Deck 16: Simple Linear Regression and Correlation

Question 1

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

Answer 1

histogram

Question 2

The variance of the error variable is required to be constant.When this requirement is satisfied, the condition is called homoscedasticity.

Answer 2

True

Question 3

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

Answer 3

heteroscedasticity

Question 4

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 5

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

Question 6

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

Question 7

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 8

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 9

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

Question 10

When the variance of the error variable is a constant no matter what the value of x is, this condition is called:

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

Question 11

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

Question 12

The variance of the error variable is required to be constant.When this requirement is violated, the condition is called heteroscedasticity.

Question 13

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

Question 14

The least squares method requires that the variance of the error variable 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 https://d2lvgg3v3hfg70.cloudfront.net/TB7453/.

Question 15

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

Question 16

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

Question 17

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

Question 18

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

Question 19

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 20

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

Question 21

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.

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

Question 22

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:
{Marc Anthony Concert Narrative} Use the regression equation to determine the predicted values of y.

Question 23

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:
{Marc Anthony Concert Narrative} Use the predicted values and the actual values of y to calculate the residuals.

Question 24

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.

{Game Winnings & Education Narrative} Identify possible outliers.

Question 25

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.


-{Game Winnings & Education Narrative} Use the predicted and actual values of y to calculate the residuals.

Question 26

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:
{Marc Anthony Concert Narrative} Plot the residuals against the predicted values .

Question 27

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.


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

Question 28

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.

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

Question 29

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

Question 30

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.

{Comedy Shows Revenues Narrative} Use the regression equation to determine the predicted values of y.

Question 31

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.

{Comedy Shows Revenues Narrative} Plot the residuals against the predicted values of y.What does the graph tell you?

Question 32

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.

{Telemarketer Sales and Experience Narrative} Identify possible outliers.

Question 33

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.


-{Game Winnings & Education Narrative} Compute the standardized residuals.

Question 34

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.

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

Question 35

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:
{Marc Anthony Concert Narrative} Does it appear that heteroscedasticity is a problem? Explain.

Question 36

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

Question 37

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

Question 38

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.


-{Telemarketer Sales and Experience Narrative} Use the predicted and actual values of y to calculate the residuals.

Question 39

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.


-{Telemarketer Sales and Experience Narrative} Compute the standardized residuals.

Question 40

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.

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

Question 41

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:

{Oil Quality and Price Narrative} Use the regression equation to determine the predicted values of y.

Question 42

A regression analysis between weight (y in pounds) and height (x in inches) resulted in the following least squares line: .This implies that if the height is increased by 1 inch, the weight is expected to increase by an average of 6 pounds.

Question 43

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:
{Marc Anthony Concert Narrative} Draw a histogram of the residuals.

Question 44

A simple linear regression equation is given by .The point estimate of y when x = 4 is 20.45.

Question 45

A direct relationship between an independent variable x and a dependent variably y means that the variables x and y increase or decrease together.

Question 46

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:

{Oil Quality and Price Narrative} Does it appear that the errors are normally distributed? Explain.

Question 47

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:


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

Question 48

A regression analysis between sales (in $) and advertising (in $) resulted in the following least squares line: .This implies that an increase of $1 in advertising is associated with an increase of $60 in sales.

Question 49

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:

{Oil Quality and Price Narrative} Identify possible outliers.

Question 50

The method of least squares requires that the sum of the squared deviations between actual y values in the scatter diagram and y values predicted by the regression line be minimized.

Question 51

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:

{Oil Quality and Price Narrative} Plot the residuals against the predicted values .

Question 52

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:
{Marc Anthony Concert Narrative} Does it appear that the errors are normally distributed? Explain.

Question 53

The vertical spread of the data points about the regression line is measured by the y-intercept.

Question 54

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:
{Marc Anthony Concert Narrative} Identify possible outliers.

Question 55

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:

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

Question 56

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:

{Oil Quality and Price Narrative} Draw a histogram of the residuals.

Question 57

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:

{Oil Quality and Price Narrative} Does it appear that heteroscedasticity is a problem? Explain.

Question 58

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:


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

Question 59

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

Question 60

An inverse relationship between an independent variable x and a dependent variably y means that as x increases, y decreases, and vice versa.

Question 61

If an estimated regression line has a y-intercept of 10 and a slope of 4, then when x = 2 the actual value of y is:

A) 18
B) 15
C) 14
D) unknown.

Question 62

In the simple linear regression model, the slope represents the:

A) value of y when x = 0.
B) average change in y per unit change in x.
C) value of x when y = 0.
D) average change in x per unit change in y.

Question 63

The regression line has been fitted to the data points (4, 8), (2, 5), and (1, 2).The sum of the squared residuals will be:

A) 7
B) 15
C) 8
D) 22

Question 64

A regression analysis between sales (in $1,000) and advertising (in $1,000) resulted in the following least squares line: .This implies that:

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 65

A regression analysis between sales (in $1000) and advertising (in $100) resulted in the following least squares line: .This implies that if advertising is $800, then the predicted amount of sales (in dollars) is:

A) $4875
B) $123,000
C) $487,500
D) $12,300

Question 66

The residuals are observations of the error variable https://d2lvgg3v3hfg70.cloudfront.net/TB7453/.Consequently, the minimized sum of squared deviations is called the sum of squares for error, denoted SSE.

Question 67

The first-order linear model is sometimes called the simple linear regression model.

Question 68

In regression analysis, the residuals represent the:

A) difference between the actual y values and their predicted values.
B) difference between the actual x values and their predicted values.
C) square root of the slope of the regression line.
D) change in y per unit change in x.

Question 69

In the first order linear regression model, the population parameters of the y-intercept and the slope are estimated, respectively, by:

A) b₀ and b₁
B) b₀ and $\beta$ ₁
C) $\beta$ ₀ and b₁
D) $\beta$ ₀ and $\beta$ ₁

Question 70

The residual r_i is defined as the difference between the actual value y_i and the estimated value .

Question 71

To create a deterministic model, we start with a probabilistic model that approximates the relationship we want to model.

Question 72

Given the least squares regression line :

A) the relationship between x and y is positive.
B) the relationship between x and y is negative.
C) as x decreases, so does y.
D) None of these choices.

Question 73

A regression analysis between weight (y in pounds) and height (x in inches) resulted in the following least squares line: .This implies that if the height is increased by 1 inch, the weight, on average, is expected to:

A) increase by 1 pound.
B) decrease by 1 pound.
C) increase by 5 pounds.
D) increase by 24 pounds.

Question 74

The regression line has been fitted to the data points (4, 11), (2, 7), and (1, 5).The sum of squares for error will be 10.0.

Question 75

Which of the following techniques is used to predict the value of one variable on the basis of other variables?

A) Correlation analysis
B) Coefficient of correlation
C) Covariance
D) Regression analysis

Question 76

If cov(x, y) = 7.5075 and , then the sample slope coefficient is 2.145.

Question 77

In the simple linear regression model, the y-intercept represents the:

A) change in y per unit change in x.
B) change in x per unit change in y.
C) value of y when x = 0.
D) value of x when y = 0.

Question 78

A regression analysis between sales (in $1000) and advertising (in $100) resulted in the following least squares line: .This implies that if advertising is $600, then the predicted amount of sales (in dollars) is $125,000.

Question 79

Statisticians have shown that sample y-intercept b₀ and sample slope coefficient b₁ are unbiased estimators of the population regression parameters $\beta$ ₀ and $\beta$ ₁, respectively.

Question 80

The residual is defined as the difference between:

A) the actual value of y and the estimated value of y
B) the actual value of x and the estimated value of x
C) the actual value of y and the estimated value of x
D) the actual value of x and the estimated value of y