Question 1

In regression analysis, the independent variable is a variable whose value is known and is being used to explain or predict the value of another variable.

Accepted Answer

A) True 
 B)False

Question 2

The prediction interval developed from a simple linear regression model will be very narrow when the value of x used to predict y is equal to the mean value  .

Accepted Answer

A) True 
 B)False

Question 3

In regression analysis, what do the residuals represent?

Accepted Answer

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

Question 4

If the coefficient of determination is 0.975, then what may be said about the slope of the regression line?

Accepted Answer

A)  It must be positive. 
B)  It must be negative. 
C)  It could be either positive or negative.

Question 5

Which of the following is measured by the coefficient of determination  ?

Accepted Answer

A)  the amount of variation in y that is explained by variation in x 
B)  the amount of variation in x that is explained by variation in y 
C)  the amount of variation in y that is not explained by variation in x 
D)  the amount of variation in x that is not explained by variation in y

Question 6

If all the values of an independent variable x are equal, then regressing a dependent variable y on x will result in a coefficient of determination of 0.

Accepted Answer

A) True 
 B)False

Question 7

The value of the sum of squares for regression can never be smaller than 0.0.

Accepted Answer

A) True 
 B)False

Question 8

A study of 20 students showed that the correlation between the time spent writing a test and the number of hours studied the night before the test was 0.35. Using a level of significance equal to 0.05, what does this imply?

Accepted Answer

A)  The sample correlation coefficient could be 0 since the test statistic does not fall into the rejection region. 
B)  The null hypothesis that the population mean is equal to 0 should not be rejected, and we should conclude that the true correlation coefficient is 0. 
C)  There is not enough statistical evidence to conclude that the true correlation coefficient is different from 0. 
D)  The null hypothesis that the population variance is equal to 0 should be rejected, and we should conclude that the true correlation coefficient is 0.

Question 9

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

Accepted Answer

A) True 
 B)False

Question 10

A regression analysis between weight (y in kg) and height (x in cm) resulted in the following least-squares line:  = -20 + 0.5x. Taking this into consideration, if the height is increased by 1 cm, what does this imply about the change in the weight, on average?

Accepted Answer

A)  The weight will increase by 1/2 kg. 
B)  The weight will increase by 6 kg. 
C)  The weight will decrease by 1/2 kg. 
D)  The weight will decrease by 20 kg.

Question 11

A regression analysis between sales (in $1000) and advertising (in $100) resulted in the following least-squares line:  = 75 +6x. From this information, if advertising is $800, then what is the predicted amount of sales (in dollars)?

Accepted Answer

A)  $4,875 
B)  $12,300 
C)  $123,000 
D)  $487,500

Question 12

In developing a 90% confidence interval for the expected value of y from a simple linear regression involving a sample of size 15, the appropriate t-table value would be 1.761.

Accepted Answer

A) True 
 B)False

Question 13

In simple linear regression, one can use the plot of residuals versus the fitted values of y to check for a constant variance as well as to make sure that the linear model is in fact adequate.

Accepted Answer

A) True 
 B)False

Question 14

Which of the following is a measure of how well an estimated regression line fits the sample data on which it is based, denoted by  (and equal to the proportion of the total variation in the values of the dependent variable, y, that can be explained by the association of y with x as measured by the estimated regression line)?

Accepted Answer

A)  the sample coefficient of variation 
B)  the sample coefficient of correlation 
C)  the sample coefficient of determination 
D)  the sample coefficient of non-determination

Question 15

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

Accepted Answer

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

Question 16

A regression analysis between weight (  , in kg) and height (  , in cm) resulted in the following least-squares line:  = -5 + 0.4  . This implies that if the height is increased by 1 cm, the weight is expected to increase by an average of 0.4 kg.

Accepted Answer

A) True 
 B)False

Question 17

In a simple linear regression analysis, if SSE = 27, Total SS = 63, then what is the approximate percentage of the variation in the dependent variable y that is explained by the independent variable x?

Accepted Answer

A)  27% 
B)  43% 
C)  57% 
D)  63%

Question 18

In simple linear regression analysis, if the correlation coefficient between the independent variable x and the dependent variable y is -0.85, this means that the scatterplot generated by the same data values would show points that would fall on a straight line with slope equal to -0.85.

Accepted Answer

A) True 
 B)False

Question 19

In simple linear regression, the plot of residuals versus fitted values  can be used to check for which of the following

Accepted Answer

A)  normality 
B)  a constant variance independent of x 
C)  independence

Question 20

When all the points in a scatter diagram lie precisely on the estimated regression line, the sample coefficient of correlation will equal 0.

Accepted Answer

A) True 
 B)False

Exam 12: A: linear Regression and Correlation

In regression analysis, the independent variable is a variable whose value is known and is being used to explain or predict the value of another variable.

The prediction interval developed from a simple linear regression model will be very narrow when the value of x used to predict y is equal to the mean value .

In regression analysis, what do the residuals represent?

If the coefficient of determination is 0.975, then what may be said about the slope of the regression line?

Which of the following is measured by the coefficient of determination ?

If all the values of an independent variable x are equal, then regressing a dependent variable y on x will result in a coefficient of determination of 0.

The value of the sum of squares for regression can never be smaller than 0.0.

A study of 20 students showed that the correlation between the time spent writing a test and the number of hours studied the night before the test was 0.35. Using a level of significance equal to 0.05, what does this imply?

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

A regression analysis between weight (y in kg) and height (x in cm) resulted in the following least-squares line: = -20 + 0.5x. Taking this into consideration, if the height is increased by 1 cm, what does this imply about the change in the weight, on average?

A regression analysis between sales (in $1000) and advertising (in $100) resulted in the following least-squares line: = 75 +6x. From this information, if advertising is $800, then what is the predicted amount of sales (in dollars) ?

In developing a 90% confidence interval for the expected value of y from a simple linear regression involving a sample of size 15, the appropriate t-table value would be 1.761.

In simple linear regression, one can use the plot of residuals versus the fitted values of y to check for a constant variance as well as to make sure that the linear model is in fact adequate.

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

A regression analysis between weight ( , in kg) and height ( , in cm) resulted in the following least-squares line: = -5 + 0.4 . This implies that if the height is increased by 1 cm, the weight is expected to increase by an average of 0.4 kg.

In a simple linear regression analysis, if SSE = 27, Total SS = 63, then what is the approximate percentage of the variation in the dependent variable y that is explained by the independent variable x?

In simple linear regression analysis, if the correlation coefficient between the independent variable x and the dependent variable y is -0.85, this means that the scatterplot generated by the same data values would show points that would fall on a straight line with slope equal to -0.85.

In simple linear regression, the plot of residuals versus fitted values can be used to check for which of the following

When all the points in a scatter diagram lie precisely on the estimated regression line, the sample coefficient of correlation will equal 0.