Question 1

For a regression analysis to be valid, the value of the error variable associated with any particular value of y is ____________________ of the value of the error variable associated with any other value of y.

Accepted Answer

The answer of For a regression analysis to be valid,...

Question 2

NARRBEGIN: Sales and Experience
Sales and Experience
The general manager of a chain of Designer stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief she records last month's sales (in $1,000s) and the years of experience of 10 randomly selected salespeople. These data are listed below. $$\begin{array} { | c | c | c | } 
\hline \text { Sales person } & \text { Years of Experience } & \text { Sales } \
\hline 1 & 0 & 7 \
2 & 2 & 9 \
3 & 10 & 20 \
4 & 3 & 15 \
5 & 8 & 18 \
6 & 5 & 14 \
7 & 12 & 20 \
8 & 7 & 17 \
9 & 20 & 30 \
10 & 15 & 25 \
\hline
\end{array}$$ NARREND
-{Sales and Experience Narrative} Estimate with 95% confidence the average monthly sales of all salespersons with 10 years of experience.

Accepted Answer

The answer of NARRBEGIN: Sales and Experience
Sales and Experience
The general...

Question 3

NARRBEGIN: Grateful Dead Concert
Grateful Dead Concert
At a recent Grateful Dead 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. It is suspected that older concert goers tend to go to more of his concerts in one year than younger concert goers. The data and analysis are shown below. $$\begin{array}{l}
\begin{array} { | l | c c c c c c c c c c | } 
\hline \text { Age } & 62 & 57 & 40 & 49 & 67 & 54 & 43 & 65 & 54 & 41 \
\hline \text { Number af Concerts } & 6 & 5 & 4 & 3 & 5 & 5 & 2 & 6 & 3 & 1 \
\hline
\end{array}\\
\begin{array} { | l | c c c c c c c c c c | } 
\hline \text { Age } & 44 & 48 & 55 & 60 & 59 & 63 & 69 & 40 & 38 & 52 \
\hline \text { Number of Concerts } & 3 & 2 & 4 & 5 & 4 & 5 & 4 & 2 & 1 & 3 \
\hline
\end{array}
\end{array}$$ An Excel output follows: SUMMARY OUTPUT
$\begin{array}{lc}
\hline {\text { Regression Statistics }} \
\hline \text { Multiple R } & 0.80203 \
\text { R Square } & 0.64326 \
\text { Adjusted R Square } & 0.62344 \
\text { Standard Error } & 0.93965 \
\text { Observations } & 20 \
\hline
\end{array}$

$\text { DESCRIPTIVE STATISTICS }$
$\begin{array}{lclc}
\hline{\text { AGe }}& & {\text { Concerts }} \
\hline \text { Mean } & 53 & \text { Mean } & 3.65 \
\text { Standard Error } & 2.1849 & \text { Standard Error } & 0.3424 \
\text { Standard Deviation } & 9.7711 & \text { Standard Deviation } & 1.5313 \
\text { Sample Variance } & 95.4737 & \text { Sample Variance } & 2.3447 \
\text { Count } & 20 & \text { Court } & 20 \
\hline
\end{array}$

$\text { SPEARMAN RANK CORRELATION COEFFICIENT }=0.8306$
$\begin{array}{l}
\text { ANOVA }\
\begin{array}{lccccc}
\hline & df & S S & M S & F & \text { Signficance F } \
\hline \text { Regression } & 1 & 28.65711 & 28.65711 & 32.45653 & 2.1082 E-05 \
\text { Residual } & 18 & 15.89289 & 0.88294 & & \
\text { Total } & 19 & 44.55 & & & \
\hline
\end{array}
\end{array}$
$\begin{array}{lcccccc}
\hline & \text { Coefficients Standard Error } & \text { tStat } & \text { p-value } & \text { Lower 95\% } & \text { Upper 95\% } \
\hline \text { Intercept } & -3.01152 & 1.18802 & -2.53491 & 0.02074 & -5.50746 & -0.5156 \
\text { Age } & 0.12569 & 0.02206 & 5.69706 & 0.00002 & 0.07934 & 0.1720 \
\hline
\end{array}$ NARREND
-{Grateful Dead Concert Narrative} Calculate the Pearson correlation coefficient and interpret.

Accepted Answer

The answer of NARRBEGIN: Grateful Dead Concert
Grateful Dead Concert
At a...

Question 4

In performing a regression analysis which of the following must be true about the distribution of the error variable?

Accepted Answer

A) The distribution is normal with mean zero. 
B) The errors associated with one y value are independent of errors associated with another y value. 
C) The standard deviation is constant for each value of x. 
D) All of these choices are true.

Question 5

Suppose the slope of a simple linear regression line between hours studying and exam score is 5. That means as ____________________ increases by one, ____________________ increases by 5.

Accepted Answer

The answer of Suppose the slope of a simple linear...

Question 6

If the value of the sum of squares for error SSE equals zero, then the coefficient of determination must equal zero.

Accepted Answer

A) True 
 B)False

Question 7

The standardized residual is defined as:

Accepted Answer

A) residual multiplied by the square root of the standard error of estimate. 
B) residual multiplied by the standard error of estimate. 
C) residual divided by the square of the standard error of estimate. 
D) residual divided by the standard error of estimate.

Question 8

Error terms that are correlated over time are said to be ____________________.

Accepted Answer

The answer of Error terms that are correlated over time...

Question 9

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...

Question 10

NARRBEGIN: Allman Brothers Concert
Allman Brothers Concert
At a recent Allman Brothers 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:
 $$\begin{array}{l}
\begin{array} { | l | c c c c c c c c c c | } 
\hline \text { Age } & 62 & 57 & 40 & 49 & 67 & 54 & 43 & 65 & 54 & 41 \
\hline \text { Number of Concerts } & 6 & 5 & 4 & 3 & 5 & 5 & 2 & 6 & 3 & 1 \
\hline
\
\hline \text { Age } & 44 & 48 & 55 & 60 & 59 & 63 & 69 & 40 & \text { 38 } & 52 \
\hline \text { Number of Concerts } & 3 & 2 & 4 & 5 & 4 & 5 & 4 & 2 & 1 & 3 \
\hline
\end{array}
\end{array}$$ An Excel output follows: $\begin{array} { l  } 
 \text { SUMMARY OUTPUT}&\text { DESCRIPTIVE STATISTICS }\
\begin{array}{lc}
\hline{\text { Reqression Statistics }} \
\hline \text { Mutiple R } & 0.80203 \
\text { R Square } & 0.64326 \
\text { Adjusted R Square } & 0.62344 \
\text { Standard Error } & 0.93965 \
\text { Observations } & 20 \
\hline
\end{array}&\begin{array}{lclc}
\hline {\text { Age }} &&{\text { Concerts }} \
\hline \text { Mean } & 53 & \text { Mean } & 3.65 \
\text { Standard Error } & 2.1849 & \text { Standard Error } & 0.3424 \
\text { Standard Deviation } & 9.7711 & \text { Standard Deviation } & 1.5313 \
\text { Sample Variance } & 95.4737 & \text { Sample Variance } & 2.3447 \
\text { Count } & 20 & \text { Count } & 20\\hline
\end{array}
\end{array}$
$\text { SPEARMAN RANK CORRELATION COEFFICIENT }=0.8306$
$\text { ANOVA }$
$\begin{array}{lccccc} 
\hline& d f & S S & M S & F & \text { Sianificance } F \
\hline \text { Regression } & 1 & 28.65711 & 28.65711 & 32.45653 & 2.1082 \mathrm{E}-05 \
\text { Residual } & 18 & 15.89289 & 0.88294 & & \
\text { Total } & 19 & 44.55 & & &\\hline
\end{array}$

$\begin{array}{lcccccc} 
\hline& \text { Coefficients } & \text { Standard Error } & \text { tStat } & \text { Pvalue } & \text { Lower 95\% } & \text { Upoer 95\% } \
\hline\text { Intercept } & -3.01152 & 1.18802 & -2.53491 & 0.02074 & -5.50746 & -0.5156 \
\text { Age } & 0.12569 & 0.02206 & 5.69706 & 0.00002 & 0.07934 & 0.1720\\hline
\end{array}$ NARREND
-{Allman Brothers Concert Narrative} Plot the least squares regression line on the scatter diagram.

Accepted Answer

The answer of NARRBEGIN: Allman Brothers Concert
Allman Brothers Concert
At a...

Question 11

In a regression problem, if the coefficient of determination is 0.95, this means that:

Accepted Answer

A) 95% of the y values are positive. 
B) 95% of the variation in y can be explained by the variation in x. 
C) 95% of the y values are predicted correctly by the model. 
D) None of these choices.

Question 12

If the standard error of estimate s$\varepsilon$ = 20 and n = 10, then the sum of squares for error, SSE, is:

Accepted Answer

A) 400 
B) 3,200 
C) 4,000 
D) 40,000

Question 13

NARRBEGIN: Game Winnings & Ed.Game Winnings & 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. $$\begin{array} { | c | c | c | } 
\hline \text { Contestant } & \text { Years of Education } & \text { Winnings } \
\hline 1 & 11 & 750 \
2 & 15 & 400 \
3 & 12 & 600 \
4 & 16 & 350 \
5 & 11 & 800 \
0 & 16 & 300 \
7 & 13 & 650 \
8 & 14 & 400 \
\hline
\end{array}$$ NARREND
-{Game Winnings & Education Narrative} Estimate with 95% confidence the average winnings of all contestants who have 10 years of education.

Accepted Answer

The answer of NARRBEGIN: Game Winnings & Ed.Game Winnings &...

Question 14

NARRBEGIN: Telemarketing Sales and E
Telemarketing Sales and Experience
The general manager of a telemarketing company believes that experience is the most important factor in determining the level of success of a telemarketer. To examine this belief she records last month's sales (in $1,000s) and the years of experience of 10 randomly selected telemarketers. These data are listed below. $$\begin{array} { | c | c | c | } 
\hline \text { Telemarketer } & \text { Years of Experience } & \text { Sales } \
\hline 1 & 0 & 7 \
2 & 2 & 9 \
3 & 10 & 20 \
4 & 3 & 15 \
5 & 8 & 18 \
6 & 5 & 14 \
7 & 12 & 20 \
8 & 7 & 17 \
9 & 20 & 30 \
10 & 15 & 25 \
\hline
\end{array}$$ NARREND
-{Telemarketer Sales and Experience Narrative} Use the predicted and actual values of y to calculate the residuals.

Accepted Answer

The answer of NARRBEGIN: Telemarketing Sales and E
Telemarketing Sales and...

Question 15

Consider the following data values of variables x and y. $$\begin{array} { | l | l c c c c c | } 
\hline \boldsymbol { x } & 2 & 4 & 6 & \text { g } & 10 & 13 \
\hline \boldsymbol { y } & 7 & 11 & 17 & 21 & 27 & 36 \
\hline
\end{array}$$ 
a.Determine the least squares regression line.
b.Find the predicted value of y for x = 9.
c.What does the value of the slope of the regression line tell you?

Accepted Answer

The answer of Consider the following data values of variables...

Question 16

NARRBEGIN: Theatre Revenues
Theatre Revenues
A financier whose specialty is investing in stage productions has observed that, in general, movies with "big-name" stars seem to generate more revenue than those plays 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 play for ten recently staged plays. $$\begin{array} { | c | c | c | } 
\hline \text { Play } & \begin{array} { c } 
\text { Cost of Two Highest Paid } \
\text { Performers (\$mil) }
\end{array} & \begin{array} { c } 
\text { Gross Revenue } \
( \mathbf { \$ m i l } )
\end{array} \
\hline 1 & 5.3 & 48 \
2 & 7.2 & 65 \
3 & 1.3 & 18 \
4 & 1.8 & 20 \
5 & 3.5 & 31 \
6 & 2.6 & 26 \
7 & 8.0 & 73 \
8 & 2.4 & 23 \
9 & 4.5 & 39 \
10 & 0.7 & 58 \
\hline
\end{array}$$ NARREND
-{Theatre Revenues Narrative} Are the two highest paid performers worth all the money paid for them? Comment using the statistical analyses you have done.

Accepted Answer

The answer of NARRBEGIN: Theatre Revenues
Theatre Revenues
A financier whose specialty...

Question 17

A regression analysis between sales (in $1000) and advertising (in $100) resulted in the following least squares line: $\hat { y } = 77 + 8 x$ . This implies that if advertising is $600, then the predicted amount of sales (in dollars) is $125,000.

Accepted Answer

A) True 
 B)False

Question 18

NARRBEGIN: Sales and Experience
Sales and Experience
The general manager of a chain of hardware stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief she records last month's sales (in $1,000s) and the years of experience of 10 randomly selected salespeople. These data are listed below. $$\begin{array} { | c | c | c | } 
\hline \text { Salesperson } & \text { Years of Exgperience } & \text { Sales } \
\hline 1 & 0 & 7 \
2 & 2 & 9 \
3 & 10 & 20 \
4 & 3 & 15 \
5 & 8 & 18 \
6 & 5 & 14 \
7 & 12 & 20 \
8 & 7 & 17 \
9 & 20 & 30 \
10 & 15 & 25 \
\hline
\end{array}$$ NARREND
-{Sales and Experience Narrative} Calculate the Pearson correlation coefficient. Interpret this result.

Accepted Answer

The answer of NARRBEGIN: Sales and Experience
Sales and Experience
The general...

Question 19

There is more error in estimating a mean value of y as opposed to predicting an individual value of y.

Accepted Answer

A) True 
 B)False

Question 20

A prediction interval is used when we want to predict a one-time occurrence for a particular value of y when the independent variable is a given x value.

Accepted Answer

A) True 
 B)False

Exam 16: Simple Linear Regression and Correlation

For a regression analysis to be valid, the value of the error variable associated with any particular value of y is ____________________ of the value of the error variable associated with any other value of y.

In performing a regression analysis which of the following must be true about the distribution of the error variable?

Suppose the slope of a simple linear regression line between hours studying and exam score is 5. That means as increases by one, increases by 5.

If the value of the sum of squares for error SSE equals zero, then the coefficient of determination must equal zero.

The standardized residual is defined as:

Error terms that are correlated over time are said to be ____________________.

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.

In a regression problem, if the coefficient of determination is 0.95, this means that:

If the standard error of estimate s_{$\varepsilon$} = 20 and n = 10, then the sum of squares for error, SSE, is:

A regression analysis between sales (in $1000) and advertising (in $100) resulted in the following least squares line: $\hat { y } = 77 + 8 x$ . This implies that if advertising is $600, then the predicted amount of sales (in dollars) is $125,000.

There is more error in estimating a mean value of y as opposed to predicting an individual value of y.

A prediction interval is used when we want to predict a one-time occurrence for a particular value of y when the independent variable is a given x value.

Exam 16: Simple Linear Regression and Correlation

For a regression analysis to be valid, the value of the error variable associated with any particular value of y is ____________________ of the value of the error variable associated with any other value of y.

In performing a regression analysis which of the following must be true about the distribution of the error variable?

Suppose the slope of a simple linear regression line between hours studying and exam score is 5. That means as ____________________ increases by one, ____________________ increases by 5.

If the value of the sum of squares for error SSE equals zero, then the coefficient of determination must equal zero.

The standardized residual is defined as:

Error terms that are correlated over time are said to be ____________________.

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.

In a regression problem, if the coefficient of determination is 0.95, this means that:

If the standard error of estimate s ε\varepsilonε = 20 and n = 10, then the sum of squares for error, SSE, is:

A regression analysis between sales (in $1000) and advertising (in $100) resulted in the following least squares line: y^=77+8x\hat { y } = 77 + 8 xy^​=77+8x . This implies that if advertising is $600, then the predicted amount of sales (in dollars) is $125,000.

There is more error in estimating a mean value of y as opposed to predicting an individual value of y.

A prediction interval is used when we want to predict a one-time occurrence for a particular value of y when the independent variable is a given x value.

Suppose the slope of a simple linear regression line between hours studying and exam score is 5. That means as increases by one, increases by 5.

If the standard error of estimate s_{$\varepsilon$} = 20 and n = 10, then the sum of squares for error, SSE, is:

A regression analysis between sales (in $1000) and advertising (in $100) resulted in the following least squares line: $\hat { y } = 77 + 8 x$ . This implies that if advertising is $600, then the predicted amount of sales (in dollars) is $125,000.