Question 1

If the coefficient of correlation is -0.60, then the coefficient of determination is:

Accepted Answer

A)  -0.60 
B)  -0.36 
C)  0.36 
D)  0.77

Question 2

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.

Accepted Answer

A) True 
 B)False

Question 3

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.
 
-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 Theatre Revenues: A financier whose specialty is...

Question 4

If the error variable $\varepsilon$ is normally distributed, the test statistic for testing H0: $\beta$1 = 0 has a Student t-distribution with n - 2 degrees of freedom.

Accepted Answer

A) True 
 B)False

Question 5

When the actual values y of a dependent variable and the corresponding predicted values  are the same, the standard error of estimate s$\varepsilon$ will be 0.0.

Accepted Answer

A) True 
 B)False

Question 6

Car Speed and Gas Mileage: An economist wanted to analyze the relationship between the speed of a car (x) and its gas mileage (y). As an experiment a car is operated at several different speeds and for each speed the gas mileage is measured. These data are shown below.
 
-What does the coefficient of correlation tell you about the direction and strength of the relationship between the two variables?

Accepted Answer

The answer of Car Speed and Gas Mileage: An economist...

Question 7

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

Accepted Answer

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

Question 8

Income and Education: A professor of economics wants to study the relationship between income (y in $1000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
 
-Draw a scatter diagram of the data. Comment on whether it appears that a linear model might be appropriate.

Accepted Answer

The answer of Income and Education: A professor of economics...

Question 9

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

Accepted Answer

A) True 
 B)False

Question 10

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.
  Predict with 95% confidence the skin discolorations per 100,000 in a county with a daily average of 6.5 hours of sunshine.

Accepted Answer

The answer of A medical statistician wanted to examine the...

Question 11

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.

Accepted Answer

A) True 
 B)False

Question 12

Sales and Experience: The general manager of a chain of department 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.
 
-Determine the least squares regression line.

Accepted Answer

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

Question 13

If we are interested in determining whether two variables are linearly related, it is necessary to:

Accepted Answer

A)  perform the t-test of the slope $\beta$1. 
B)  perform the t-test of the coefficient of correlation $\rho$. 
C)  either a or b since they are identical. 
D)  None of these choices.

Question 14

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

Accepted Answer

The answer of In a simple linear regression model b₁...

Question 15

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

Accepted Answer

A) True 
 B)False

Question 16

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

Accepted Answer

A) True 
 B)False

Question 17

Accidents and Rain
A statistician investigating the relationship between the amount of rain (in inches) and the number of automobile accidents gathered data on accidents in her city for 10 randomly selected days throughout the year. The results are shown below.
 
-Estimate the number of accidents in a day with 0.25 inches of rain.

Accepted Answer

The answer of Accidents and Rain
A statistician investigating the relationship...

Question 18

For a regression analysis to be valid, the error variable must have a mean of ____________________.

Accepted Answer

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

Question 19

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.

Question 20

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

Accepted Answer

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

Exam 16: Simple Linear Regression and Correlation

If the coefficient of correlation is -0.60, then the coefficient of determination is:

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.

If the error variable $\varepsilon$ is normally distributed, the test statistic for testing H₀: $\beta$ ₁ = 0 has a Student t-distribution with n - 2 degrees of freedom.

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

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

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.

If we are interested in determining whether two variables are linearly related, it is necessary to:

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

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

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

For a regression analysis to be valid, the error variable must have a mean of ____________________.

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

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

Exam 16: Simple Linear Regression and Correlation

If the coefficient of correlation is -0.60, then the coefficient of determination is:

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.

If the error variable ε\varepsilonε is normally distributed, the test statistic for testing H0: β\betaβ 1 = 0 has a Student t-distribution with n - 2 degrees of freedom.

When the actual values y of a dependent variable and the corresponding predicted values are the same, the standard error of estimate s ε\varepsilonε will be 0.0.

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

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

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.

If we are interested in determining whether two variables are linearly related, it is necessary to:

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

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

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

For a regression analysis to be valid, the error variable must have a mean of ____________________.

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

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

If the error variable $\varepsilon$ is normally distributed, the test statistic for testing H₀: $\beta$ ₁ = 0 has a Student t-distribution with n - 2 degrees of freedom.

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