Question 1

Which of the following best describes the relationship of the least squares regression line: Estimated y = 2 - x? $\begin{array}{|l|l|}
\hline  A&\text {As $ x $ increases by 1 unit, y increases by 1 unit, estimated, on average. }\
\hline  B&\text { As $ \mathrm{x} $ increases by 1 unit $ \mathrm{y} $ decreases by $ (2-\mathrm{x}) $ units, estimated, on average}\
\hline  C&\text {As $ \mathrm{x} $ increases by 1 unit, y decreases by 1 unit, estimated, on average. }\
\hline  D&\text { All of these choices are correct.}\
\hline 
\end{array}$

Accepted Answer

C

Question 2

The regression line Estimated y = 3 + 2x has been fitted to the data points (4,8), (2,5), and (1,2). The sum of the squared residuals will be: $\begin{array}{|l|l|}
\hline\text { A. } & 7 . \
\hline \text { B. } & 15 \
\hline \text { C. } & 8 . \
\hline \text { D. } & 22 . \
\hline
\end{array}$

Accepted Answer

D

Question 3

Which of the following statements best describes correlation analysis in a simple linear regression? $\begin{array}{|l|l|}
\hline\text { A. } & \text {Correlation analysis measures the strength of a relationship between two  }\
& \text {numerical variables. }\
\hline \text { B. } & \text { Correlation analysis measures the strength and direction of a linear} \
& \text {elationship between two numerical variables. }\
\hline \text { C. } &\text {Correlation analysis measures the direction of a relationship between two  }\
& \text { numerical variables.}\
\hline \text { D. } &\text {Correlation analysis measures the strength of a relationship between }\
& \text {two categorical variables. }\
\hline
\end{array}$

Accepted Answer

B

Question 4

Given a specific value of x and confidence level, which of the following statements is correct? $\begin{array}{|l|l|}
\hline  A&\text {The confidence interval estimate of the expected value of $ y $ can be calculated but the }\
&\text {prediction interval of $ y $ for the given value of $ x $ cannot be calculated. }\
\hline  B&\text {The confidence interval estimate of the expected value of $ y $ will be wider than  }\
&\text { the prediction interval.}\
\hline  C&\text { The prediction interval of $ y $ for the given value of $ x $ can be calculated but the confidence}\
&\text {  interval estimate of the expected value of $ y $ cannot be calculated.}\
\hline  D&\text {The confidence interval estimate of the expected value of $ y $ will be narrower than }\
&\text {the prediction interval. }\
\hline 
\end{array}$

Accepted Answer

The answer of Given a specific value of x and...

Question 5

If an estimated regression line has a y-intercept of 10 and a slope of -5, then when x = 0, the estimated value of y is: $$\begin{array} { | l | l | } 
\hline \text { A. } & - 5 \
\hline \text { B. } & 0 \
\hline \text { C. } & 5 \
\hline \text { D. } & 10 \
\hline
\end{array}$$

Accepted Answer

The answer of If an estimated regression line has a...

Question 6

Given that the sum of squares for error is 50 and the sum of squares for regression is 140, the coefficient of determination is: $\begin{array}{|l|l|}
\hline\text { A. } & 0.736 . \
\hline \text { B. } & 0.357 . \
\hline \text { C. } & 0.263 . \
\hline \text { D. } & 2.800 . \
\hline
\end{array}$

Accepted Answer

The answer of Given that the sum of squares for...

Question 7

The Spearman rank correlation coefficient must be used to determine whether a relationship exists between two variables when: $\begin{array}{|l|l|}
\hline\text { A. } & \text { one of the variables may be ordinal.}\
\hline \text { B. } & \text { both of the variables may be ordinal.} \
\hline \text { C. } &\text { both variables are interval and the normality requirement may not be satisfied.}\
\hline \text { D. } &\text { All of these choices are correct.}\
\hline
\end{array}$

Accepted Answer

The answer of The Spearman rank correlation coefficient must be...

Question 8

The symbol for the population coefficient of correlation is: $\begin{array}{|l|l|}
\hline  A&r \
\hline  B&\rho\
\hline  C&r^2 \
\hline  D&\rho^2\
\hline 
\end{array}$

Accepted Answer

The answer of The symbol for the population coefficient of...

Question 9

If the coefficient of correlation is 0.80, the percentage of the variation in y that is explained by the variation in x is: $\begin{array}{|l|l|}
\hline\text { A. } & 80 \% \
\hline \text { B. } & 0.64 \% \
\hline \text { C. } & -80 \% \
\hline \text { D. } & 64 \% \
\hline
\end{array}$

Accepted Answer

The answer of If the coefficient of correlation is 0.80,...

Question 10

In regression analysis, if the coefficient of determination is 1.0, then: $\begin{array}{|l|l|}
\hline\text { A. } & \text { the sum of squares for error must be 1.0 .}\
\hline \text { B. } & \text { the sum of squares for regression must be 1.0. } \
\hline \text { C. } &\text { the sum of squares for error must be 0.0 .}\
\hline \text { D. } &\text {the sum of squares for regression must be 0.0 . }\
\hline
\end{array}$

Accepted Answer

The answer of In regression analysis, if the coefficient of...

Question 11

Given the least squares regression line y-hat = 3.52 - 1.27x, and a coefficient of determination of 0.81, the coefficient of correlation is: $\begin{array}{|l|l|}
\hline\text { A. } & -0.85 \
\hline \text { B. } & 0.85 \
\hline \text { C. } & -0.90 \
\hline \text { D. } & 0.90 \
\hline
\end{array}$

Accepted Answer

The answer of Given the least squares regression line y-hat...

Question 12

A regression line using 25 observations produced SSR = 118.68 and SSE = 56.32. The standard error of estimate was: $$\begin{array} { | l | l | } 
\hline \text { A. } & 2.1788 . \
\hline \text { B. } & 1.5648 . \
\hline \text { C. } & 1.5009 . \
\hline \text { D. } & 2.2716 . \
\hline
\end{array}$$

Accepted Answer

The answer of A regression line using 25 observations produced...

Question 13

Given that ss_x = 2500, ss_y = 3750, ss_xy = 500 and n = 6, the standard error of estimate is: $\begin{array}{|l|l|} \hline A&\text { 12.247}\ \hline B&\text {24.933 }\ \hline C&\text { 30.2076}\ \hline D&\text { 11.180}\ \hline \end{array}$

Accepted Answer

The answer of Given that ss_x = 2500, ss_y =...

Question 14

The following sums of squares are produced: $\Sigma$(y_i-(y-bar))² = 250, $\Sigma$(y_i-(y_i-hat))² = 100, $\Sigma$((y_i-hat)-(y-bar))² = 150 The percentage of the variation in y that is explained by the variation in x is: $\begin{array}{|l|l|} \hline\text { A. } & 60 \% \ \hline \text { B. } & 75 \% \ \hline \text { C. } & 40 \% \ \hline \text { D. } & 50 \% \ \hline \end{array}$

Accepted Answer

The answer of The following sums of squares are produced:...

Question 15

Which of the following best describes the value of the slope, if the coefficient of determination is 0.95? $\begin{array}{|l|l|}
\hline\text { A. } & \text { Slope must be 1 .}\
\hline \text { B. } & \text {Slope must be negative. } \
\hline \text { C. } &\text {Slope must be 0.95 . }\
\hline \text { D. } &\text {Slope must be positive. }\
\hline
\end{array}$

Accepted Answer

The answer of Which of the following best describes the...

Question 16

In simple linear regression, most often we perform a two-tail test of the population slope $$\beta _ { 1 }$$ to determine whether there is sufficient evidence to infer that a linear relationship exists. Which of the following best describes the null and alternative hypotheses needed for a test of significance? $\begin{array}{|l|l|}
\hline  A&H_{0}: \beta_{0}=0 \
&\mathrm{H}_{\mathrm{a}}: \beta_{0} \neq 0\
\hline  B&\mathrm{H}_{0}: \beta_{1} \neq 0\
&\mathrm{H}_{a}: \beta_{1}=0 \
\hline  C&\mathrm{H}_{0}: \beta_{0}=0 \
&\mathrm{H}_{\mathrm{a}}: \beta_{0} \neq 0\
\hline  D&\mathrm{Ho}: \beta_{1}=0\
&\mathrm{H}_{a}: \beta_{1} \neq 0 \
\hline 
\end{array}$

Accepted Answer

The answer of In simple linear regression, most often we...

Question 17

If the coefficient of correlation is −0.50, the percentage of the variation in the dependent variable y that is explained by the variation in the independent variable x is: $$\begin{array} { | l | l | } 
\hline \text { A. } & - 50 \% \
\hline \text { B. } & 25 \% . \
\hline \text { C. } & 50 \% \
\hline \text { D. } & - 25 \% . \
\hline
\end{array}$$

Accepted Answer

The answer of If the coefficient of correlation is −0.50,...

Question 18

In a simple linear regression, which of the following is equivalent to testing the significance of the population slope? $\begin{array}{|l|l|}
\hline  A&\text { Testing the signi ficance of the population intercept.}\
\hline  B&\text {Testing the significance of the mean. }\
\hline  C&\text { Testing the significance of the coefficient of correlation.}\
\hline  D&\text {All of these choices are correct. }\
\hline 
\end{array}$

Accepted Answer

The answer of In a simple linear regression, which of...

Question 19

The symbol for the sample coefficient of correlation is: $\begin{array}{|l|l|}
\hline  A&r\
\hline  B&\rho\
\hline  C&r^2\
\hline  D&\rho^2\
\hline 
\end{array}$

Accepted Answer

The answer of The symbol for the sample coefficient of...

Question 20

Which value of the coefficient of correlation r indicates a stronger correlation than − 0.85? $$\begin{array} { | c | c | } 
\hline \text { A. } & - 0.50 \
\hline \text { B. } & 0.75 \
\hline \text { C. } & - 0.90 \
\hline \text { D. } & 0.85 \
\hline
\end{array}$$

Accepted Answer

The answer of Which value of the coefficient of correlation...

Quiz 18: Simple Linear Regression and Correlation

The regression line Estimated y = 3 + 2x has been fitted to the data points (4,8), (2,5), and (1,2). The sum of the squared residuals will be: $\begin{array}{|l|l|}\hline\text { A. } & 7 . \\\hline \text { B. } & 15 \\\hline \text { C. } & 8 . \\\hline \text { D. } & 22 . \\\hline\end{array}$

If an estimated regression line has a y-intercept of 10 and a slope of -5, then when x = 0, the estimated value of y is: $\begin{array} { | l | l | } \hline \text { A. } & - 5 \\\hline \text { B. } & 0 \\\hline \text { C. } & 5 \\\hline \text { D. } & 10 \\\hline\end{array}$

Given that the sum of squares for error is 50 and the sum of squares for regression is 140, the coefficient of determination is: $\begin{array}{|l|l|}\hline\text { A. } & 0.736 . \\\hline \text { B. } & 0.357 . \\\hline \text { C. } & 0.263 . \\\hline \text { D. } & 2.800 . \\\hline\end{array}$

The symbol for the population coefficient of correlation is: $\begin{array}{|l|l|}\hline A&r \\\hline B&\rho\\\hline C&r^2 \\\hline D&\rho^2\\\hline \end{array}$

If the coefficient of correlation is 0.80, the percentage of the variation in y that is explained by the variation in x is: $\begin{array}{|l|l|}\hline\text { A. } & 80 \% \\\hline \text { B. } & 0.64 \% \\\hline \text { C. } & -80 \% \\\hline \text { D. } & 64 \% \\\hline\end{array}$

Given the least squares regression line y-hat = 3.52 - 1.27x, and a coefficient of determination of 0.81, the coefficient of correlation is: $\begin{array}{|l|l|}\hline\text { A. } & -0.85 \\\hline \text { B. } & 0.85 \\\hline \text { C. } & -0.90 \\\hline \text { D. } & 0.90 \\\hline\end{array}$

A regression line using 25 observations produced SSR = 118.68 and SSE = 56.32. The standard error of estimate was: $\begin{array} { | l | l | } \hline \text { A. } & 2.1788 . \\\hline \text { B. } & 1.5648 . \\\hline \text { C. } & 1.5009 . \\\hline \text { D. } & 2.2716 . \\\hline\end{array}$

Given that ss_x = 2500, ss_y = 3750, ss_xy = 500 and n = 6, the standard error of estimate is: $\begin{array}{|l|l|}\hline A&\text { 12.247}\\\hline B&\text {24.933 }\\\hline C&\text { 30.2076}\\\hline D&\text { 11.180}\\\hline \end{array}$

The symbol for the sample coefficient of correlation is: $\begin{array}{|l|l|}\hline A&r\\\hline B&\rho\\\hline C&r^2\\\hline D&\rho^2\\\hline \end{array}$

Which value of the coefficient of correlation r indicates a stronger correlation than − 0.85? $\begin{array} { | c | c | } \hline \text { A. } & - 0.50 \\\hline \text { B. } & 0.75 \\\hline \text { C. } & - 0.90 \\\hline \text { D. } & 0.85 \\\hline\end{array}$

Quiz 18: Simple Linear Regression and Correlation

The symbol for the population coefficient of correlation is: ArBρCr2Dρ2\begin{array}{|l|l|}\hline A&r \\\hline B&\rho\\\hline C&r^2 \\\hline D&\rho^2\\\hline \end{array}ABCD​rρr2ρ2​​

The symbol for the sample coefficient of correlation is: ArBρCr2Dρ2\begin{array}{|l|l|}\hline A&r\\\hline B&\rho\\\hline C&r^2\\\hline D&\rho^2\\\hline \end{array}ABCD​rρr2ρ2​​

The symbol for the population coefficient of correlation is: $\begin{array}{|l|l|}\hline A&r \\\hline B&\rho\\\hline C&r^2 \\\hline D&\rho^2\\\hline \end{array}$

The symbol for the sample coefficient of correlation is: $\begin{array}{|l|l|}\hline A&r\\\hline B&\rho\\\hline C&r^2\\\hline D&\rho^2\\\hline \end{array}$