Question 1

In order for applicants to work for the foreign-service department, they must take a test in the language of the
country where they plan to work. The data below show the relationship between the number of years that
applicants have studied a particular language and the grades they received on the proficiency exam. Construct
a scatter plot for the data. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | } 
\text { Number of years, } \mathrm { x } & 3 & 4 & 4 & 5 & 3 & 6 & 2 & 7 & 3 \
\hline \text { Grades on test, } \mathrm { y } & 61 & 68 & 75 & 82 & 73 & 90 & 58 & 93 & 72
\end{array}$$

Accepted Answer

The answer of In order for applicants to work for...

Question 2

A researcher found a significant relationship between a person?s age, $\mathrm { x } _ { 1 } ,$ the number of hours a person works per weekweek, $\mathrm { x } _ { 2 }$ and the number of accidents, y, the person has per year. The relationship can be represented by
The multiple regression equation ? = - $3.2 + 0.012 \mathrm { x } _ { 1 } + 0.23 \mathrm { x } _ { 2 }$ Predict the number of accidents per year (to the
Nearest whole number)for a person whose age is 50 and who works 38 hours per week.

Accepted Answer

A) 6 accidents 
B) 7 accidents 
C) 8 accidents 
D) 5 accidents

Question 3

Given a sample with r = -0.765 and n = 22, test the significance of the correlation r using α $\alpha$ = 0.02 and the claim $Q$ ρ = 0.

Accepted Answer

The answer of Given a sample with r = -0.765...

Question 4

For the data below, test the significance of the correlation coefficient using α $a$ = 0.05 and the claim ρ $Q$
 = 0. $$\begin{array} { c | c | c | c | c | c | c | c | c | c | c | } 
\mathrm { x } & - 10 & - 8 & - 1 & - 4 & - 6 & - 7 & - 5 & - 3 & - 2 & - 9 \
\hline \mathrm { y } & - 2 & 0 & 17 & 9 & 6 & 2 & 7 & 11 & 14 & 0
\end{array}$$

Accepted Answer

The answer of For the data below, test the significance...

Question 5

Given a sample with r = 0.321 and n = 30, test the significance of the correlation r using α $\alpha$ = 0.10 and the claim $\varrho$ ρ = 0.

Accepted Answer

The answer of Given a sample with r = 0.321...

Question 6

The data below are the temperatures on randomly chosen days during a summer class and the number of absences on those days. Find the standard error of estimate, $\mathrm { Se }$ given that ? = 0.449x - 30.27. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | } 
\text { Temperature, } \mathrm { x } & 72 & 85 & 91 & 90 & 88 & 98 & 75 & 100 & 80 \
\hline \text { Number of absences, y } & 3 & 7 & 10 & 10 & 8 & 15 & 4 & 15 & 5
\end{array}$$

Accepted Answer

A) 0.935 
B) 1.162 
C) 1.007 
D) 0.815

Question 7

In an area of the Midwest, records were kept on the relationship between the rainfall (in inches)and the yield of wheat (bushels per acre). Calculate the correlation coefficient, r. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | } 
\text { Rain fall (in inches), } x & 9.5 & 7.8 & 12.4 & 11.5 & 17.8 & 9.3 & 6 & 14.6 & 15 \
\hline \text { Yield (bushels per acre), y } & 45.5 & 41.2 & 53.8 & 54 & 77.4 & 44.2 & 26.9 & 71 & 73.8
\end{array}$$

Accepted Answer

A) 0.981 
B) 0.998 
C) 0.900 
D) 0.899

Question 8

The data below are the temperatures on randomly chosen days during a summer class and the number of absences on those days. Construct a 95% prediction interval for y, the number of days absent, given x = 95
Degrees,? = 0.449x - 30.27 and $\mathrm { s } _ { \mathrm { e } }$ = 0.934. Round interval to three decimal places. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | } 
\text { Temperature, } \mathrm { x } & 72 & 85 & 91 & 90 & 88 & 98 & 75 & 100 & 80 \
\hline \text { Number of absences, } \mathrm { y } & 3 & 7 & 10 & 10 & 8 & 15 & 4 & 15 & 5
\end{array}$$

Accepted Answer

A)  $9.957 < y < 14.813$ 
B)  $3.176 < y < 5.341$ 
C)  $4.321 < y < 6.913$ 
D)  $6.345 < y < 8.912$

Question 9

The data below are the ages and systolic blood pressures (measured in millimeters of mercury)of 9 randomly selected adults. Find the standard error of estimate, $\mathrm { Se } ,$ given that ? = 1.488x + 60.46. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | } 
\text { Age, } \mathrm { x } & 38 & 41 & 45 & 48 & 51 & 53 & 57 & 61 & 65 \
\hline \text { Pressure, } \mathrm { y } & 116 & 120 & 123 & 131 & 142 & 145 & 148 & 150 & 152
\end{array}$$

Accepted Answer

A) 4.199 
B) 6.981 
C) 5.572 
D) 3.099

Question 10

The data below are the ages and systolic blood pressures (measured in millimeters of mercury)of 9 randomly
selected adults. Construct a scatter plot for the data. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | } 
\text { Age, } x & 38 & 41 & 45 & 48 & 51 & 53 & 57 & 61 & 65 \
\hline \text { Pressure, } y & 116 & 120 & 123 & 131 & 142 & 145 & 148 & 150 & 152
\end{array}$$

Accepted Answer

The answer of The data below are the ages and...

Question 11

Find the standard error of estimate, se, for the data below, given that y = 2x + 1. $$\begin{array} { l | l | l | l | l | } 
\mathrm { x } & 1 & 2 & 3 & 4 \
\hline \mathrm { y } & 3 & 5 & 7 & 9
\end{array}$$

Accepted Answer

A) 0 
B) 1 
C) 2 
D) 3

Question 12

The data below are the number of absences and the final grades of 9 randomly selected students from a statistics class. Find the equation of the regression line for the given data. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | } 
\text { Number of absences, } \mathrm { x } & 0 & 3 & 6 & 4 & 9 & 2 & 15 & 8 & 5 \
\hline \text { Final grade, } \mathrm { y } & 98 & 86 & 80 & 82 & 71 & 92 & 55 & 76 & 82
\end{array}$$

Accepted Answer

A)  $\hat {\mathrm { y }}$

= -2.755x + 96.139 
B)  $\hat { y }$ = 96.139x - 2.755 
C)  $\hat { \mathrm { y } }$ = -2.755x - 96.139 
D)  $\mathrm { y }$ = -96.139x + 2.755

Question 13

The data below are the average monthly temperatures, in ${ } ^ { \circ } \mathrm { F } $ and the monthly natural gas consumption, in ccf,
for a household in northwestern Pennsylvania. What is the best-predicted value for the gas consumption, y,
given x = 50°F? Assume that the variables x and y have a significant correlation. $$\begin{array} { l | c c c c c c c c c } 
\text { Temperature } & 47 & 35 & 21 & 27 & 39 & 48 & 61 & 65 & 70 \
\hline \text { Consumption } & 34 & 169 & 248 & 134 & 137 & 100 & 19 & 34 & 12
\end{array}$$

Accepted Answer

The answer of The data below are the average monthly...

Question 14

The data below are the gestation periods, in months, of randomly selected animals and their corresponding life
spans, in years. Construct a 95% prediction interval for y, the life span, given x = 10 months, ŷ = 1.523x + 6.343,
and $\mathrm { S } \mathrm { e }$ = 5.618. Round interval to two decimal places. $$\begin{array} { l | l l l l l l l l } 
\text { Gestation, } \mathrm { x } & 8 & 2.1 & 1.3 & 1 & 11.5 & 5.3 & 3.8 & 24.3 \
\hline \text { Life span, } \mathrm { y } & 30 & 12 & 6 & 3 & 25 & 12 & 10 & 40
\end{array}$$

Accepted Answer

The answer of The data below are the gestation periods,...

Question 15

Given a sample with r = 0.823 and n = 10, test the significance of the correlation r using α $\alpha$ = 0.05 and the claim $Q$ ρ ρ= 0.

Accepted Answer

The answer of Given a sample with r = 0.823...

Question 16

Find the equation of the regression line for the given data. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | c } 
\mathrm { x } & - 5 & - 3 & 4 & 1 & - 1 & - 2 & 0 & 2 & 3 & - 4 \
\hline \mathrm { y } & 11 & - 6 & 8 & - 3 & - 2 & 1 & 5 & - 5 & 6 & 7
\end{array}$$

Accepted Answer

A)  $\hat{\mathrm { y }}$ = -0.206x + 2.097 
B)  $\hat { y }$ = 2.097x - 0.206 
C)  $\hat { \mathrm { y } }$ = 0.206x - 2.097 
D)  $\hat { \mathrm { y } }$ = -2.097x + 0.206

Question 17

Given the equation of a regression line is y = 3x - 1, what is the best predicted value for y given x = 4? Assume that the variables x and y have a significant correlation.

Accepted Answer

A) 11 
B) 13 
C) 1 
D) 6

Question 18

Calculate the coefficient of determination, given that the linear correlation coefficient, r, is -0.625. What does
this tell you about the explained variation and the unexplained variation of the data about the regression line?

Accepted Answer

The answer of Calculate the coefficient of determination, given that...

Question 19

The data below are the number of absences and the final grades of 9 randomly selected students from a statistics class. Find the standard error of estimate, $\mathrm { s } _ { \mathrm { e } }$ given that ? = -2.75X + 96.14. $$\begin{array} { l | c | c | c | c | c | c | c | c | c | } 
\text { Number of absences, } \mathrm { x } & 0 & 3 & 6 & 4 & 9 & 2 & 15 & 8 & 5 \
\hline \text { Final grade, } \mathrm { y } & 98 & 86 & 80 & 82 & 71 & 92 & 55 & 76 & 82
\end{array}$$

Accepted Answer

A) 1.799 
B) 4.531 
C) 3.876 
D) 2.160

Question 20

Find the standard error of estimate, $\mathrm { s } \mathrm { e }$ for the data below, given that $\hat { y } = - 1.885 x + 0.758$ $$\begin{array} { l | c | c | c | c | c | c | c | c | c | c | } 
\mathrm { x } & - 5 & - 3 & 4 & 1 & - 1 & - 2 & 0 & 2 & 3 & - 4 \
\hline \mathrm { y } & 11 & 6 & - 6 & - 1 & 3 & 4 & 1 & - 4 & - 5 & 8
\end{array}$$

Accepted Answer

A) 0.613 
B) 0.981 
C) 0.312 
D) 0.011

Exam 9: Correlation and Regression

Given a sample with r = -0.765 and n = 22, test the significance of the correlation r using α $\alpha$ = 0.02 and the claim $Q$ ρ = 0.

Given a sample with r = 0.321 and n = 30, test the significance of the correlation r using α $\alpha$ = 0.10 and the claim $\varrho$ ρ = 0.

Find the standard error of estimate, se, for the data below, given that y = 2x + 1. $\begin{array} { l | l | l | l | l | } \mathrm { x } & 1 & 2 & 3 & 4 \\\hline \mathrm { y } & 3 & 5 & 7 & 9\end{array}$

Given a sample with r = 0.823 and n = 10, test the significance of the correlation r using α $\alpha$ = 0.05 and the claim $Q$ ρ ρ= 0.

Find the equation of the regression line for the given data. $\begin{array} { l | c | c | c | c | c | c | c | c | c | c } \mathrm { x } & - 5 & - 3 & 4 & 1 & - 1 & - 2 & 0 & 2 & 3 & - 4 \\\hline \mathrm { y } & 11 & - 6 & 8 & - 3 & - 2 & 1 & 5 & - 5 & 6 & 7\end{array}$

Given the equation of a regression line is y = 3x - 1, what is the best predicted value for y given x = 4? Assume that the variables x and y have a significant correlation.

Calculate the coefficient of determination, given that the linear correlation coefficient, r, is -0.625. What does this tell you about the explained variation and the unexplained variation of the data about the regression line?

Exam 9: Correlation and Regression

Given a sample with r = -0.765 and n = 22, test the significance of the correlation r using α α\alphaα = 0.02 and the claim QQQ ρ = 0.

Given a sample with r = 0.321 and n = 30, test the significance of the correlation r using α α\alphaα = 0.10 and the claim ϱ\varrhoϱ ρ = 0.

Find the standard error of estimate, se, for the data below, given that y = 2x + 1. x1234y3579\begin{array} { l | l | l | l | l | } \mathrm { x } & 1 & 2 & 3 & 4 \\\hline \mathrm { y } & 3 & 5 & 7 & 9\end{array}xy​13​25​37​49​​

Given a sample with r = 0.823 and n = 10, test the significance of the correlation r using α α\alphaα = 0.05 and the claim QQQ ρ ρ= 0.

Given the equation of a regression line is y = 3x - 1, what is the best predicted value for y given x = 4? Assume that the variables x and y have a significant correlation.

Calculate the coefficient of determination, given that the linear correlation coefficient, r, is -0.625. What does this tell you about the explained variation and the unexplained variation of the data about the regression line?

Given a sample with r = -0.765 and n = 22, test the significance of the correlation r using α $\alpha$ = 0.02 and the claim $Q$ ρ = 0.

Given a sample with r = 0.321 and n = 30, test the significance of the correlation r using α $\alpha$ = 0.10 and the claim $\varrho$ ρ = 0.

Find the standard error of estimate, se, for the data below, given that y = 2x + 1. $\begin{array} { l | l | l | l | l | } \mathrm { x } & 1 & 2 & 3 & 4 \\\hline \mathrm { y } & 3 & 5 & 7 & 9\end{array}$

Given a sample with r = 0.823 and n = 10, test the significance of the correlation r using α $\alpha$ = 0.05 and the claim $Q$ ρ ρ= 0.