Question 1

Two different tests are designed to measure employee productivity and dexterity. Several employees are randomly selected and tested with these results.

$\begin{array}{cc|c|c|c|c|c|c|c|c|c}
\text { Productivity } & 23 & 25 & 28 & 21 & 21 & 25 & 26 & 30 & 34 & 36 \
\hline\text { Dexterity } & 49 & 53 & 59 & 42 & 47 & 53 & 55 & 63 & 67 & 75
\end{array}$
A) $\hat { y } = 75.3 - 0.329 x$
B) $\hat { y }= 5.05 + 1.91 x$
C) $\hat { y } = 2.36 + 2.03 x$
D) $\hat { y } = 10.7 + 1.53 \mathrm { x }$

Accepted Answer

The answer of Two different tests are designed to measure...

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.
-$r = - 0.853 , n = 5$

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

Accepted Answer

The critical values are $\pm 0.878$. Since the given r (-0.853) is within these critical values, it does not represent a significant linear correlation.

Question 3

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.
-$\mathrm { r } = 0.71 , \mathrm { n } = 25$
A) Critical values: $r = \pm 0.396$, significant linear correlation
B) Critical values: $\mathrm { r } = \pm 0.487$, no significant linear correlation
C) Critical values: $\mathrm { r } = \pm 0.487$, significant linear correlation
D) Critical values: $r = \pm 0.396$, no significant linear correlation

Accepted Answer

The critical values of r for a sample size of 25 and a significance level of 0.05 are $\pm 0.396$. Since the given r value of 0.71 is greater than the critical value of 0.396, it represents a significant linear correlation.

Question 4

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.

$\begin{array}{c|ccccc}
\mathrm{x} & 1.2 & 2.7 & 4.4 & 6.6 & 9.5 \
\hline \mathrm{y} & 1.6 & 4.7 & 8.9 & 9.5 & 12.0
\end{array}$

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

Accepted Answer

After replacing each $x$-value with $\ln x$, the least squares regression line is calculated, resulting in the equation $\hat { y } = 0.457 + 5.06 \ln x$.

Question 5

Nine pairs of data yield $\mathrm { r } = 0.867$ and the regression equation $\hat { y } = 19.4 + 0.93 \mathrm { x }$. Also, $\overline { \mathrm { y } } = 64.7$. What is the best predicted value of $y$ for $x = 48$ ?
A) 79.6
B) 64.7
C) 57.8
D) 64

Accepted Answer

The answer of Nine pairs of data yield \(\mathrm {...

Question 6

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 $\alpha$ .
-$\mathrm { n } = 6 , \alpha = 0.01$

A) $r = \pm 0.917$
B) $r = 0.959$
C) $r = \pm 0.811$
D) $\mathrm { r } = 0.917$

Accepted Answer

The answer of Suppose you will perform a test to...

Question 7

Use the given data to find the best predicted value of the response variable.
-Ten pairs of data yield $r = 0.003$ and the regression equation $\hat { y } = 2 + 3 x$. Also, $\bar { y } = 5.0$. What is the best predicted value of $\mathrm { y }$ for $\mathrm { x } = 2$ ?
A) 8.0
B) 7.0
C) 17.0
D) 5.0

Accepted Answer

Since the correlation coefficient $r$ is close to 0, the best predicted value is the mean of $y$, which is $\bar{y} = 5.0$.

Question 8

Find the value of the linear correlation coefficient r.
-$\begin{array}{r|rrrrr}
\mathrm{x} & 19.3 & 23.4 & 10.3 & 17.7 & 23.2 \
\hline \mathrm{y} & 6 & 2 & 3 & 3 & 3
\end{array}$
A) 0
B) $- 0.094$
C) $0.094$
D) $- 0.084$

Accepted Answer

The answer of Find the value of the linear correlation...

Question 9

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.
-$\begin{array}{r|rrrr}
x & 2 & 4 & 5 & 6 \
\hline y & 7 & 11 & 13 & 20
\end{array}$

A) $\hat{y} = 0.15 + 3.0 x$
B) $\hat { y } = 0.15 + 2.8 x$
C) $\hat { y } = 3.0 x$
D) $\hat { y } = 2.8 x$

Accepted Answer

The answer of Use the given data to find the...

Question 10

Find the value of the linear correlation coefficient r.
-$\begin{array}{r|rrrrrrr}
\mathrm{x} & 62 & 53 & 64 & 52 & 52 & 54 & 58 \
\hline \mathrm{y} & 158 & 176 & 151 & 164 & 164 & 174 & 162
\end{array}$
A) $- 0.775$
B)$0.754$
C) 0
D) $- 0.081$

Accepted Answer

The answer of Find the value of the linear correlation...

Question 11

Use the given data to find the best predicted value of the response variable.
-Based on the data from six students, the regression equation relating number of hours of preparation $( \mathrm { x } )$ and test score $( \mathrm { y } )$ is $\hat { \mathrm { y } } = 67.3 + 1.07 \mathrm { x }$. The same data yield $\mathrm { r } = 0.224$ and $\overline { \mathrm { y } } = 75.2$. What is the best predicted test score for a student who spent 5 hours preparing for the test?
A) 72.7
B) 78.1
C) 59.7
D) 75.2

Accepted Answer

The answer of Use the given data to find the...

Question 12

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

A) $\hat { y } = 150.7 - 6.8 x$
B) $\hat { y } = - 150.7 + 6.8 x$
C) $\hat { y } = - 140.4 + 6.2 x$
D) $\hat { y } = 140.4 - 6.2 x$

Accepted Answer

The answer of Use the given data to find the...

Question 13

A rank correlation coefficient is to be calculated for a collection of paired data. The values lie between -10 and 10. Which of the following could affect the value of the rank correlation coefficient?

I: Multiplying every value of one variable by 3
II: Interchanging the two variables
III: Adding 2 to each value of one variable
IV: Replacing every value of one variable by its absolute value

A) III
B) I
C) IV
D) I and IV

Accepted Answer

Replacing every value of one variable by its absolute value (IV) can affect the rank correlation coefficient because it changes the order of the data, which is crucial for rank correlation.

Question 14

Construct a scatterplot for the given data
-$\begin{array}{r|r|r|r|r|r|r}
\mathrm{x} & 15 & -14 & -18 & 9 & -20 & -11 \
\hline \mathrm{y} & -96 & 25 & 45 & -42 & 92 & 5
\end{array}$

A)

B)

C)

D)

Accepted Answer

The answer of Construct a scatterplot for the given data
-\(\begin{array}{r|r|r|r|r|r|r}
\mathrm{x}...

Question 15

Is the data point, P, an outlier, an influential point, both, or neither?
-
A) Outlier
B) Influential point
C) Both
D) Neither

Accepted Answer

The answer of Is the data point, P, an outlier,...

Question 16

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

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

Accepted Answer

The correct answer is A because the equation of the regression line is $\hat{y} = - 3.79 + 0.897 x$.

Question 17

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): $$\begin{array} { c | r r r r r r r r } 
\text { Cost } & 9 & 2 & 3 & 4 & 2 & 5 & 9 & 10 \
\hline \text { Number } & 85 & 52 & 55 & 68 & 67 & 86 & 83 & 73
\end{array}$$
A) 0.235
B) 0.708
C) - 0.071
D) 0.246

Accepted Answer

The linear correlation coefficient r measures the strength and direction of a linear relationship between two variables. Calculating r for the given data results in approximately 0.708, indicating a moderate positive correlation.

Question 18

When performing a rank correlation test, one alternative to using the Critical Values of Spearman's Rank Correlation Coefficient table to find critical values is to compute them using this approximation:
$$r _ { S } = \pm \sqrt { \frac { t ^ { 2 } } { t ^ { 2 } + n - 2 } }$$
where $\mathrm { t }$ is the $\mathrm { t }$-score from the $t$ Distribution table corresponding to $\mathrm { n } - 2$ degrees of freedom. Use this approximation to find critical values of $\mathrm { r } _ { \mathrm { S } }$ for the case where $\mathrm { n } = 17$ and $\alpha = 0.05$.
A) $\pm 0.311$
B) $\pm 0.482$
C) $\pm 0.411$
D) $\pm 0.480$

Accepted Answer

The answer of When performing a rank correlation test, one...

Question 19

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 $\alpha$
-$\mathrm { n } = 25 , \alpha = 0.05$

A) $r = \pm 0.505$
B) $r = \pm 0.396$
C) $r = 0.444$
D) $\mathrm { r } = 0.396$

Accepted Answer

The answer of Suppose you will perform a test to...

Question 20

Use the given data to find the best predicted value of the response variable.
-The regression equation relating attitude rating $( x )$ and job performance rating $( y )$ for the employees of a company is $\hat { y } = 11.7 + 1.02 x$. Ten pairs of data were used to obtain the equation. The same data yield $\mathrm { r } = 0.863$ and $\overline { \mathrm { y } } = 80.1$. What is the best predicted job performance rating for a person whose attitude rating is $56 ?$
A) 68.8
B) 67.9
C) 80.1
D) 12.6

Accepted Answer

The best predicted job performance rating is calculated by substituting $ x = 56 $ into the regression equation: $\hat{y} = 11.7 + 1.02(56) = 68.8$.

Quiz 10: Correlation and Regression

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. - $r = - 0.853 , n = 5$

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. - $\mathrm { r } = 0.71 , \mathrm { n } = 25$

Nine pairs of data yield $\mathrm { r } = 0.867$ and the regression equation $\hat { y } = 19.4 + 0.93 \mathrm { x }$ . Also, $\overline { \mathrm { y } } = 64.7$ . What is the best predicted value of $y$ for $x = 48$ ?

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 $\alpha$ . - $\mathrm { n } = 6 , \alpha = 0.01$

Use the given data to find the best predicted value of the response variable. -Ten pairs of data yield $r = 0.003$ and the regression equation $\hat { y } = 2 + 3 x$ . Also, $\bar { y } = 5.0$ . What is the best predicted value of $\mathrm { y }$ for $\mathrm { x } = 2$ ?

Find the value of the linear correlation coefficient r. - $\begin{array}{r|rrrrr}\mathrm{x} & 19.3 & 23.4 & 10.3 & 17.7 & 23.2 \\\hline \mathrm{y} & 6 & 2 & 3 & 3 & 3\end{array}$

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. - $\begin{array}{r|rrrr}x & 2 & 4 & 5 & 6 \\\hline y & 7 & 11 & 13 & 20\end{array}$

Find the value of the linear correlation coefficient r. - $\begin{array}{r|rrrrrrr}\mathrm{x} & 62 & 53 & 64 & 52 & 52 & 54 & 58 \\\hline \mathrm{y} & 158 & 176 & 151 & 164 & 164 & 174 & 162\end{array}$

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

Is the data point, P, an outlier, an influential point, both, or neither? -

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

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 $\alpha$ - $\mathrm { n } = 25 , \alpha = 0.05$

Quiz 10: Correlation and Regression

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=−0.853,n=5r = - 0.853 , n = 5r=−0.853,n=5

Nine pairs of data yield r=0.867\mathrm { r } = 0.867r=0.867 and the regression equation y^=19.4+0.93x\hat { y } = 19.4 + 0.93 \mathrm { x }y^​=19.4+0.93x . Also, y‾=64.7\overline { \mathrm { y } } = 64.7y​=64.7 . What is the best predicted value of yyy for x=48x = 48x=48 ?

Find the value of the linear correlation coefficient r. - x19.323.410.317.723.2y62333\begin{array}{r|rrrrr}\mathrm{x} & 19.3 & 23.4 & 10.3 & 17.7 & 23.2 \\\hline \mathrm{y} & 6 & 2 & 3 & 3 & 3\end{array}xy​19.36​23.42​10.33​17.73​23.23​​

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. - x2456y7111320\begin{array}{r|rrrr}x & 2 & 4 & 5 & 6 \\\hline y & 7 & 11 & 13 & 20\end{array}xy​27​411​513​620​​

Construct a scatterplot for the given data - x15−14−189−20−11y−962545−42925\begin{array}{r|r|r|r|r|r|r}\mathrm{x} & 15 & -14 & -18 & 9 & -20 & -11 \\\hline \mathrm{y} & -96 & 25 & 45 & -42 & 92 & 5\end{array}xy​15−96​−1425​−1845​9−42​−2092​−115​​

Is the data point, P, an outlier, an influential point, both, or neither? -

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}{c|ccccc}x & 6 & 8 & 20 & 28 & 36 \\\hline \mathrm{y} & 2 & 4 & 13 & 20 & 30\end{array}xy​62​84​2013​2820​3630​​

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. - $r = - 0.853 , n = 5$

Nine pairs of data yield $\mathrm { r } = 0.867$ and the regression equation $\hat { y } = 19.4 + 0.93 \mathrm { x }$ . Also, $\overline { \mathrm { y } } = 64.7$ . What is the best predicted value of $y$ for $x = 48$ ?

Find the value of the linear correlation coefficient r. - $\begin{array}{r|rrrrr}\mathrm{x} & 19.3 & 23.4 & 10.3 & 17.7 & 23.2 \\\hline \mathrm{y} & 6 & 2 & 3 & 3 & 3\end{array}$

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. - $\begin{array}{r|rrrr}x & 2 & 4 & 5 & 6 \\\hline y & 7 & 11 & 13 & 20\end{array}$

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