Question 1

Find the best predicted value of y corresponding to the given value of x.
-Four pairs of data yield $\mathrm { r } = 0.942$ and the regression equation $\mathrm { y } = 3 \mathrm { x }$. Also, $\overline { \mathrm { y } } = 12.75$. What is the best predicted value of $y$ for $x = 2.8$ ?

Accepted Answer

A)  $2.826$ 
B)  $0.942$ 
C)  $8.4$ 
D)  $12.75$

Question 2

Determine which plot shows the strongest linear correlation

Accepted Answer

A) 
 
B) 
 
C)

Question 3

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

Accepted Answer

A)  $13.479$ 
B)  $6,693.27$ 
C)  $6,531.37$ 
D)  $6,544.86$

Question 4

Provide an appropriate response.
-Define the term independent, or predictor, variable and the term dependent, or response, variable. Give examples for each.

Accepted Answer

The answer of Provide an appropriate response.
-Define the term independent,...

Question 5

Find the best predicted value of y corresponding to the given value of x.
-The regression equation relating attitude rating $( \mathrm { x } )$ and job performance rating $( \mathrm { y } )$ 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 $r = 0.863$ and $\bar { y } = 80.1$. What is the best predicted job performance rating for a person whose attitude rating is 73 ?

Accepted Answer

A)  $80.1$ 
B)  $12.6$ 
C)  $86.2$ 
D)  $84.9$

Question 6

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

Accepted Answer

A)  $1,119.3$ 
B)  $100.06$ 
C)  $979.44$ 
D)  $1,079.5$

Question 7

The paired data below consists of heights and weights of 6 randomly selected adults. The equation of the regression line is $\hat{\mathrm { y }} = - 181.342 + 144.46 \mathrm { x }$ and the standard error of estimate is $\mathrm { se } = 5.0015$. Find the $95 \%$ prediction interval for the weight of a person whose height is $1.75 \mathrm {~m}$.
$\begin{array}{c|rrrrrr}
\text { x Height (meters) } & 1.61 & 1.72 & 1.78 & 1.80 & 1.67 & 1.88 \
\hline \mathrm{y} \text { Weight }(\mathrm{kg}) & 54 & 62 & 70 & 84 & 61 & 92
\end{array}$

Accepted Answer

A)  $65.4 < y < 77.6$ 
B)  $56.5 < y < 86.5$ 
C)  $52.1 < y < 90.9$ 
D)  $58.5 <$ y $< 84.5$

Question 8

Provide an appropriate response.
-Create a scatterplot that shows a perfect positive correlation between x and y. How would the scatterplot change if the correlation showed a)a strong positive correlation, b)a positive correlation, and c)no correlation?

Accepted Answer

The answer of Provide an appropriate response.
-Create a scatterplot that...

Question 9

Use computer software to obtain the regression and identify RS1U1P12S1S1P0, adjusted RS1U1P12S1S1P0, and the P-value
-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. $\begin{array}{cccc}
\hline\text { WEIGHT } & \text { CHEST } & \text { LENGTH } & \text { SEX } \
\hline 344 & 45.0 & 67.5 & 1 \
416 & 54.0 & 72.0 & 1 \
220 & 41.0 & 70.0 & 2 \
360 & 49.0 & 68.5 & 1 \
332 & 44.0 & 73.0 & 1 \
140 & 32.0 & 63.0 & 2 \
436 & 48.0 & 72.0 & 1 \
132 & 33.0 & 61.0 & 2 \
356 & 48.0 & 64.0 & 2 \
150 & 35.0 & 59.0 & 1 \
202 & 40.0 & 63.0 & 2 \
365 & 50.0 & 70.5 & 1\\hline
\end{array}$

Accepted Answer

A)  $ 7725, .961, .014 $ 
B)  $ .927, .900, .000 $ 
C)  $ .891, .926, .003 $ 
D)  $ .971, .723, .000 $

Question 10

A regression equation is obtained for a collection of paired data. It is found that the total variation is 114, the explained variation is 91.7, and the unexplained variation is 22.3. Find the coefficient of determination.

Accepted Answer

A) 0.804 
B) 1.243 
C) 0.243 
D) 0.196

Question 11

Construct a scatterplot and identify the mathematical model that best fits the 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. Use a calculator or computer to obtain the regression equation of the model that best fits the data. You may need to fit several
models and compare the values of RS1U1P12S1S1P0
-$\begin{array}{c|cccccc}
\mathrm{x} & 1 & 2 & 3 & 4 & 5 & 6 \
\hline \mathrm{y} & 9 & 13 & 25 & 27 & 31 & 46
\end{array}$

Accepted Answer

A)  $y = 1.07 + 6.89 x$ 
B)  $y = 8.34 x ^ { 0.88 }$ 
C)  $y = 4.87 + 18.5 \ln x$ 
D)  $y = 3.14 + 6.59 x$

Question 12

Provide an appropriate response.
-Describe what correlation is, and explain the purpose of correlation.

Accepted Answer

The answer of Provide an appropriate response.
-Describe what correlation is,...

Question 13

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

Accepted Answer

A)  0.754 
B)  -0.081 
C)  -0.775 
D)  0

Question 14

Is the data point, P
-

Accepted Answer

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

Question 15

Use computer software to obtain the regression and identify RS1U1P12S1S1P0, adjusted RS1U1P12S1S1P0, and the P-value
-FPEA, the Farm Production Enhancement Agency, regressed corn output against acreage, rainfall, and a trend line. The trend line is proxy for technological advancement in farming from improved pest control, fertilization, land management, and farming implements. $\begin{array}{cccc}
\hline \text { CORNPROD } & \text { ACRES } & \text { RAINFALL } & \text { TREND } \
\hline 456 & 9896 & 29.1 & 1 \
421 & 9680 & 42.3 & 2 \
653 & 10449 & 29.8 & 3 \
573 & 10811 & 26.0 & 4 \
546 & 10014 & 34.3 & 5 \
499 & 10293 & 22.7 & 6 \
504 & 9413 & 24.2 & 7 \
611 & 9860 & 31.6 & 8 \
646 & 9782 & 25.6 & 9\
789 & 12139 & 37.9 & 10 \
773 & 12166 & 33.9 & 11 \
753 & 9976 & 37.4 & 12 \
852 & 10645 & 27.0 & 13 \
755 & 9738 & 31.5 & 14 \
815 & 9933 & 39.9 & 15 \
902 & 10132 & 25.3 & 16 \
986 & 11145 & 30.4 & 17 \
909 & 9775 & 32.7 & 18\
945 & 9549 & 35.0 & 19 \
866 & 10077 & 33.8 & 20 \
1178 & 11550 & 29.4 & 21 \
1230 & 10600 & 37.1 & 22 \
1207 & 11280 & 42.9 & 23 \
968 & 12100 & 32.2 & 24 \
1118 & 12420 & 30.5 & 25\
\hline
\end{array}$

Accepted Answer

A)  CORNPROD $ =-21.1+.036 \mathrm{ACRES}+2.62 $ RAINFALL + 27.6TREND;
 No, because the $ \mathrm{P} $-value is low 
B)  CORNPROD $ =-.9+1.68 \mathrm{ACRES}+.79 \mathrm{RAINFALL}+10.2 \mathrm{TREND} $; 
Yes, because the adjusted $ \mathrm{R}^{2} $ is high 
C)  CORNPROD $ =-21.1+.036 \mathrm{ACRES}+2.62 \mathrm{RAINFALL}+27.6 \mathrm{TREND} $; 
Yes, because the $ \mathrm{R}^{2} $ is high 
D)  CORNPROD $ =-16.3+2.6 \mathrm{ACRES}+3.9 \mathrm{RAINFALL}+21.3 $ TREND; 
Yes, because the the $ \mathrm{R}^{2} $ is high

Question 16

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. $$\begin{array}{l}
\text { The regression equation is }\
\begin{array} { l } 
\text { Score } = 31.55 + 10.90 \text { Years. } \
\begin{array} { l c c c c } 
\text { Predictor } & \text { Coef } & \text { StDev } & \text { T } & \text { P } \
\text { Constant } & 31.55 & 6.360 & 4.96 & 0.000 \
\text { Years } & 10.90 & 1.744 & 6.25 & 0.000 \
\mathrm {~S} = 5.651 & \mathrm { R } - \mathrm { Sq } = 83.0 \% & \mathrm { R } - \mathrm { Sq } ( \mathrm { Adj } ) = 82.7 \% \
\text { Predicted values } \
\text { Fit } & \text { StDev Fit } & 95.0 \% \text { CI } & 95.0 \% \text { PI } \
53.35 & 3.168 & ( 42.72,63.98 ) & ( 31.61,75.09 )
\end{array}
\end{array}
\end{array}$$ What percentage of the total variation in test scores is unexplained by the linear relationship between years of study and test scores?

Accepted Answer

A) 82.7% 
B) 83.0% 
C) 17.0% 
D) 8.9%

Question 17

Find the value of the linear correlation coefficient r.
-$\begin{array}{r|rrrrr}
\mathrm{x} & 3 & 5 & 7 & 15 & 16 \
\hline y & 8 & 11 & 7 & 14 & 20
\end{array}$

Accepted Answer

A)  $\hat { y } = 4.07 + 0.753 x$ 
B)  $\hat { y } = 5.07 + 0.850 x$ 
C)  $\hat { y } = 4.07 + 0.850 x$ 
D)  $\hat { y } = 5.07 + 0.753 x$

Question 18

The paired data below consists of test scores and hours of preparation for 5 randomly selected students. The equation of the regression line is $\hat{\mathrm { y }} = 44.8447 + 3.52427 \mathrm { x }$. Find the standard error of estimate.
$\begin{array}{c|rrrrr}
\text { x Hours of preparation } & 5 & 2 & 9 & 6 & 10 \
\hline y \text { Test score } & 64 & 48 & 72 & 73 & 80
\end{array}$

Accepted Answer

A)  $7.1720$ 
B)  $13.060$ 
C)  $4.1097$ 
D)  $5.3999$

Question 19

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 1
$\begin{array}{c|ccccc}
\mathrm{x} & 1.2 & 2.7 & 4.4 & 6.6 & 9.5 \
\hline \mathrm{y} & 1.6 & 4.7 & 8.9 & 9.5 & 12.0
\end{array}$

Accepted Answer

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

Question 20

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. The regression equation is
$\begin{array}{lcccc}
{\text { Score }=31.55+10.90 \text { Years. }} \
\text { Predictor } & \text { Coef } & \text { StDev } & \text { T } & \text { P } \
\text { Constant } & 31.55 & 6.360 & 4.96 & 0.000 \
\text { Years } & 10.90 & 1.744 & 6.25 & 0.000
\end{array}$
$$
\mathrm{S}=5.651 \quad \mathrm{R}-\mathrm{Sq}=83.0 \% \quad \mathrm{R}-\mathrm{Sq}(\mathrm{Adj})=82.7 \%
$$
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} $
For a person who studies for 2 years, obtain the $ 95 \% $ prediction interval and write a statement interpreting the in

Accepted Answer

A)  $ (42.72,63.98) $; We can be $ 95 \% $ confident that the mean test score of all individuals who study 2 years will lie in the interval $ (42.72,63.98) $ 
B)  $ (31.61,75.09) $; We can be $ 95 \% $ confident that the test score of an individual who studies 2 years will lie in the interval $ (31.61,75.09) $ 
C)  $ (31.61,75.09) $; We can be $ 95 \% $ confident that the mean test score of all individuals who study 2 years will lie in the interval $ (31.61,75.09) $ 
D)  $ (42.72,63.98) $; We can be $ 95 \% $ confident that the test score of an individual who studies 2 years will lie in the interval $ (42.72 .63 .98) $

Exam 10: Correlation and Regression

Find the best predicted value of y corresponding to the given value of x. -Four pairs of data yield $\mathrm { r } = 0.942$ and the regression equation $\mathrm { y } = 3 \mathrm { x }$ . Also, $\overline { \mathrm { y } } = 12.75$ . What is the best predicted value of $y$ for $x = 2.8$ ?

Determine which plot shows the strongest linear correlation

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

Provide an appropriate response. -Define the term independent, or predictor, variable and the term dependent, or response, variable. Give examples for each.

Provide an appropriate response. -Create a scatterplot that shows a perfect positive correlation between x and y. How would the scatterplot change if the correlation showed a)a strong positive correlation, b)a positive correlation, and c)no correlation?

A regression equation is obtained for a collection of paired data. It is found that the total variation is 114, the explained variation is 91.7, and the unexplained variation is 22.3. Find the coefficient of determination.

Provide an appropriate response. -Describe what correlation is, and explain the purpose of correlation.

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

Is the data point, P -

Find the value of the linear correlation coefficient r. - $\begin{array}{r|rrrrr}\mathrm{x} & 3 & 5 & 7 & 15 & 16 \\\hline y & 8 & 11 & 7 & 14 & 20\end{array}$

Exam 10: Correlation and Regression

Determine which plot shows the strongest linear correlation

Provide an appropriate response. -Define the term independent, or predictor, variable and the term dependent, or response, variable. Give examples for each.

Provide an appropriate response. -Create a scatterplot that shows a perfect positive correlation between x and y. How would the scatterplot change if the correlation showed a)a strong positive correlation, b)a positive correlation, and c)no correlation?

A regression equation is obtained for a collection of paired data. It is found that the total variation is 114, the explained variation is 91.7, and the unexplained variation is 22.3. Find the coefficient of determination.

Provide an appropriate response. -Describe what correlation is, and explain the purpose of correlation.

Find the value of the linear correlation coefficient r - x62536452525458y158176151164164174162\begin{array}{r|rrrrrrr}\mathrm{x} & 62 & 53 & 64 & 52 & 52 & 54 & 58 \\\hline y & 158 & 176 & 151 & 164 & 164 & 174 & 162\end{array}xy​62158​53176​64151​52164​52164​54174​58162​​

Is the data point, P -

Find the value of the linear correlation coefficient r. - x3571516y81171420\begin{array}{r|rrrrr}\mathrm{x} & 3 & 5 & 7 & 15 & 16 \\\hline y & 8 & 11 & 7 & 14 & 20\end{array}xy​38​511​77​1514​1620​​

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

Find the value of the linear correlation coefficient r. - $\begin{array}{r|rrrrr}\mathrm{x} & 3 & 5 & 7 & 15 & 16 \\\hline y & 8 & 11 & 7 & 14 & 20\end{array}$