Question 1

In the least squares regression line   = 3 - 2x, the predicted value of y equals:

Accepted Answer

A)  1.0 when x = -1.0 
B)  2.0 when x = 1.0 
C)  2.0 when x = -1.0 
D)  1.0 when x = 1.0 
E)  1.0 when x = 2.0 
A)  1.0 when x = -1.0 
B)  2.0 when x = 1.0 
C)  2.0 when x = -1.0 
D)  1.0 when x = 1.0 
E)  1.0 when x = 2.0

Question 2

If there is no linear relationship between two variables x and y, the coefficient of determination must be   1.0.

Accepted Answer

A) True 
 B)False

Question 3

The value of the sum of squares for error (SSE) can never be larger than the total sum of squares (Total SS).

Accepted Answer

A) True 
 B)False

Question 4

A regression analysis between sales (y in $1000) and advertising (x in $100) resulted in the following least squares line:   = 82 +7x. This implies that if advertising is $900, then the predicted amount of sales (in dollars) is:

Accepted Answer

A)  $6,382 
B)  $88,300 
C)  $145,000 
D)  $82,063 
E)  6382000 
A)  $6,382 
B)  $88,300 
C)  $145,000 
D)  $82,063 
E)  6382000

Question 5

In developing a 90% confidence interval for the average value of y from a simple linear regression problem involving 12 observations, the appropriate table value would be 1.796.

Accepted Answer

A) True 
 B)False

Question 6

In studying the relationship between two variables x and y, a scatterplot can be used to detect which of the following?

Accepted Answer

A)  A positive linear relationship. 
B)  A negative linear relationship. 
C)  A relationship that is not linear. 
D)  All of these. 
E)  None of these. 
A)  A positive linear relationship. 
B)  A negative linear relationship. 
C)  A relationship that is not linear. 
D)  All of these. 
E)  None of these.

Question 7

The values of   and b found in the equation of the estimated regression line,   , represent the line's y-intercept and slope, respectively, and are called estimated regression coefficients.

Accepted Answer

A) True 
 B)False

Question 8

The following are coefficients of correlation (r). The one that indicates a strong negative linear relationship between the two variables of interest is:

Accepted Answer

A)  0.8 
B)  -0.9 
C)  0.9 
D)  -1.3 
E)  1 
A)  0.8 
B)  -0.9 
C)  0.9 
D)  -1.3 
E)  1

Question 9

If all of the values of an independent variable x are equal, then regressing a dependent variable y on this independent variable x will result in a coefficient of determination (   ) equal to:

Accepted Answer

A)  -1.3 
B)  -1.0 
C)  0.0 
D)  1.0 
E)  1.3 
A)  -1.3 
B)  -1.0 
C)  0.0 
D)  1.0 
E)  1.3

Question 10

If a sample of 25 observations is selected, and the sample correlation coefficient between the variables x and y is r = 0.525, what is the test statistic value for testing

Accepted Answer

A)  About 3.65. 
B)  About 2.96. 
C)  About 3.08. 
D)  About 3.81. 
E)  About 3.96. 
A)  About 3.65. 
B)  About 2.96. 
C)  About 3.08. 
D)  About 3.81. 
E)  About 3.96.

Question 11

A microwave manufacturer has collected the data shown below on number of units sold (y) in the thousands of dollars and the number of ads (x) placed during the month.   Calculate the preliminary sums of squares and cross-products.
Sxx = ______________
Syy = ______________
Sxy = ______________
Calculate:
SSE = ______________
MSE = ______________
Determine the least-squares regression line.   = ______________
Compute a point estimate of number of units sold if there are 140 ads.
______________
Compute the standard error of the point estimate of number of units sold if there are 140 ads.
______________
Compute a 95% confidence interval for the average number of units sold in all months with 140 ads.
______________ Enter (n1, n2)
Compute a 95% prediction interval for sales during the next month that happens to be associated with 140 ads.
______________ Enter (n1, n2)

Accepted Answer

71079.75; 404.55; 2933.25; 283

Question 12

In the simple linear regression model   which of the following is true regarding the values of the random error term   ?

Accepted Answer

A)  They are independent. 
B)  They have a mean of 0 and a common variance, independent of x. 
C)  They are normally distributed. 
D)  All of these. 
E)  None of these. 
A)  They are independent. 
B)  They have a mean of 0 and a common variance, independent of x. 
C)  They are normally distributed. 
D)  All of these. 
E)  None of these.

Question 13

In a simple linear regression analysis, the standard error of the slope is:

Accepted Answer

A)  a measure of the amount of change in the dependent variable y for a one unit change in the independent variable x 
B)  a measure of the variation in the regression slope from sample to sample 
C)  the square root of the standard error of the estimate 
D)  the square of the standard error of the estimate 
E)  all of these 
A)  a measure of the amount of change in the dependent variable y for a one unit change in the independent variable x 
B)  a measure of the variation in the regression slope from sample to sample 
C)  the square root of the standard error of the estimate 
D)  the square of the standard error of the estimate 
E)  all of these

Question 14

For the values of the coefficient of determination listed below, which one yields the greatest value of sum of squares for regression given that the total sum of squares is 200?

Accepted Answer

A)  0.90 
B)  -0.90 
C)  0.00 
D)  0.98 
E)  -0.98 
A)  0.90 
B)  -0.90 
C)  0.00 
D)  0.98 
E)  -0.98

Question 15

Simple regression analysis is a statistical technique that establishes an index that provides, in a single number, a measure of the strength of association between two variables.

Accepted Answer

A) True 
 B)False

Question 16

Given the least squares regression line   = -4.63 + 1.38x, and a coefficient of determination of 0.9025, the correlation coefficient must be:

Accepted Answer

A)  -0.95 
B)  +0.95 
C)  +1.38 
D)  -0.81 
E)  0.81 
A)  -0.95 
B)  +0.95 
C)  +1.38 
D)  -0.81 
E)  0.81

Question 17

A stochastic relationship is a relationship between any two variables, Y and X, such that many possible values of Y can be associated with any one value of X.

Accepted Answer

A) True 
 B)False

Question 18

Given that the sum of squares for error is 60 and the sum of squares for regression is 140, then the coefficient of determination is:

Accepted Answer

A)  0.429 
B)  0.300 
C)  0.700 
D)  0.837 
E)  1 
A)  0.429 
B)  0.300 
C)  0.700 
D)  0.837 
E)  1

Question 19

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, which of the following statements is true?

Accepted Answer

A)  The sample correlation coefficient could be zero since the test statistic does not fall in the rejection region. 
B)  The null hypothesis that the population mean is equal to zero should not be rejected, and we should conclude that the true correlation coefficient is zero. 
C)  There is not enough statistical evidence to conclude that the true correlation coefficient is different from zero. 
D)  The null hypothesis that the population variance is equal to zero should be rejected, and we should conclude that the true correlation coefficient is zero. 
E)  None of these. 
A)  The sample correlation coefficient could be zero since the test statistic does not fall in the rejection region. 
B)  The null hypothesis that the population mean is equal to zero should not be rejected, and we should conclude that the true correlation coefficient is zero. 
C)  There is not enough statistical evidence to conclude that the true correlation coefficient is different from zero. 
D)  The null hypothesis that the population variance is equal to zero should be rejected, and we should conclude that the true correlation coefficient is zero. 
E)  None of these.

Question 20

A university admissions committee was interested in examining the relationship between a student's score on the SAT exam, x, and the student's grade point average, y, (GPA) at the end the student's freshman year of college. The committee selected a random sample of 25 students and recorded the SAT score and GPA at the end of the freshman year of college for each student. Use the following output that was generated using Minitab to answer the questions below:   Determine the correlation between a student's SAT score and GPA at the end of the freshman year.
Since b is ______________ the correlation is ______________.
Interpret the value.
There is a ______________ linear relationship between a student's SAT score and GPA at the end of the freshman year.

Accepted Answer

positive;

In the least squares regression line = 3 - 2x, the predicted value of y equals:

If there is no linear relationship between two variables x and y, the coefficient of determination must be 1.0.

The value of the sum of squares for error (SSE) can never be larger than the total sum of squares (Total SS).

A regression analysis between sales (y in $1000) and advertising (x in $100) resulted in the following least squares line: = 82 +7x. This implies that if advertising is $900, then the predicted amount of sales (in dollars) is:

In developing a 90% confidence interval for the average value of y from a simple linear regression problem involving 12 observations, the appropriate table value would be 1.796.

In studying the relationship between two variables x and y, a scatterplot can be used to detect which of the following?

The values of and b found in the equation of the estimated regression line, , represent the line's y-intercept and slope, respectively, and are called estimated regression coefficients.

The following are coefficients of correlation (r). The one that indicates a strong negative linear relationship between the two variables of interest is:

If all of the values of an independent variable x are equal, then regressing a dependent variable y on this independent variable x will result in a coefficient of determination ( ) equal to:

If a sample of 25 observations is selected, and the sample correlation coefficient between the variables x and y is r = 0.525, what is the test statistic value for testing

In the simple linear regression model which of the following is true regarding the values of the random error term ?

In a simple linear regression analysis, the standard error of the slope is:

For the values of the coefficient of determination listed below, which one yields the greatest value of sum of squares for regression given that the total sum of squares is 200?

Simple regression analysis is a statistical technique that establishes an index that provides, in a single number, a measure of the strength of association between two variables.

Given the least squares regression line = -4.63 + 1.38x, and a coefficient of determination of 0.9025, the correlation coefficient must be:

A stochastic relationship is a relationship between any two variables, Y and X, such that many possible values of Y can be associated with any one value of X.

Given that the sum of squares for error is 60 and the sum of squares for regression is 140, then the coefficient of determination is:

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, which of the following statements is true?

Describing Data With Graphs

Describing Data With Numerical Measures

Describing Bivariate Data

Probability and Probability Distributions

Several Useful Discrete Distributions

The Normal Probability Distribution

Sampling Distributions

Large-Sample Estimation

Large-Sample Tests of Hypotheses

Inference From Small Samples

The Analysis of Variance

Multiple Regression Analysis

Analysis of Categorical Data

Nonparametric Statistics

Filters

Exam 12: Linear Regression and Correlation

In the least squares regression line = 3 - 2x, the predicted value of y equals:

If there is no linear relationship between two variables x and y, the coefficient of determination must be 1.0.

The value of the sum of squares for error (SSE) can never be larger than the total sum of squares (Total SS).

A regression analysis between sales (y in $1000) and advertising (x in $100) resulted in the following least squares line: = 82 +7x. This implies that if advertising is $900, then the predicted amount of sales (in dollars) is:

In developing a 90% confidence interval for the average value of y from a simple linear regression problem involving 12 observations, the appropriate table value would be 1.796.

In studying the relationship between two variables x and y, a scatterplot can be used to detect which of the following?

The values of and b found in the equation of the estimated regression line, , represent the line's y-intercept and slope, respectively, and are called estimated regression coefficients.

The following are coefficients of correlation (r). The one that indicates a strong negative linear relationship between the two variables of interest is:

If all of the values of an independent variable x are equal, then regressing a dependent variable y on this independent variable x will result in a coefficient of determination ( ) equal to:

If a sample of 25 observations is selected, and the sample correlation coefficient between the variables x and y is r = 0.525, what is the test statistic value for testing

In the simple linear regression model which of the following is true regarding the values of the random error term ?

In a simple linear regression analysis, the standard error of the slope is:

For the values of the coefficient of determination listed below, which one yields the greatest value of sum of squares for regression given that the total sum of squares is 200?

Simple regression analysis is a statistical technique that establishes an index that provides, in a single number, a measure of the strength of association between two variables.

Given the least squares regression line = -4.63 + 1.38x, and a coefficient of determination of 0.9025, the correlation coefficient must be:

A stochastic relationship is a relationship between any two variables, Y and X, such that many possible values of Y can be associated with any one value of X.

Given that the sum of squares for error is 60 and the sum of squares for regression is 140, then the coefficient of determination is:

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, which of the following statements is true?

Describing Data With Graphs

Describing Data With Numerical Measures

Describing Bivariate Data

Probability and Probability Distributions

Several Useful Discrete Distributions

The Normal Probability Distribution

Sampling Distributions

Large-Sample Estimation

Large-Sample Tests of Hypotheses

Inference From Small Samples

The Analysis of Variance

Multiple Regression Analysis

Analysis of Categorical Data

Nonparametric Statistics

Filters