Question 1

Provide an appropriate response.
-Explain why having a significant linear correlation does not imply causality. Give an example to support your answer.

Accepted Answer

Having a significant linear co

Question 2

Solve the problem.
-The sum of squares of residuals $\sum ( y - \hat { y } ) ^ { 2 }$ can be used to assess the quality of a regression model. A residual is the difference between an observed y value and the value of y predicted from the model, $\hat { \mathrm { y } }$ . The better the model, the smaller the sum of squares of residuals. For the data below find the sum of squares of residuals which results from fitting a linear model, and the sum of squares of residuals which results from fitting a logarithmic model. Which model fits better? How can you tell? $\begin{array} { c | c c c c c } 
x & 1 & 2 & 3 & 4 & 5 \
\hline y & 7 & 17 & 20 & 25 & 28
\end{array}$

Accepted Answer

Sum of squares of residuals for linear m

Question 3

A regression equation can be used to make predictions of the y value corresponding to a particular x value. Determine whether the following statement is true or false: The 95% confidence interval for the mean of all values of y for which x = x0 will be wider than the 95% confidence interval for a single y for which x = x0.

Accepted Answer

A) True 
 B)False

Question 4

Is the data point, P
-The regression equation for a set of paired data is $y = - 21.1 + 1.3 x$. The values of $x$ run from 100 to 400 . A new data point, $\mathrm { P } ( 175,206.4 )$, is added to the set.

Accepted Answer

A) Both 
B) Influential point 
C) Neither 
D) Outlier 
A) Both 
B) Influential point 
C) Neither 
D) Outlier

Question 5

The equation of the regression line for the paired data below is $\hat { y } = 3 x$. Find the standard error of estimate.
$\begin{array}{r|rrrr}
\mathrm{x} & 2 & 4 & 5 & 6 \
\hline \mathrm{y} & 7 & 11 & 13 & 20
\end{array}$

Accepted Answer

A)  $2.2361$ 
B)  $4.1892$ 
C)  $5.00$ 
D)  $6.2750$ 
A)  $2.2361$ 
B)  $4.1892$ 
C)  $5.00$ 
D)  $6.2750$

Question 6

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 $16.02$ and that the $y$-values are $11,14,19,22,26,27$, find
$$R ^ { 2 } = 1 - \frac { \sum ( y - \hat { y } ) ^ { 2 } } { \sum ( y - \bar { y } ) ^ { 2 } } .$$

Accepted Answer

A)  $0.077$ 
B)  $0.935$ 
C)  $0.916$ 
D)  $0.923$ 
A)  $0.077$ 
B)  $0.935$ 
C)  $0.916$ 
D)  $0.923$

Question 7

Determine which plot shows the strongest linear correlation

Accepted Answer

A)

B) 
  
C) 
  
A)

B) 
  
C)

Question 8

Provide an appropriate response.
-Discuss the guidelines under which the linear regression equation should be used for prediction. Refer to the correlation coefficient, the type of data used to create the linear regression, and the predicting value.

Accepted Answer

The linear regression equation should be

Question 9

A collection of paired data consists of the number of years that students have studied Spanish and their scores on a Spanish language proficiency test. A computer program was used to obtain the least squares linear regression line and the computer output is shown below. Along with the paired sample data, the program was also given an x value of 2 (years of study)to be used for predicting test score. $$\text { The regression equation is }$$
$\begin{array}{l}
\text { Score }=31.55+10.90 \text { Years. }\
\begin{array}{lllcc}
\text { Predictor } & \text { Coef } & \text { StDev } & \text { T } & \text { P } \
\text { Constant } & 31.55 & 6.360 & 4.96 & 0.000 \
\text { Years } & 10.90 & 1.744 & 6.25 & 0.000
\end{array}
\end{array}$
$$
S=5.651 \quad R-S q=83.0 \% \quad R-S q(\text { Adj })=82.7 \%
$$
Predicted values
$ \begin{array}{llcc}\text { Fit } & \text { StDev Fit } & 95.0 \% \text { CI } & 95.0 \% \text { PI } \ 53.35 & 3.168 & (42.72,63.98) & (31.61,75.09)\end{array} $ If a person studies 4.5 years, what is the single value that is the best predicted test score? Assume that there is a significant linear correlation between years of study and test score.

Accepted Answer

A) 53.35 
B) 80.6 
C) 83.0 
D) 49.1 
A) 53.35 
B) 80.6 
C) 83.0 
D) 49.1

Question 10

Find the value of the linear correlation coefficient r.
-$\begin{array}{r|rrrr}
x & 2 & 4 & 5 & 6 \
\hline y & 7 & 11 & 13 & 20
\end{array}$

Accepted Answer

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

Question 11

Use computer software to find the best regression equation to explain the variation in the dependent variable, Y, in terms of the independent variables, X1, X2, X3
-$\begin{array} { c c c l c } \mathrm { Y } & \mathrm { X } _ { 1 } & \mathrm { X } _ { 2 } & \mathrm { X } _ { 3 } & \ 344 & 45.0 & 67.5 & 1 & \text { CORRELATION COEFFICIENTS } \ 416 & 54.0 & 72.0 & 1 & \mathrm { Y } / \mathrm { X } _ { 1 } = .951 \ 220 & 41.0 & 70.0 & 2 & \mathrm { Y } / \mathrm { X } _ { 2 } = .789 \ 360 & 49.0 & 68.5 & 1 & \mathrm { Y } / \mathrm { X } _ { 3 } = - .616 \ 332 & 44.0 & 73.0 & 1 & \ 140 & 32.0 & 63.0 & 2 & \ 436 & 48.0 & 72.0 & 1 & \text { COEFFICIENTS OF DETERMINATION } \ 132 & 33.0 & 61.0 & 2 & \ 356 & 48.0 & 64.0 & 2 & \mathrm { Y } _ { 1 } / \mathrm { X } _ { 1 } = .905 \ 150 & 35.0 & 59.0 & 1 & \mathrm { X } _ { 1 } , \mathrm { X } _ { 2 } = .919 \ 202 & 40.0 & 63.0 & 2 & \mathrm { Y } _ { 1 } , \mathrm { X } _ { 2 } , \mathrm { X } _ { 3 } = .927 \ 365 & 50.0 & 70.5 & 1 & \end{array}$

Accepted Answer

A)  $\hat { Y } = - 355 + 14.9 X _ { 1 }$ 
B)  $\hat { Y } = - 442 + 12.1 X _ { 1 } + 3.58 X _ { 2 } - 23.8 X _ { 3 }$ 
C)  $\hat { Y } = - 412 + 13.6 X _ { 1 } + 3.15 X _ { 2 }$ 
D)  $\hat { Y } = - 543 + 12.8 X _ { 1 } + 4.15 X _ { 2 }$ 
A)  $\hat { Y } = - 355 + 14.9 X _ { 1 }$ 
B)  $\hat { Y } = - 442 + 12.1 X _ { 1 } + 3.58 X _ { 2 } - 23.8 X _ { 3 }$ 
C)  $\hat { Y } = - 412 + 13.6 X _ { 1 } + 3.15 X _ { 2 }$ 
D)  $\hat { Y } = - 543 + 12.8 X _ { 1 } + 4.15 X _ { 2 }$

Question 12

Use computer software to obtain the regression equation. Use the estimated equation to find the predicted value
-A study of food consumption in the country related the level of food consumed to an index of food prices and an index of personal disposable income. Next year, the income index number is expected to be 104.2, and the price index is expected to be 107.9. These numbers would indicate a predicted value for food consumption. $\begin{array}{ccc}\hline
\text { FOODCONS } & \text { INCOME } & \text { PRICE } \\hline
98.6 & 87.4 & 108.5 \
101.2 & 97.6 & 110.1 \
102.4 & 96.7 & 110.4 \
100.9 & 98.2 & 104.3 \
102.3 & 99.8 & 107.2 \
101.5 & 100.5 & 105.8 \
101.6 & 103.2 & 107.8 \
101.6 & 107.8 & 103.4 \
99.8 & 96.6 & 102.7 \
100.3 & 88.9 & 104.1 \
97.6 & 75.1 & 99.2 \
97.2 & 76.9 & 99.7 \
97.3 & 84.6 & 102.0 \
96.0 & 90.6 & 94.3 \
99.2 & 103.1 & 97.7 \
100.3 & 105.1 & 101.1 \
100.3 & 96.4 & 102.3 \
104.1 & 104.4 & 104.4 \
105.3 & 110.7 & 108.5 \
107.6 & 127.1 & 111.3\\hline
\end{array}$

Accepted Answer

A)  94.5 
B)  105.9 
C)  99.4 
D)  102.3 
A)  94.5 
B)  105.9 
C)  99.4 
D)  102.3

Question 13

Find the value of the linear correlation coefficient r.
-Two different tests are designed to measure employee productivity and dexterity. Several employees are randomly selected and tested with these results. $\begin{array}{cc|c|c|c|c|c|c|c|c|c}
\text { Productivity } & 23 & 25 & 28 & 21 & 21 & 25 & 26 & 30 & 34 & 36 \
\hline
\text { Dexterity } & 49 & 53 & 59 & 42 & 47 & 53 & 55 & 63 & 67 & 75
\end{array}$

Accepted Answer

A)  $\hat{y} = 10.7 + 1.53 x$ 
B)  $\hat{y} = 5.05 + 1.91 \mathrm { x }$ 
C)  $\hat { y } = 2.36 + 2.03 x$ 
D)  $\hat { y } = 75.3 - 0.329 \mathrm { x }$ 
A)  $\hat{y} = 10.7 + 1.53 x$ 
B)  $\hat{y} = 5.05 + 1.91 \mathrm { x }$ 
C)  $\hat { y } = 2.36 + 2.03 x$ 
D)  $\hat { y } = 75.3 - 0.329 \mathrm { x }$

Question 14

Construct a scatter diagram for the given data
-$\begin{array}{lr|r|r|r|r|r|r|r|r|r}
\mathrm{x} & -4 & -3 & -5 & -7 & 4 & 3 & -6 & 9 & -4 & -1 \
\hline y & 2 & -7 & 2 & -7 & 2 & -2 & -4 & 4 & -10 & -2
\end{array}$

Accepted Answer

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

Question 15

Find the value of the linear correlation coefficient r
-The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test. $\begin{array}{l|rrrrrr}
\text { Hours } & 5 & 10 & 4 & 6 & 10 & 9 \
\hline \text { Score } & 64 & 86 & 69 & 86 & 59 & 87
\end{array}$

Accepted Answer

A)  $- 0.678$ 
B)  $- 0.224$ 
C)  $0.678$ 
D)  $0.224$ 
A)  $- 0.678$ 
B)  $- 0.224$ 
C)  $0.678$ 
D)  $0.224$

Question 16

Provide an appropriate response.
-What is the importance of correlation in terms of the linear regression equation?

Accepted Answer

The linear regression equation

Question 17

Find the value of the linear correlation coefficient r.
-Based on the data from six students, the regression equation relating number of hours of preparation (x)and test score $( \mathrm { y } )$ is $y = 67.3 + 1.07 x$. The same data yield $r = 0.224$ and $\bar{y} = 75.2$. What is the best predicted test score for a student who spent 2 hours preparing for the test?

Accepted Answer

A) 69.4 
B) 78.1 
C) 75.2 
D) 59.7 
A) 69.4 
B) 78.1 
C) 75.2 
D) 59.7

Question 18

The paired data below consists of heights and weights of 6 randomly selected adults. The equation of the regression line is $\hat { y } = - 181.342 + 144.46 \mathrm { x }$. Find the standard error of estimate.
$\begin{array}{c|rrrrrr}
\text { x Height (meters) } & 1.61 & 1.72 & 1.78 & 1.80 & 1.67 & 1.88 \
\hline \mathrm{y} \text { Weight }(\mathrm{kg}) & 54 & 62 & 70 & 84 & 61 & 92
\end{array}$

Accepted Answer

A)  $5.0015$ 
B)  $15.648$ 
C)  $6.9205$ 
D)  $9.7944$ 
A)  $5.0015$ 
B)  $15.648$ 
C)  $6.9205$ 
D)  $9.7944$

Question 19

Find the value of the linear correlation coefficient r
-A study was conducted to compare the average time spent in the lab each week versus course grade for computer students. The results are recorded in the table below. $\begin{array}{cc}
\text { Number of hours spent in lab } & \text { Grade (percent) } \
\hline 10 & 96 \
11 & 51 \
16 & 62 \
9 & 58 \
7 & 89 \
15 & 81 \
16 & 46 \
10 & 51
\end{array}$

Accepted Answer

A)  $- 0.335$ 
B)  $- 0.284$ 
C)  $0.462$ 
D)  $0.017$ 
A)  $- 0.335$ 
B)  $- 0.284$ 
C)  $0.462$ 
D)  $0.017$

Question 20

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.
-$$\mathrm { r } = 0.221 , \mathrm { n } = 90$$

Accepted Answer

A)  Critical values: $r = \pm 0.217$, no significant linear correlation 
B)  Critical values: $r = 0.217$, significant linear correlation 
C)  Critical values: $r = \pm 0.207$, no significant linear correlation 
D)  Critical values: $\mathrm { r } = \pm 0.207$, significant linear correlation 
A)  Critical values: $r = \pm 0.217$, no significant linear correlation 
B)  Critical values: $r = 0.217$, significant linear correlation 
C)  Critical values: $r = \pm 0.207$, no significant linear correlation 
D)  Critical values: $\mathrm { r } = \pm 0.207$, significant linear correlation

Provide an appropriate response. -Explain why having a significant linear correlation does not imply causality. Give an example to support your answer.

Is the data point, P -The regression equation for a set of paired data is $y = - 21.1 + 1.3 x$ . The values of $x$ run from 100 to 400 . A new data point, $\mathrm { P } ( 175,206.4 )$ , is added to the set.

The equation of the regression line for the paired data below is $\hat { y } = 3 x$ . Find the standard error of estimate. 2 4 5 6 7 11 13 20

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 $16.02$ and that the $y$ -values are $11,14,19,22,26,27$ , find $R ^ { 2 } = 1 - \frac { \sum ( y - \hat { y } ) ^ { 2 } } { \sum ( y - \bar { y } ) ^ { 2 } } .$

Determine which plot shows the strongest linear correlation

Provide an appropriate response. -Discuss the guidelines under which the linear regression equation should be used for prediction. Refer to the correlation coefficient, the type of data used to create the linear regression, and the predicting value.

Find the value of the linear correlation coefficient r. - x 2 4 5 6 y 7 11 13 20

Find the value of the linear correlation coefficient r. -Two different tests are designed to measure employee productivity and dexterity. Several employees are randomly selected and tested with these results. Productivity 23 25 28 21 21 25 26 30 34 36 Dexterity 49 53 59 42 47 53 55 63 67 75

Find the value of the linear correlation coefficient r -The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test. Hours 5 10 4 6 10 9 Score 64 86 69 86 59 87

Provide an appropriate response. -What is the importance of correlation in terms of the linear regression equation?

The paired data below consists of heights and weights of 6 randomly selected adults. The equation of the regression line is $\hat { y } = - 181.342 + 144.46 \mathrm { x }$ . Find the standard error of estimate. x Height (meters) 1.61 1.72 1.78 1.80 1.67 1.88 Weight () 54 62 70 84 61 92

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. - $\mathrm { r } = 0.221 , \mathrm { n } = 90$

Introduction to Statistics

Summarizing and Graphing Data

Statistics for Describing, Exploring, and Comparing Data

Probability

Probability Distributions

Normal Probability Distributions

Estimates and Sample Sizes

Hypothesis Testing

Inferences From Two Samples

Multinomial Experiments and Contingency Tables

Analysis of Variance

Nonparametric Statistics

Statistical Process Control

Filters

Exam 10: Correlation and Regression

Provide an appropriate response. -Explain why having a significant linear correlation does not imply causality. Give an example to support your answer.

Is the data point, P -The regression equation for a set of paired data is y=−21.1+1.3xy = - 21.1 + 1.3 xy=−21.1+1.3x . The values of xxx run from 100 to 400 . A new data point, P(175,206.4)\mathrm { P } ( 175,206.4 )P(175,206.4) , is added to the set.

The equation of the regression line for the paired data below is y^=3x\hat { y } = 3 xy^​=3x . Find the standard error of estimate. 2 4 5 6 7 11 13 20

Determine which plot shows the strongest linear correlation

Provide an appropriate response. -Discuss the guidelines under which the linear regression equation should be used for prediction. Refer to the correlation coefficient, the type of data used to create the linear regression, and the predicting value.

Find the value of the linear correlation coefficient r. - x 2 4 5 6 y 7 11 13 20

Find the value of the linear correlation coefficient r. -Two different tests are designed to measure employee productivity and dexterity. Several employees are randomly selected and tested with these results. Productivity 23 25 28 21 21 25 26 30 34 36 Dexterity 49 53 59 42 47 53 55 63 67 75

Construct a scatter diagram for the given data - -4 -3 -5 -7 4 3 -6 9 -4 -1 y 2 -7 2 -7 2 -2 -4 4 -10 -2

Find the value of the linear correlation coefficient r -The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test. Hours 5 10 4 6 10 9 Score 64 86 69 86 59 87

Provide an appropriate response. -What is the importance of correlation in terms of the linear regression equation?

Introduction to Statistics

Summarizing and Graphing Data

Statistics for Describing, Exploring, and Comparing Data

Probability

Probability Distributions

Normal Probability Distributions

Estimates and Sample Sizes

Hypothesis Testing

Inferences From Two Samples

Multinomial Experiments and Contingency Tables

Analysis of Variance

Nonparametric Statistics

Statistical Process Control

Filters

Is the data point, P -The regression equation for a set of paired data is $y = - 21.1 + 1.3 x$ . The values of $x$ run from 100 to 400 . A new data point, $\mathrm { P } ( 175,206.4 )$ , is added to the set.

The equation of the regression line for the paired data below is $\hat { y } = 3 x$ . Find the standard error of estimate. 2 4 5 6 7 11 13 20