$, no significant linear correlation 
B)  Critical values: $r = \pm 0.396$, no significant linear correlation 
C)  Critical values: $r = \pm 0.487$, significant linear correlation 
D)  Critical values: $r = \pm 0.396$, significant linear correlation 
A)  Critical values: $r = \pm 0.487$, no significant linear correlation 
B)  Critical values: $r = \pm 0.396$, no significant linear correlation 
C)  Critical values: $r = \pm 0.487$, significant linear correlation 
D)  Critical values: $r = \pm 0.396$, significant linear correlation D

Question 3

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

Accepted Answer

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

Question 4

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

Question 5

For the data below, determine the value of the linear correlation coefficient r between y and X₂. $\begin{array}{r|rrrrr}
x & 1.2 & 2.7 & 4.4 & 6.6 & 9.5 \
\hline y & 1.6 & 4.7 & 9.9 & 24.5 & 39.0
\end{array}$

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 6

Construct a scatterplot for the given data._ \begin{tabular} { c | l l l l l l l c } 
$x$ & $0.33$ & $0.92$ & $0.36$ & $0.29$ & $- 0.09$ & $0.97$ & $0.39$ & $0.3$ \
\hline$y$ & $0.5$ & $0.49$ & $0.08$ & $0.27$ & $- 0.13$ & $0.44$ & $0.95$ & $- 0.09$
\end{tabular}

Accepted Answer

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

Question 7

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 8

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 9

Use computer software to find the multiple regression equation. Can the equation be used for_ prediction? A wildlife analyst gathered the data in the table to develop an equation to predict
The weights of bears. He used WEIGHT as the dependent variable and CHEST, LENGTH,
And SEX as the independent variables. For SEX, he used male=1 and female=2. $\begin{array}{cccc}
\hline \text { WEIGHT } & \text { CHEST } & \text { LENGTH } & \text { SEX } \
\hline 344 & 45.0 & 67.5 & 1 \
416 & 54.0 & 72.0 & 1 \
220 & 41.0 & 70.0 & 2 \
360 & 49.0 & 68.5 & 1 \
332 & 44.0 & 73.0 & 1 \
140 & 32.0 & 63.0 & 2 \
436 & 48.0 & 72.0 & 1 \
132 & 33.0 & 61.0 & 2 \
356 & 48.0 & 64.0 & 2 \
150 & 35.0 & 59.0 & 1 \
202 & 40.0 & 63.0 & 2 \
365 & 50.0 & 70.5 & 1 \
\hline
\end{array}$

A) WEIGHT $= 196 + 2.35$ CHEST $+ 3.40 \mathrm { LENGTH } + 25 \mathrm { SEX }$; Yes, because the $R ^ { 2 }$ is high.
B) WEIGHT $= - 320 + 10.6 \mathrm { CHEST } + 7.3 \mathrm { LENGTH } - 10.7 \mathrm { SEX }$; Yes, because the $P$-value is high. C) WEIGHT $= - 442.6 + 12.1$ CHEST + 3.6LENGTH $- 23.8$ SEX; Yes, because the adjusted $R ^ { 2 }$ is high.
D) WEIGHT $= 442.6 + 12$.1CHEST $+ 4.2$ LENGTH $- 21$ SEX; Yes, because the $P$-value is low.

Accepted Answer

The answer of Use computer software to find the multiple...

Question 10

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

Yes, the residual plot suggests that the

Question 11

When testing to determine if correlation is significant, we use the hypotheses $H _ { 0 } : \rho = 0$ $H _ { 1 } : \rho \neq 0$ What does the symbol $\rho$ represent? Explain the meaning of the null and altemative hypotheses.

Accepted Answer

The symbol ρ represents the population c

Question 12

Define the terms predictor variable and response variable. Give examples for each._

Accepted Answer

The predictor variable is x, representin

Question 13

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

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 14

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 15

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

Accepted Answer

Scatterplots are graphs in which paired

Question 16

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, $X _ { 1 } , X _ { 2 } , X _ { 3 }$
$\begin{array} { c c c c c } 
Y & X _ { 1 } & X _ { 2 } & \
15 & 1.2 & 16 & \
15 & 1.2 & 16 & \text { CORRELATION COEFFICIENT } \
17 & 1.0 & 16 & Y / X _ { 1 } = 0.886 \
6 & 0.8 & 9 & Y / X _ { 2 } = 0.965 \
1 & 0.1 & 1 & \
8 & 0.8 & 8 & \
10 & 0.8 & 10 & \text { COEFFICIENTS OF DETERMINATION } \
17 & 1.0 & 16 & \
15 & 1.2 & 15 & \
11 & 0.7 & 9 & \
18 & 1.4 & 18 & \
16 & 1.0 & 15 & X _ { 2 } = 0.932 \
10 & 0.8 & 9 & X _ { 1 } = 0.943 \
7 & 0.5 & 5 & \
18 & 1.1 & 16 &
\end{array}$

Accepted Answer

A)  $\hat { Y } = 0.42 + 0.99 X _ { 2 }$ 
B)  $\hat { Y } = 1.38 - 5.53 X _ { 1 } + 1.33 X _ { 2 }$ 
C)  $\hat { Y } = 1.25 - 1.55 X _ { 1 } + 5.79 X _ { 2 }$ 
D)  $\hat { Y } = - 0.49 + 14.07 X _ { 1 }$ 
A)  $\hat { Y } = 0.42 + 0.99 X _ { 2 }$ 
B)  $\hat { Y } = 1.38 - 5.53 X _ { 1 } + 1.33 X _ { 2 }$ 
C)  $\hat { Y } = 1.25 - 1.55 X _ { 1 } + 5.79 X _ { 2 }$ 
D)  $\hat { Y } = - 0.49 + 14.07 X _ { 1 }$

Question 17

Given the linear correlation coefficient r and the sample size n, determine the critical values of_ r and use your finding to state whether or not the given r represents a significant linear
Correlation. Use a significance level of 0.05. $$r = - 0.816 , n = 5$$

Accepted Answer

A)  Critical values: $r = \pm 0.878$, significant linear correlation 
B)  Critical values: $r = \pm 0.878$, no significant linear correlation 
C)  Critical values: $r = 0.950$, significant linear correlation 
D)  Critical values: $r = \pm 0.950$, no significant linear correlation 
A)  Critical values: $r = \pm 0.878$, significant linear correlation 
B)  Critical values: $r = \pm 0.878$, no significant linear correlation 
C)  Critical values: $r = 0.950$, significant linear correlation 
D)  Critical values: $r = \pm 0.950$, no significant linear correlation

Question 18

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, $$X _ { 1 } , X _ { 2 } , X _ { 3 }$$ $\begin{array} { c c c c } Y & X _ { 1 } & X _ { 2 } & \ 98.6 & 87.4 & 108.5 & \ 101.2 & 97.6 & 110.1 & \ 102.4 & 96.7 & 110.4 & \text { CORRELATION COEFFICIENTS } \ 100.9 & 98.2 & 104.3 & \ 102.3 & 99.8 & 107.2 & Y / X _ { 1 } = 0.850 \ 101.5 & 100.5 & 105.8 & Y X _ { 2 } = 0.742 \ 101.6 & 103.2 & 107.8 & \ 101.6 & 107.8 & 103.4 & \ 99.8 & 96.6 & 102.7 & \text { COEFFICIENT OF DETERMINATION } \ 100.3 & 88.9 & 104.1 & \ 97.6 & 75.1 & 99.2 & \ 97.2 & 76.9 & 99.7 & \ 97.3 & 84.6 & 102.0 & \ 96.0 & 90.6 & 94.3 & \ 99.2 & 103.1 & 97.7 & \ 100.3 & 105.1 & 101.1 & \ 100.3 & 96.4 & 102.3 & \ 104.1 & 104.4 & 104.4 & \ 105.3 & 110.7 & 108.5 & \ 107.6 & 127.1 & 111.3 & \end{array}$

Accepted Answer

A)  $\hat { Y } = 57.6 + 0.153 X _ { 1 } + 0.270 X _ { 2 }$ 
B)  $\hat { Y } = 58.9 + 0.612 X _ { 1 }$ 
C)  $\hat { Y } = 52.6 + 0.462 X _ { 2 }$ 
D)  $\hat { Y } = 48.0 + 0.398 X _ { 1 } + 0.228 X _ { 2 }$ 
A)  $\hat { Y } = 57.6 + 0.153 X _ { 1 } + 0.270 X _ { 2 }$ 
B)  $\hat { Y } = 58.9 + 0.612 X _ { 1 }$ 
C)  $\hat { Y } = 52.6 + 0.462 X _ { 2 }$ 
D)  $\hat { Y } = 48.0 + 0.398 X _ { 1 } + 0.228 X _ { 2 }$

Question 19

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 20

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

Accepted Answer

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

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

Given the linear correlation coefficient r and the sample size n, determine the critical values of r_ and use your finding to state whether or not the given r represents a significant linear Correlation. Use a significance level of 0.05. $r = 0.543 , n = 25$

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

For the data below, determine the value of the linear correlation coefficient r between y and X₂. x 1.2 2.7 4.4 6.6 9.5 y 1.6 4.7 9.9 24.5 39.0

Construct a scatterplot for the given data._ \begin{tabular} { c | l l l l l l l c } $x$ & $0.33$ & $0.92$ & $0.36$ & $0.29$ & $- 0.09$ & $0.97$ & $0.39$ & $0.3$ \\ \hline $y$ & $0.5$ & $0.49$ & $0.08$ & $0.27$ & $- 0.13$ & $0.44$ & $0.95$ & $- 0.09$ \end{tabular}

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?

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

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?

When testing to determine if correlation is significant, we use the hypotheses $H _ { 0 } : \rho = 0$ $H _ { 1 } : \rho \neq 0$ What does the symbol $\rho$ represent? Explain the meaning of the null and altemative hypotheses.

Define the terms predictor variable and response variable. Give examples for each._

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

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

Given the linear correlation coefficient r and the sample size n, determine the critical values of_ r and use your finding to state whether or not the given r represents a significant linear Correlation. Use a significance level of 0.05. $r = - 0.816 , n = 5$

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

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

Statistical Control Charts, Nonparametric Tests, and Hypothesis Testing

Filters

Exam 10: Correlation and Regression

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

Given the linear correlation coefficient r and the sample size n, determine the critical values of r_ and use your finding to state whether or not the given r represents a significant linear Correlation. Use a significance level of 0.05. r=0.543,n=25r = 0.543 , n = 25r=0.543,n=25

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

For the data below, determine the value of the linear correlation coefficient r between y and X₂. x 1.2 2.7 4.4 6.6 9.5 y 1.6 4.7 9.9 24.5 39.0

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?

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 α\alphaα n=14,α=0.01n = 14 , \alpha = 0.01n=14,α=0.01

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?

When testing to determine if correlation is significant, we use the hypotheses H0:ρ=0H _ { 0 } : \rho = 0H0​:ρ=0 H1:ρ≠0H _ { 1 } : \rho \neq 0H1​:ρ=0 What does the symbol ρ\rhoρ represent? Explain the meaning of the null and altemative hypotheses.

Define the terms predictor variable and response variable. Give examples for each._

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

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

Given the linear correlation coefficient r and the sample size n, determine the critical values of_ r and use your finding to state whether or not the given r represents a significant linear Correlation. Use a significance level of 0.05. r=−0.816,n=5r = - 0.816 , n = 5r=−0.816,n=5

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

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

Statistical Control Charts, Nonparametric Tests, and Hypothesis Testing

Filters

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

Given the linear correlation coefficient r and the sample size n, determine the critical values of r_ and use your finding to state whether or not the given r represents a significant linear Correlation. Use a significance level of 0.05. $r = 0.543 , n = 25$

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

When testing to determine if correlation is significant, we use the hypotheses $H _ { 0 } : \rho = 0$ $H _ { 1 } : \rho \neq 0$ What does the symbol $\rho$ represent? Explain the meaning of the null and altemative hypotheses.

Given the linear correlation coefficient r and the sample size n, determine the critical values of_ r and use your finding to state whether or not the given r represents a significant linear Correlation. Use a significance level of 0.05. $r = - 0.816 , n = 5$