Question 1

Given the least squares regression line $\hat { y } = 2.48 - 1.63 x$ ,and a coefficient of determination of 0.81,the coefficient of correlation is:

Accepted Answer

A)  -0.66 
B)  0.81 
C)  -0.90 
D)  0.90 
A)  -0.66 
B)  0.81 
C)  -0.90 
D)  0.90

Question 2

{Sales and Experience Narrative} Predict with 95% confidence the monthly sales of a salesperson with 10 years of experience.

Accepted Answer

19.450 ± 3.818.Thus

Question 3

Wayne Newton Concert
At a recent Wayne Newton concert,a survey was conducted that asked a random sample of 20 people their age and how many concerts they have attended since the first of the year.The following data were collected:
 $$\begin{array}{l}
\begin{array} { | l | c c c c c c c c c c| } 
\hline \text { Age } & 62 & 57 & 40 & 49 & 67 & 54 & 43 & 65 & 54 & 41 \
\hline \text { Number af Concerts } & 6 & 5 & 4 & 3 & 5 & 5 & 2 & 6 & 3 & 1 \
\hline
\end{array}\\
\begin{array} { | l | c c c c c c c c c c | } 
\hline \text { Age } & 44 & 48 & 55 & 60 & 59 & 63 & 69 & 40 & 38 & 52 \
\hline \text { Number af Concerts } & 3 & 2 & 4 & 5 & 4 & 5 & 4 & 2 & 1 & 3 \
\hline
\end{array}
\end{array}$$ An Excel output follows:  
-{Wayne Newton Concert Narrative} Which interval in the previous two questions is narrower: the confidence interval estimate of the expected value of y or the prediction interval for the same given value of x (10 years)and same confidence level? Why?

Accepted Answer

The confidence interval estimate of the

Question 4

If the coefficient of correlation is 0.90,then the percentage of the variation in the dependent variable y that is explained by the variation in the independent variable x is:

Accepted Answer

A)  90% 
B)  81% 
C)  95% 
D)  None of these choices. 
A)  90% 
B)  81% 
C)  95% 
D)  None of these choices.

Question 5

Truck Speed and Gas Mileage
An economist wanted to analyze the relationship between the speed of a truck (x)and its gas mileage (y).As an experiment a truck is operated at several different speeds and for each speed the gas mileage is measured.These data are shown below.
 $$\begin{array} { | l | l l l l l l l | } 
\hline \text { Speed } & 25 & 35 & 45 & 50 & 60 & 65 & 70 \
\hline \text { Gas Mileage } & 40 & 39 & 37 & 33 & 30 & 27 & 25 \
\hline
\end{array}$$
-{Truck Speed and Gas Mileage Narrative} Calculate the Pearson coefficient of correlation.

Accepted Answer

The answer of Truck Speed and Gas Mileage
An economist wanted...

Question 6

Trivia Games & Education
An ardent fan of television game shows has observed that,in general,the more educated the contestant,the less money he or she wins.To test her belief she gathers data about the last eight winners of her favorite game show.She records their winnings in dollars and the number of years of education.The results are as follows.
 $$\begin{array} { | c | c | c | } 
\hline \text { Contestant } & \text { Years of Education } & \text { Winnings } \
\hline 1 & 11 & 750 \
2 & 15 & 400 \
3 & 12 & 600 \
4 & 16 & 350 \
5 & 11 & 800 \
0 & 16 & 300 \
7 & 13 & 650 \
8 & 14 & 400 \
\hline
\end{array}$$
-{Trivia Games & Education Narrative} Estimate the game winnings for a contestant with 15 years of education.

Accepted Answer

The answer of Trivia Games & Education
An ardent fan of...

Question 7

A regression analysis between sales (in $1,000)and advertising (in $1,000)resulted in the following least squares line: $\hat { y } = 80 + 5 x$ .This implies that:

Accepted Answer

A)  as advertising increases by $1,000,sales increases by $5,000. 
B)  as advertising increases by $1,000,sales increases by $80,000. 
C)  as advertising increases by $5,sales increases by $80. 
D)  None of these choices. 
A)  as advertising increases by $1,000,sales increases by $5,000. 
B)  as advertising increases by $1,000,sales increases by $80,000. 
C)  as advertising increases by $5,sales increases by $80. 
D)  None of these choices.

Question 8

The symbol for the population coefficient of correlation is:

Accepted Answer

A)  r 
B)  $\rho$ 
C)  r2 
D)  $\rho$2 
A)  r 
B)  $\rho$ 
C)  r2 
D)  $\rho$2

Question 9

Rock Concert Revenues
A financier whose specialty is investing in rock concerts has observed that,in general,concerts with "big-name" stars seem to generate more revenue than those concerts whose stars are less well known.To examine his belief he records the gross revenue and the payment (in $ millions)given to the two highest-paid performers in the concert for ten concert tours.
 $$\begin{array} { | c | c | c | } 
\hline \text { Concert } & \begin{array} { c } 
\text { Cost of Twa Highest Paid } \
\text { Perfarmers (\$mil) }
\end{array} & \begin{array} { c } 
\text { Grass Revenue } \
( \mathbf {\$ m i l } )
\end{array} \
\hline 1 & 5.3 & 48 \
2 & 7.2 & 65 \
3 & 1.3 & 18 \
4 & 1.8 & 20 \
5 & 3.5 & 31 \
6 & 2.6 & 26 \
7 & 8.0 & 73 \
8 & 2.4 & 23 \
9 & 4.5 & 39 \
10 & 0.7 & 58 \
\hline
\end{array}$$
-{Rock Concert Revenues Narrative} Conduct a test of the population slope to determine at the 5% significance level whether a positive linear relationship exists between payment to the two highest-paid performers and gross revenue.

Accepted Answer

H₀: @#LAT-DLM&₁ = 0 vs.H

Question 10

Graphically,a confidence interval for the mean of y is represented as two ____________________ lines.

Accepted Answer

The answer of Graphically,a confidence interval for the mean of...

Question 11

Another name for the residual term in a regression equation is random error.

Accepted Answer

A) True 
 B)False

Question 12

In a simple linear regression problem,the following sum of squares are produced: $$\sum \left( y _ { i } - \bar { y } \right) ^ { 2 } = 200$$ , $$\sum \left( \gamma _ { i } - \hat { y } _ { i } \right) ^ { 2 } = 50$$ ,and $$\sum \left( \tilde { y } _ { i } - \bar { y } \right) ^ { 2 } = 150$$ .The percentage of the variation in y that is explained by the variation in x is:

Accepted Answer

A)  25% 
B)  75% 
C)  33% 
D)  50% 
A)  25% 
B)  75% 
C)  33% 
D)  50%

Question 13

If the coefficient of determination is 0.975,then which of the following is true regarding the slope of the regression line?

Accepted Answer

A)  All we can tell is that it must be positive. 
B)  It must be 0.975. 
C)  It must be 0.987. 
D)  Cannot tell the sign or the value. 
A)  All we can tell is that it must be positive. 
B)  It must be 0.975. 
C)  It must be 0.987. 
D)  Cannot tell the sign or the value.

Question 14

In a simple linear regression model b1 is the ____________________ of the straight line.

Accepted Answer

Question 15

The residual ri is defined as the difference between the actual value yi and the estimated value $\tilde { \gamma } _ { i }$ .

Accepted Answer

A) True 
 B)False

Question 16

Cost of Textbooks
The editor of a higher education book publisher claims that a large part of the cost of books is the cost of paper.This implies that larger textbooks will cost more money.As an experiment to analyze the claim,a university student visits the bookstore and records the number of pages and the selling price of twelve randomly selected textbooks.These data are listed below.
 $$\begin{array} { | c | c | c | } 
\hline \text { Textbouk } & \text { Number af Peges } & \text { Selling Price (\$) } \
\hline 1 & 844 & 55 \
2 & 727 & 50 \
3 & 360 & 35 \
4 & 915 & 60 \
5 & 295 & 30 \
6 & 706 & 50 \
7 & 410 & 40 \
8 & 905 & 53 \
9 & 1058 & 65 \
10 & 865 & 54 \
11 & 677 & 42 \
12 & 912 & 58 \
\hline
\end{array}$$
-{Cost of Textbooks Narrative} Estimate the selling price for a 650 pages book.

Accepted Answer

The answer of Cost of Textbooks
The editor of a higher...

Question 17

U V's and Skin Cancer
A medical statistician wanted to examine the relationship between the amount of UV's (x)and incidence of skin cancer (y).As an experiment he found the number of skin cancers detected per 100,000 of population and the average daily sunshine in eight states around the country.These data are shown below.
 $\begin{array}{|l|cccccccc|}
\hline \text { Average Daily UV's } & 5 & 7 & 6 & 7 & 8 & 6 & 4 & 3 \
\hline \text { Skin Cancer per } 100,000 & 7 & 11 & 9 & 12 & 15 & 10 & 7 & 5\
\hline 
\end{array}$ 
-{Sales and Experience Narrative} Calculate the Pearson correlation coefficient.Interpret this result.

Accepted Answer

r = 0.9765.It has a positive s

Question 18

In a simple linear regression model b0 is the ____________________ of the straight line.

Accepted Answer

y-intercep

Question 19

You use a(n)____________________ interval whenever you want to estimate a one-time occurrence for a particular value of y when x is a given value.

Accepted Answer

The answer of You use a(n)____________________ interval whenever you want...

Question 20

Cost of Textbooks
The editor of a higher education book publisher claims that a large part of the cost of books is the cost of paper.This implies that larger textbooks will cost more money.As an experiment to analyze the claim,a university student visits the bookstore and records the number of pages and the selling price of twelve randomly selected textbooks.These data are listed below.
 $$\begin{array} { | c | c | c | } 
\hline \text { Textbouk } & \text { Number af Peges } & \text { Selling Price (\$) } \
\hline 1 & 844 & 55 \
2 & 727 & 50 \
3 & 360 & 35 \
4 & 915 & 60 \
5 & 295 & 30 \
6 & 706 & 50 \
7 & 410 & 40 \
8 & 905 & 53 \
9 & 1058 & 65 \
10 & 865 & 54 \
11 & 677 & 42 \
12 & 912 & 58 \
\hline
\end{array}$$
-{Cost of Textbooks Narrative} Draw a scatter diagram of the data.Comment on whether it appears that a linear model might be appropriate.

Accepted Answer

@#IMG-DLM& It appears that a l

Given the least squares regression line $\hat { y } = 2.48 - 1.63 x$ ,and a coefficient of determination of 0.81,the coefficient of correlation is:

{Sales and Experience Narrative} Predict with 95% confidence the monthly sales of a salesperson with 10 years of experience.

If the coefficient of correlation is 0.90,then the percentage of the variation in the dependent variable y that is explained by the variation in the independent variable x is:

A regression analysis between sales (in $1,000)and advertising (in $1,000)resulted in the following least squares line: $\hat { y } = 80 + 5 x$ .This implies that:

The symbol for the population coefficient of correlation is:

Graphically,a confidence interval for the mean of y is represented as two ____________________ lines.

Another name for the residual term in a regression equation is random error.

If the coefficient of determination is 0.975,then which of the following is true regarding the slope of the regression line?

In a simple linear regression model b₁ is the ____________________ of the straight line.

The residual r_i is defined as the difference between the actual value y_i and the estimated value $\tilde { \gamma } _ { i }$ .

In a simple linear regression model b₀ is the ____________________ of the straight line.

You use a(n)____________________ interval whenever you want to estimate a one-time occurrence for a particular value of y when x is a given value.

What Is Statistics

Graphical Descriptive Techniques I

Graphical Descriptive Techniques II

A: Numerical Descriptive Techniques

B: Numerical Descriptive Techniques

C: Numerical Descriptive Techniques

Data Collection and Sampling

Probability

A: Random Variables and Discrete Probability Distributions

B: Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Introduction to Estimation

Introduction to Hypothesis Testing

Inference About a Population

Inference About Comparing Two Populations

Analysis of Variance

Chi-Squared Tests

B: Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Statistics

Time-Series Analysis and Forecasting

Statistical Process Control

Decision Analysis

Conclusion

Filters

Exam 16: A: Simple Linear Regression and Correlation

Given the least squares regression line y^=2.48−1.63x\hat { y } = 2.48 - 1.63 xy^​=2.48−1.63x ,and a coefficient of determination of 0.81,the coefficient of correlation is:

{Sales and Experience Narrative} Predict with 95% confidence the monthly sales of a salesperson with 10 years of experience.

If the coefficient of correlation is 0.90,then the percentage of the variation in the dependent variable y that is explained by the variation in the independent variable x is:

A regression analysis between sales (in $1,000)and advertising (in $1,000)resulted in the following least squares line: y^=80+5x\hat { y } = 80 + 5 xy^​=80+5x .This implies that:

The symbol for the population coefficient of correlation is:

Graphically,a confidence interval for the mean of y is represented as two ____________________ lines.

Another name for the residual term in a regression equation is random error.

If the coefficient of determination is 0.975,then which of the following is true regarding the slope of the regression line?

In a simple linear regression model b1 is the ____________________ of the straight line.

The residual ri is defined as the difference between the actual value yi and the estimated value γ~i\tilde { \gamma } _ { i }γ~​i​ .

In a simple linear regression model b0 is the ____________________ of the straight line.

You use a(n)____________________ interval whenever you want to estimate a one-time occurrence for a particular value of y when x is a given value.

What Is Statistics

Graphical Descriptive Techniques I

Graphical Descriptive Techniques II

A: Numerical Descriptive Techniques

B: Numerical Descriptive Techniques

C: Numerical Descriptive Techniques

Data Collection and Sampling

Probability

A: Random Variables and Discrete Probability Distributions

B: Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Introduction to Estimation

Introduction to Hypothesis Testing

Inference About a Population

Inference About Comparing Two Populations

Analysis of Variance

Chi-Squared Tests

B: Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Statistics

Time-Series Analysis and Forecasting

Statistical Process Control

Decision Analysis

Conclusion

Filters

Given the least squares regression line $\hat { y } = 2.48 - 1.63 x$ ,and a coefficient of determination of 0.81,the coefficient of correlation is:

A regression analysis between sales (in $1,000)and advertising (in $1,000)resulted in the following least squares line: $\hat { y } = 80 + 5 x$ .This implies that:

In a simple linear regression model b₁ is the ____________________ of the straight line.

The residual r_i is defined as the difference between the actual value y_i and the estimated value $\tilde { \gamma } _ { i }$ .

In a simple linear regression model b₀ is the ____________________ of the straight line.