Deck 16: Simple Linear Regression and Correlation

Question 1

The least squares method requires that the variance $\sigma _ { z } ^ { 2 }$ of the error variable $\varepsilon$ is a constant no matter what the value of x is. When this requirement is violated, the condition is called:

A)heteroscedasticity.
B)homoscedasticity.
C)influential observation.
D)non-independence of $\varepsilon$ .

Answer 1

heteroscedasticity.

Question 2

When the variance $\sigma _ { z } ^ { 2 }$ of the error variable $\varepsilon$ is a constant no matter what the value of x is, this condition is called:

A)heterocausality.
B)homoscedasticity.
C)homocausality.
D)heteroscedasticity.

Answer 2

homoscedasticity.

Question 3

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

Answer 3

autocorrelated
serially correlated

Question 4

Error terms that are autocorrelated ____________________ (are/are not) independent.

Question 5

We check for normality by drawing a pie chart of the residuals.

Question 6

If you take the residuals, subtract their mean and divide by their standard deviation, the result is called the ____________________ residuals.

Question 7

We check for normality by drawing a(n) ____________________ of the residuals.

Question 8

If the plot of the residuals vs. the predicted values resembles a straight line with non-zero slope, then the regression line fits well.

Question 9

We standardize residuals by subtracting their mean and dividing by their variance.

Question 10

If the plot of the residuals is fan shaped, which assumption of regression analysis (if any) is violated?

A)No assumptions are violated.
B)Independence of errors
C)Homoscedasticity
D)Normality

Question 11

The plot of residuals vs. predicted values should show no patterns if the conditions of a regression analysis are met.

Question 12

The variance of the error variable $\sigma _ { z } ^ { 2 }$ is required to be constant. When this requirement is satisfied, the condition is called homoscedasticity.

Question 13

Data that exhibit an autocorrelation effect violate the regression assumption of independence.

Question 14

The standardized residual is defined as:

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 15

An outlier is an observation that is unusually small or unusually large.

Question 16

When the error variable does not have constant variance, this condition is called ____________________.

Question 17

One method of diagnosing heteroscedasticity is to plot the residuals against the predicted values of y, then look for a change in the spread of the plotted values.

Question 18

The variance of the error variable $\sigma _ { z } ^ { 2 }$ is required to be constant. When this requirement is violated, the condition is called heteroscedasticity.

Question 19

The spread in the residuals should increase as the predicted value of y increases.

Question 20

If the variance of the errors is constant for each predicted y value, the condition is called ____________________.

Question 21

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} Compute the standardized residuals.

Question 22

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.

Question 23

We can often detect autocorrelation by graphing the residuals against ____________________.

Question 24

NARRBEGIN: Marc Anthony Concert
Marc Anthony Concert
At a recent Marc Anthony 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:
An Excel output follows: NARREND
{Marc Anthony Concert Narrative} Use the regression equation to determine the predicted values of y.

Question 25

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. NARREND
{Game Winnings & Education Narrative} Use the regression equation to determine the predicted values of y.

Question 26

NARRBEGIN: Comedy Shows Revenues
Comedy Shows Revenues
A financier whose specialty is investing in comedy shows has observed that, in general, shows with "big-name" stars seem to generate more revenue than those shows 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 comedians in the show for ten recently staged shows. NARREND
{Comedy Shows Revenues Narrative} Plot the residuals against the predicted values of y. What does the graph tell you?

Question 27

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. NARREND
{Telemarketer Sales and Experience Narrative} Plot the residuals against the predicted values of y. What does the graph tell you?

Question 28

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} Compute the standardized residuals.

Question 29

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. NARREND
{Telemarketer Sales and Experience Narrative} Identify possible outliers.

Question 30

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. NARREND
{Game Winnings & Education Narrative} Identify possible outliers.

Question 31

NARRBEGIN: Marc Anthony Concert
Marc Anthony Concert
At a recent Marc Anthony 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:
An Excel output follows: NARREND
{Marc Anthony Concert Narrative} Does it appear that heteroscedasticity is a problem? Explain.

Question 32

NARRBEGIN: Comedy Shows Revenues
Comedy Shows Revenues
A financier whose specialty is investing in comedy shows has observed that, in general, shows with "big-name" stars seem to generate more revenue than those shows 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 comedians in the show for ten recently staged shows. NARREND
{Comedy Shows Revenues Narrative} Use the regression equation to determine the predicted values of y.

Question 33

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. NARREND
{Game Winnings & Education Narrative} Plot the residuals against the predicted values . What does the graph tell you?

Question 34

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. NARREND
{Telemarketer Sales and Experience Narrative} Use the regression equation to determine the predicted values of y.

Question 35

NARRBEGIN: Marc Anthony Concert
Marc Anthony Concert
At a recent Marc Anthony 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:
An Excel output follows: NARREND
{Marc Anthony Concert Narrative} Plot the residuals against the predicted values .

Question 36

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} Use the predicted and actual values of y to calculate the residuals.

Question 37

A(n) ____________________ is an observation that is unusually small or large.

Question 38

NARRBEGIN: Marc Anthony Concert
Marc Anthony Concert
At a recent Marc Anthony 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:
An Excel output follows: NARREND
{Marc Anthony Concert Narrative} Use the predicted values and the actual values of y to calculate the residuals.

Question 39

NARRBEGIN: Comedy Shows Revenues
Comedy Shows Revenues
A financier whose specialty is investing in comedy shows has observed that, in general, shows with "big-name" stars seem to generate more revenue than those shows 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 comedians in the show for ten recently staged shows. $$\begin{array} { | c | c | c | } \hline \text { Show } & \begin{array} { c } \text { Cost of Two Highest } \\\text { Paid Comedian (\$mil) }\end{array} & \begin{array} { c } \text { Gross Revenue } \\( \mathbf { 4 m i l } )\end{array} \\\hline 1 & 5.3 & 48 \\2 & 7.2 & 65 \\3 & 1.3 & 18 \\4 & 1.8 & 20 \\5 & 3.5 & 31 \\6 & 2.6 & 26 \\7 & 8.0 & 73 \\8 & 2.4 & 23 \\9 & 4.5 & 39 \\10 & 0.7 & 58 \\\hline\end{array}$$ NARREND

-{Comedy Shows Revenues Narrative} Use the predicted and actual values of y to calculate the residuals.

Question 40

If a single point has a large impact on the equation of the regression line, it is called a(n) ____________________ point.

Question 41

The confidence interval estimate of the expected value of y will be narrower than the prediction interval for the same given value of x and confidence level. This is because there is less error in estimating a mean value as opposed to predicting an individual value.

Question 42

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.

Question 43

A confidence interval estimate for the expected value of y will always be wider than the prediction interval for the same given value of x and the same confidence level.

Question 44

NARRBEGIN: Marc Anthony Concert
Marc Anthony Concert
At a recent Marc Anthony 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:
An Excel output follows: NARREND
{Marc Anthony Concert Narrative} Identify possible outliers.

Question 45

A confidence interval (as opposed to a prediction interval) is used to estimate the long-run average value of y.

Question 46

NARRBEGIN: Oil Quality and Price
Oil Quality and Price
Quality of oil is measured in API gravity degrees--the higher the degrees API, the higher the quality. The table shown below is produced by an expert in the field who believes that there is a relationship between quality and price per barrel. $$\begin{array} { | c | c | } \hline \text { Oil degrees API } & \text { Price per barrel (in \$) } \\\hline 27.0 & 12.02 \\28.5 & 12.04 \\30.8 & 12.32 \\31.3 & 12.27 \\31.9 & 12.49 \\34.5 & 12.70 \\34.0 & 12.80 \\34.7 & 13.00 \\37.0 & 13.00 \\41.0 & 13.17 \\41.0 & 13.19 \\38.8 & 13.22 \\39.3 & 13.27 \\\hline\end{array}$$ A partial Minitab output follows:
$$\begin{array}{l}\text { Dascriptive atafistics }\\\begin{array} { l l l l l } \text { Variable } & \mathrm { N } & \text { Mear } & \text { StDev } & \text { SE Mear } \\\text { Degrees } & 13 & 34.60 & 4.613 & 1.280 \\\text { Price } & 13 & 1270 & 0.757 & 0.127\end{array}\end{array}$$
$\begin{array}{lll} \text { Bavarifinces }\\& \text { Degrees } & \text { Price } \\\text { Degrees } & 21.281667 & \\\text { Price } & 2.026750 & 0208837\end{array}$ $$\begin{array}{l}\text { Rederatian Antalyis }\\\begin{array} { l l l r } \text { predictor } & \text { Coef } & \text { StDev } & \text { T } & \text { P} \\\text { Constant } & 9.4349 & 0.2867 & 32.91&0.000 \\\text { Degrees } & 0.095235 &0.008220 & 11.59&0.000\\\end{array}\\S = 0 .1314 \quad R - S q = 92.46 \% \quad R - S q ( a d ) = 91.7 \%\end{array}$$ $$\begin{array}{l}\text { Analysis of Variance }\\\begin{array} { l l r r r } \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } &\text {P} \\\text { Regeression } & 1 & 2.3162 & 2.3162 & 134.24&0.000 \\\text { Residual Error } & 11 & 0.1898 & 0.0173 & \\\text { Total } & 12 & 2.5060 & &\end{array}\end{array}$$ NARREND

-{Oil Quality and Price Narrative} Use the predicted values and the actual values of y to calculate the residuals.

Question 47

NARRBEGIN: Oil Quality and Price
Oil Quality and Price
Quality of oil is measured in API gravity degrees--the higher the degrees API, the higher the quality. The table shown below is produced by an expert in the field who believes that there is a relationship between quality and price per barrel. A partial Minitab output follows:
NARREND
{Oil Quality and Price Narrative} Does it appear that the errors are normally distributed? Explain.

Question 48

The confidence interval estimate of the expected value of y will be wider than the prediction interval for the same given value of x and confidence level. This is because there is more error in estimating a mean value as opposed to predicting an individual value.

Question 49

NARRBEGIN: Marc Anthony Concert
Marc Anthony Concert
At a recent Marc Anthony 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:
An Excel output follows: NARREND
{Marc Anthony Concert Narrative} Draw a histogram of the residuals.

Question 50

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

$\begin{array}{lcccccc} & \text { Coefficients} & \text { Standard Error } & \text { t Stat } & \text { Rvale } & \text { Lower 95\% } & \text { Upoer 95\% } \\\hline \text { Intercept } & -3.01152 & 1.18802 & -2.53491 & 0.02074 & -5.50746 & -0.5156 \\\text { Age } & 0.12569 & 0.02206 & 5.69706 & 0.00002 & 0.07934 & 0.1720 \\\hline\end{array}$ NARREND

-{Marc Anthony Concert Narrative} Use the residuals to compute the standardized residuals.

Question 51

NARRBEGIN: Oil Quality and Price
Oil Quality and Price
Quality of oil is measured in API gravity degrees--the higher the degrees API, the higher the quality. The table shown below is produced by an expert in the field who believes that there is a relationship between quality and price per barrel. A partial Minitab output follows:
NARREND
{Oil Quality and Price Narrative} Does it appear that heteroscedasticity is a problem? Explain.

Question 52

NARRBEGIN: Oil Quality and Price
Oil Quality and Price
Quality of oil is measured in API gravity degrees--the higher the degrees API, the higher the quality. The table shown below is produced by an expert in the field who believes that there is a relationship between quality and price per barrel. A partial Minitab output follows:
NARREND
{Oil Quality and Price Narrative} Identify possible outliers.

Question 53

NARRBEGIN: Oil Quality and Price
Oil Quality and Price
Quality of oil is measured in API gravity degrees--the higher the degrees API, the higher the quality. The table shown below is produced by an expert in the field who believes that there is a relationship between quality and price per barrel. A partial Minitab output follows:
NARREND
{Oil Quality and Price Narrative} Plot the residuals against the predicted values .

Question 54

NARRBEGIN: Marc Anthony Concert
Marc Anthony Concert
At a recent Marc Anthony 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:
An Excel output follows: NARREND
{Marc Anthony Concert Narrative} Does it appear that the errors are normally distributed? Explain.

Question 55

NARRBEGIN: Oil Quality and Price
Oil Quality and Price
Quality of oil is measured in API gravity degrees--the higher the degrees API, the higher the quality. The table shown below is produced by an expert in the field who believes that there is a relationship between quality and price per barrel. $$\begin{array} { | c | c | } \hline \text { Oil degrees API } & \text { Price per barrel (in \$) } \\\hline 27.0 & 12.02 \\28.5 & 12.04 \\30.8 & 12.32 \\31.3 & 12.27 \\31.9 & 12.49 \\34.5 & 12.70 \\34.0 & 12.80 \\34.7 & 13.00 \\37.0 & 13.00 \\41.0 & 13.17 \\41.0 & 13.19 \\38.8 & 13.22 \\39.3 & 13.27 \\\hline\end{array}$$ A partial Minitab output follows:
$$\begin{array}{l}\text { Dascriptive atafistics }\\\begin{array} { l l l l l } \text { Variable } & \mathrm { N } & \text { Mear } & \text { StDev } & \text { SE Mear } \\\text { Degrees } & 13 & 34.60 & 4.613 & 1.280 \\\text { Price } & 13 & 1270 & 0.757 & 0.127\end{array}\end{array}$$
$\begin{array}{lll} \text { Bavarifinces }\\& \text { Degrees } & \text { Price } \\\text { Degrees } & 21.281667 & \\\text { Price } & 2.026750 & 0208837\end{array}$ $$\begin{array}{l}\text { Rederatian Antalyis }\\\begin{array} { l l l r } \text { predictor } & \text { Coef } & \text { StDev } & \text { T } & \text { P} \\\text { Constant } & 9.4349 & 0.2867 & 32.91&0.000 \\\text { Degrees } & 0.095235 &0.008220 & 11.59&0.000\\\end{array}\\S = 0 .1314 \quad R - S q = 92.46 \% \quad R - S q ( a d ) = 91.7 \%\end{array}$$ $$\begin{array}{l}\text { Analysis of Variance }\\\begin{array} { l l r r r } \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } &\text {P} \\\text { Regeression } & 1 & 2.3162 & 2.3162 & 134.24&0.000 \\\text { Residual Error } & 11 & 0.1898 & 0.0173 & \\\text { Total } & 12 & 2.5060 & &\end{array}\end{array}$$ NARREND

-{Oil Quality and Price Narrative} Use the residuals to compute the standardized residuals.

Question 56

NARRBEGIN: Oil Quality and Price
Oil Quality and Price
Quality of oil is measured in API gravity degrees--the higher the degrees API, the higher the quality. The table shown below is produced by an expert in the field who believes that there is a relationship between quality and price per barrel. A partial Minitab output follows:
NARREND
{Oil Quality and Price Narrative} Use the regression equation to determine the predicted values of y.

Question 57

The graph of a confidence interval for the expected value of y is represented by two parallel lines, one on either side of the regression line.

Question 58

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

Question 59

NARRBEGIN: Oil Quality and Price
Oil Quality and Price
Quality of oil is measured in API gravity degrees--the higher the degrees API, the higher the quality. The table shown below is produced by an expert in the field who believes that there is a relationship between quality and price per barrel. A partial Minitab output follows:
NARREND
{Oil Quality and Price Narrative} Draw a histogram of the residuals.

Question 60

The prediction interval for a particular value of y is always wider than the confidence interval for mean value of y, given the same data set, x value, and confidence level.

Question 61

The point where confidence intervals and prediction intervals do best is $( \bar { x } , \bar { y } )$ .

Question 62

Graphically, a prediction interval is represented as two ____________________ lines.

Question 63

If you take a particular x value and plug it into a regression line equation, the result is a(n) ____________________ estimate for y.

Question 64

In order to estimate with 95% confidence the expected value of y for a given value of x in a simple linear regression problem, a random sample of 10 observations is taken. Which of the following t-table values listed below would be used?

A)2.228
B)2.306
C)1.860
D)1.812

Question 65

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. NARREND
{Sales and Experience 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?

Question 66

The graph of a confidence interval for the expected value of y is represented by two curved lines, one on either side of the regression line.

Question 67

There is ____________________ error in estimating a mean than in predicting an individual value.

Question 68

In order to predict with 90% confidence the expected value of y for a given value of x in a simple linear regression problem, a random sample of 10 observations is taken. Which of the following t-table values listed below would be used?

A)1.812
B)1.860
C)2.228
D)2.306

Question 69

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} Predict with 95% confidence the monthly sales of a salesperson with 10 years of experience.

Question 70

A prediction interval for a particular y is always ____________________ than a confidence interval for the mean of y.

Question 71

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.

Question 72

A medical statistician wanted to examine the relationship between the amount of sunshine (x) and incidence of skin discolorations (y). As an experiment he found the number of skin discolorations detected per 100,000 of population and the average daily sunshine in eight counties around the country. These data are shown below. $$\begin{array} { | l | c c c c c c c c| } \hline \text { Average Daily Sunshine } & 5 & 7 & 6 & 7 & 8 & 6 & 4 & 3 \\\hline \text { Slin Disculorations per 100,000 } & 7 & 11 & 9 & 12 & 15 & 10 & 7 & 5 \\\hline\end{array}$$ Predict with 95% confidence the skin discolorations per 100,000 in a county with a daily average of 6.5 hours of sunshine.

Question 73

The farther a given value of x is from the mean of x, the ____________________ the estimated error becomes.

Question 74

The confidence interval estimate of the expected value of y for a given value x, compared to the prediction interval of y for the same given value of x and confidence level, will be:

A)wider.
B)the same.
C)narrower.
D)impossible to know.

Question 75

In order to predict with 80% confidence the expected value of y for a given value of x in a simple linear regression problem, a random sample of 15 observations is taken. Which of the following t-table values listed below would be used?

A)1.350
B)1.771
C)2.160
D)2.650

Question 76

You use a(n) ____________________ interval whenever you want to estimate the mean of y when x is a given value.

Question 77

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

Question 78

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.

Question 79

The width of the confidence interval estimate for the predicted value of y depends on

A)the standard error of the estimate
B)the value of x for which the prediction is being made
C)the sample size
D)All of these choices are true.

Question 80

In order to predict with 98% confidence the expected value of y for a given value of x in a simple linear regression problem, a random sample of 15 observations is taken. Which of the following t-table values listed below would be used?

A)1.350
B)1.771
C)2.160
D)2.650