Question 1

In (all types of) regression analysis, a variable whose value is known and is being used to explain or predict the value of another variable is called:

Accepted Answer

A)   an independent variable
B)   a predicted variable
C)   a dependent variable
D)   a response variable
E)   all of these A

Question 2

If the sum of squares for error (SSE) is equal to zero, then the coefficient of determination (  ) must be:

Accepted Answer

A)   1.5
B)   1.0
C)   0.0
D)   -1.0
E)   100 B

Question 3

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 zero.

Accepted Answer

A) True 
 B)False  True

Question 4

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 5

In regression analysis, if the values of the dependent variable, y, decrease with larger values of the independent variable, x, the variables are said to have:

Accepted Answer

A)   a direct relationship
B)   a nonsense correlation
C)   a deterministic relationship
D)   none of these

Question 6

If a simple linear regression model is developed based on a sample where the independent and dependent variables are known to be positively related, then the sign of the slope regression coefficient will be positive also.

Accepted Answer

A) True 
 B)False

Question 7

If a simple linear regression model has no y-intercept, then:

Accepted Answer

A)   all values of x are zero
B)   all values of y are zero
C)   when y = 0 so does x
D)   when x = 0 so does y
E)   none of these

Question 8

In a simple linear regression setting, the deterministic model equation determines an exact value of the dependent variable y when the value of the independent variable x is given, since all points must lie exactly on the line.

Accepted Answer

A) True 
 B)False

Question 9

The regression model  = 36.5 + 20.1x has been computed based on a sample of 50 observations. One observation in the sample was (x, y) = (14, 350.9). Given this, the residual value for this observation is 33.

Accepted Answer

A) True 
 B)False

Question 10

The value of the sum of squares for regression (SSR) can never be larger than 100.

Accepted Answer

A) True 
 B)False

Question 11

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.

Accepted Answer

A) True 
 B)False

Question 12

In order to predict with 99% 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?

Accepted Answer

A)   1.860
B)   2.306
C)   2.896
D)   3.355
E)   2.355

Question 13

A scientist is studying the relationship between wind velocity (x) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x.  What is the least squares regression line?  = ______________
Predict the DC output for a wind velocity of 22 mph.
______________
What is the value of the error sum of squares?
______________
One of the assumptions about the random error  in the regression model is that the values of  have a common variance equal to  . What is the best estimator of  ?
______________
What is the coefficient of determination?
______________
Does a linear relationship exist between x and y? Test using  = 0.05.
What is the p-value?
______________
Conclude:
______________
A linear relationship ______________ exist between x and y.

Accepted Answer

The answer of A scientist is studying the relationship between...

Question 14

The value of the sum of squares for regression SSR can never be smaller than 1.

Accepted Answer

A) True 
 B)False

Question 15

In developing a simple linear regression model, only one independent variable is used to explain the variation in a single dependent variable.

Accepted Answer

A) True 
 B)False

Question 16

In regression analysis we use the Spearman rank correlation coefficient to measure and test to determine whether a relationship exists between the two variables if:

Accepted Answer

A)   one or both variables may be ordinal
B)   both variables are interval but the normality requirement is not met
C)   both one or both variables may be ordinal and both variables are interval but the normality requirement is not met
D)   neither one or both variables may be ordinal nor both variables are interval but the normality requirement is not met
E)   none of these

Question 17

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?

Accepted Answer

A)   2.228
B)   2.306
C)   1.860
D)   1.812
E)   2.812

Question 18

In regression analysis, a careful study of the differences,  , between observed and estimated y values, given x (in order to decide whether crucial assumptions are fulfilled that allow valid inferences about the true regression line to be made from an estimated regression line) is called residual analysis.

Accepted Answer

A) True 
 B)False

Question 19

In a simple linear regression analysis, if the t-test statistic for testing the significance of the regression model is 3.4, then the F-test statistic from the ANOVA table for regression will be 11.56.

Accepted Answer

A) True 
 B)False

Question 20

A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points.  Find the correlation coefficient.
r = ______________
There is ______________ linear relationship between x and y.

Accepted Answer

The answer of A company manager is interested in the...

Exam 12: Linear Regression and Correlation

In (all types of) regression analysis, a variable whose value is known and is being used to explain or predict the value of another variable is called:

If the sum of squares for error (SSE) is equal to zero, then the coefficient of determination ( ) must be:

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 zero.

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.

In regression analysis, if the values of the dependent variable, y, decrease with larger values of the independent variable, x, the variables are said to have:

If a simple linear regression model is developed based on a sample where the independent and dependent variables are known to be positively related, then the sign of the slope regression coefficient will be positive also.

If a simple linear regression model has no y-intercept, then:

In a simple linear regression setting, the deterministic model equation determines an exact value of the dependent variable y when the value of the independent variable x is given, since all points must lie exactly on the line.

The regression model = 36.5 + 20.1x has been computed based on a sample of 50 observations. One observation in the sample was (x, y) = (14, 350.9). Given this, the residual value for this observation is 33.

The value of the sum of squares for regression (SSR) can never be larger than 100.

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.

In order to predict with 99% 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?

The value of the sum of squares for regression SSR can never be smaller than 1.

In developing a simple linear regression model, only one independent variable is used to explain the variation in a single dependent variable.

In regression analysis we use the Spearman rank correlation coefficient to measure and test to determine whether a relationship exists between the two variables if:

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?

In a simple linear regression analysis, if the t-test statistic for testing the significance of the regression model is 3.4, then the F-test statistic from the ANOVA table for regression will be 11.56.