Question 1

In regression analysis, the independent variable is

Accepted Answer

A)  used to predict other independent variables. 
B)  used to predict the dependent variable. 
C)  the variable that is not used for prediction. 
D)  the variable that is being predicted. 
A)  used to predict other independent variables. 
B)  used to predict the dependent variable. 
C)  the variable that is not used for prediction. 
D)  the variable that is being predicted.

Question 2

You are given the following information about y and x.   ​ The coefficient of determination equals

Accepted Answer

A)  .5. 
B)  -.5. 
C)  .25. 
D)  -.25. 
A)  .5. 
B)  -.5. 
C)  .25. 
D)  -.25.

Question 3

If two variables, x and y, have a strong linear relationship, then

Accepted Answer

A)  the correlation coefficient is a positive number. 
B)  the correlation coefficient is 0. 
C)  the correlation coefficient is a negative number. 
D)  the F test is used to conclude there is a causal relationship between x and y. 
A)  the correlation coefficient is a positive number. 
B)  the correlation coefficient is 0. 
C)  the correlation coefficient is a negative number. 
D)  the F test is used to conclude there is a causal relationship between x and y.

Question 4

The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the​

Accepted Answer

A)  ​correlation coefficient. 
B)  ​standard error of the estimate. 
C)  ​coefficient of determination. 
D)  ​confidence interval estimate. 
A)  ​correlation coefficient. 
B)  ​standard error of the estimate. 
C)  ​coefficient of determination. 
D)  ​confidence interval estimate.

Question 5

The primary tool for determining whether the assumptions made about the regression model are appropriate is

Accepted Answer

A)  ​interval estimation. 
B)  ​significance testing. 
C)  ​least squares regression. 
D)  ​residual analysis. 
A)  ​interval estimation. 
B)  ​significance testing. 
C)  ​least squares regression. 
D)  ​residual analysis.

Question 6

In a residual plot against x that does not suggest we should challenge the assumptions of our regression model, we would expect to see​ a

Accepted Answer

A)  ​horizontal band of points centered near zero. 
B)  widening band of points around the x-axis. 
C)  band of points having a slope consistent with that of the regression equation. 
D)  parabolic band of points centered at the origin. 
A)  ​horizontal band of points centered near zero. 
B)  widening band of points around the x-axis. 
C)  band of points having a slope consistent with that of the regression equation. 
D)  parabolic band of points centered at the origin.

Question 7

If the coefficient of correlation is .8, the percentage of variation in the dependent variable explained by the variation in the independent variable is

Accepted Answer

A)  .85%. 
B)  85%. 
C)  .7225%. 
D)  72.25%. 
A)  .85%. 
B)  85%. 
C)  .7225%. 
D)  72.25%.

Question 8

Given the following regression source table, is the model significant at the .05 level? Explain.

Accepted Answer

Yes, the p-value is

Question 9

You are given the following information about y and x.   ​ The least squares estimate of the slope or b1 equals

Accepted Answer

A)  1. 
B)  -2. 
C)  3. 
D)  12. 
A)  1. 
B)  -2. 
C)  3. 
D)  12.

Question 10

If all the points of a scatter diagram lie on the least squares regression line, then the coefficient of determination for these variables based on these data

Accepted Answer

A)  is 0. 
B)  is 1. 
C)  is either 1 or -1, depending upon whether the relationship is positive or negative. 
D)  could be any value between -1 and 1. 
A)  is 0. 
B)  is 1. 
C)  is either 1 or -1, depending upon whether the relationship is positive or negative. 
D)  could be any value between -1 and 1.

Question 11

In a regression analysis, if SST = 4500 and SSR = 2925, then the correlation coefficient could be

Accepted Answer

A)  .35 or -.35. 
B)  .806 or -.806. 
C)  1. 
D)  .65 or -.65. 
A)  .35 or -.35. 
B)  .806 or -.806. 
C)  1. 
D)  .65 or -.65.

Question 12

Given the following information, the least squares regression line would give a predicted value for x = 4 of

Accepted Answer

A)  78.8. 
B)  47.6. 
C)  80. 
D)  11.8. 
A)  78.8. 
B)  47.6. 
C)  80. 
D)  11.8.

Question 13

In a regression analysis, the coefficient of determination is .4225. The coefficient of correlation in this situation is

Accepted Answer

A)  -.65 if b1 is negative. 
B)  .1785. 
C)  .18 if b1 is positive. 
D)  .4225. 
A)  -.65 if b1 is negative. 
B)  .1785. 
C)  .18 if b1 is positive. 
D)  .4225.

Question 14

A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation: ​   = 40 - 6x
​
The above equation implies that an

Accepted Answer

A)  increase of $1 in price is associated with a decrease of $6 in sales. 
B)  increase of $8 in price is associated with a decrease of $24,000 in sales. 
C)  increase of $1 in price is associated with a decrease of $240 in sales. 
D)  increase of $1 in price is associated with a decrease of $6000 in sales. 
A)  increase of $1 in price is associated with a decrease of $6 in sales. 
B)  increase of $8 in price is associated with a decrease of $24,000 in sales. 
C)  increase of $1 in price is associated with a decrease of $240 in sales. 
D)  increase of $1 in price is associated with a decrease of $6000 in sales.

Question 15

You are given the following information about y and x.   ​ The sample correlation coefficient equals

Accepted Answer

A)  .5. 
B)  -.5. 
C)  .25. 
D)  -.25. 
A)  .5. 
B)  -.5. 
C)  .25. 
D)  -.25.

Question 16

If the coefficient of correlation is .4, then the slope of the regression line

Accepted Answer

A)  must also be .4. 
B)  can be either negative or positive. 
C)  must be positive. 
D)  must be .16. 
A)  must also be .4. 
B)  can be either negative or positive. 
C)  must be positive. 
D)  must be .16.

Question 17

A regression and correlation analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x).   ​ The least squares estimate of the slope or b1 equals

Accepted Answer

A)  .923. 
B)  1.991. 
C)  -1.991. 
D)  -.923. 
A)  .923. 
B)  1.991. 
C)  -1.991. 
D)  -.923.

Question 18

If the coefficient of correlation is .7, the percentage of variation in the dependent variable explained by the variation in the independent variable is

Accepted Answer

A)  70%. 
B)  49%. 
C)  30%. 
D)  -51%. 
A)  70%. 
B)  49%. 
C)  30%. 
D)  -51%.

Question 19

In a regression analysis, the regression equation is given by y = 12 - 6x. If SSE = 510 and SST = 1000, then the coefficient of correlation is

Accepted Answer

A)  -.7. 
B)  +.7. 
C)  .49. 
D)  -.49. 
A)  -.7. 
B)  +.7. 
C)  .49. 
D)  -.49.

Question 20

Given the following information, when testing the least squares regression model would the model be significant at 5%?

Accepted Answer

A) Yes, p-value .1285 > .05. B) No, p-value .1285 > .05. C) Answer cannot be determined. D) Yes, p-value .1285 < .05. A) Yes, p-value .1285 > .05. B) No, p-value .1285 > .05. C) Answer cannot be determined. D) Yes, p-value .1285 < .05.

Exam 14: Simple Linear Regression

In regression analysis, the independent variable is

You are given the following information about y and x. ​ The coefficient of determination equals

If two variables, x and y, have a strong linear relationship, then

The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the​

The primary tool for determining whether the assumptions made about the regression model are appropriate is

In a residual plot against x that does not suggest we should challenge the assumptions of our regression model, we would expect to see​ a

If the coefficient of correlation is .8, the percentage of variation in the dependent variable explained by the variation in the independent variable is

Given the following regression source table, is the model significant at the .05 level? Explain.

You are given the following information about y and x. ​ The least squares estimate of the slope or b1 equals

If all the points of a scatter diagram lie on the least squares regression line, then the coefficient of determination for these variables based on these data

In a regression analysis, if SST = 4500 and SSR = 2925, then the correlation coefficient could be

Given the following information, the least squares regression line would give a predicted value for x = 4 of

In a regression analysis, the coefficient of determination is .4225. The coefficient of correlation in this situation is

A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation: ​ = 40 - 6x ​ The above equation implies that an

You are given the following information about y and x. ​ The sample correlation coefficient equals

If the coefficient of correlation is .4, then the slope of the regression line

A regression and correlation analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x). ​ The least squares estimate of the slope or b1 equals

If the coefficient of correlation is .7, the percentage of variation in the dependent variable explained by the variation in the independent variable is

In a regression analysis, the regression equation is given by y = 12 - 6x. If SSE = 510 and SST = 1000, then the coefficient of correlation is

Given the following information, when testing the least squares regression model would the model be significant at 5%?

Data and Statistics

Descriptive Statistics: Tabular and Graphical Displays

Descriptive Statistics: Numerical Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Inference About Means and Proportions With Two Populations

Inferences About Population Variances

Comparing Multiple Proportions, Tests of Independence and Goodness of Fit

Experimental Design and Analysis of Variance

Multiple Regression

Regression Analysis: Model Building

Time Series Analysis and Forecasting

Nonparametric Methods

Decision Analysis

Index Numbers

Statistical Methods for Quality Control

Sample Survey

Filters

You are given the following information about y and x. The coefficient of determination equals

The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the

In a residual plot against x that does not suggest we should challenge the assumptions of our regression model, we would expect to see a

You are given the following information about y and x. The least squares estimate of the slope or b₁ equals

A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation: = 40 - 6x The above equation implies that an

You are given the following information about y and x. The sample correlation coefficient equals

A regression and correlation analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x). The least squares estimate of the slope or b₁ equals