Test Bank

Chapter 14: Introduction to Regression Analysis

Multiple Choice

1. A researcher wishes to find out whether ambient temperature can be used to predict homicide rates. What statistical test should the researcher use?

A. independent samples t test

B. χ² analysis

C. bivariate correlation

D. regression analysis

2. Which type of regression is used by research scientists to analyze several independent variables and one dependent variable?

A. multiple regression

B. bivariate correlation

C. χ² analysis

D. dependent samples t test

3. In the regression line equation, the predicted values of the dependent variable are symbolized by ______.

A.

B. X²

C. y

D. r

4. Which symbol denotes the slope coefficient of the regression line?

A. . . . y hat

B. X²

C. b

D. r

5. The point at which the line of best fit crosses the y-axis is referred to as ______.

A. the slope

B. the predicted value of y at x

C. the intercept

D. the x intercept

6. Which of the following are the null and alternative hypotheses for inferential regression analysis?

A. H₀: B = 0 and H₁: B ≠ 0

B. H₀: p₁ = p₂ and H₁: p₁ ≠ p₂

C. H₀: r = 0 and H₁: r ≠ 0

D. H₀: μ₁ < μ₂ and H₁: μ₁ > μ₂

7. Which theoretical distribution is used in inferential regression analysis?

A. z distribution

B. χ² distribution

C. t distribution

D. No theoretical distribution is used.

8. What is the correct formula for the calculation for degrees of freedom in inferential analysis?

A. df = N – 1

B. df = N – 2

C. df = N1 + N2 – 2

D. Since there is no theoretical distribution used in inferential regression, there is no need for degrees of freedom.

9. Which of the following is a standardized measure used to determine a slope coefficient’s magnitude?

A. standardized slope coefficient

B. x intercept

C. b coefficient

D. β weight

10. The standardized slope coefficient used to determine the slope coefficient’s magnitude has a range of ______.

A. 0 to 1

B. −1 to +1

C. the range is determined by the α level.

D. the range is determined by the degrees of freedom combined with the α level.

11. A slope coefficient that measures the individual impact of an independent variable on a dependent variable while holding other independent variables constant is a ______.

A. y intercept

B. partial slope coefficient

C. coefficient of determination

D. β weight

12. In multiple regression, what are the appropriate null and alternative hypotheses?

A. H₀: B₁ = B₂ = 0: H₁: B₂ > B₁

B. H₁: B₁ = B₂ = 0: H₀: B₁ and/or B₂ ≠ 0

C. H₀: B₁ and B₂ = 0: H₁: B₁ and/or B₂ ≠ 0

D. H₀: B₁ > B₂ = 0: H₁: B₁ and/or B₂ ≠ 0

13. The regression line for multiple regression is written as ______.

A. Y = a + b₁ + x₁

B. a = y + b₁x + b₂x

C. = a + b₁x₁ + b₂x₂ + . . . + b_kx_k

D. = a + bx + ε

14. In SPSS, the first portion of regression output that should be examined is ______.

A. the regression dialogue box

B. the ANOVA box containing the F statistic

C. the t test box

D. the correlation box

15. In multiple regression, what is the proper course of action should the F statistic prove nonsignificant?

A. The analysis is viable, and the researcher should proceed to the creation of the regression line and an examination of the y intercept.

B. The analysis is viable, and the researcher should proceed to an examination of the slope coefficients.

C. The analysis is over, and the hypotheses and variables should be reexamined and possibly revised.

D. None of these; there should not be an F statistic in the output, so its presence indicates that the wrong analysis was run.

16. In multiple regression, what does the ANOVA F statistic indicate?

A. Whether the y intercept is statistically significant

B. Whether the set of independent variables included in the model explain a statistically significant amount of the variance in the dependent variable

C. Whether the β weights are statistically significant

D. Whether the slope indicates a statistically significant relationship between the independent variable and dependent variable

17. In regression, the line of best fit that is constructed through a scatterplot of data points is represented by which of the following equations?

A. = a + bx

B. Y = mx + b

C. a = Y + βx

D. Y = a + βx

18. In multiple regression, if the unstandardized slope coefficient is found to be statistically significant, what is the next step for the researcher?

A. The researcher is finished with the analysis and should proceed to the creation of the regression line.

B. The regression model is not a viable model, therefore the work is done, and the researcher should return to the database and begin analysis anew.

C. The researcher should proceed on to an examination of the y intercept coefficient to determine its significance.

D. The researcher should next examine the slope’s accompanying β weight.

19. A researcher ran a regression model in SPSS and is examining the output. He notices that the slope coefficient for his primary independent variable has a p value of .12. What conclusion should he draw from this?

A. That the model is no good and should be thrown out.

B. That the slope coefficient is statistically significant.

C. That the data must have been gathered incorrectly.

D. That the slope coefficient is not statistically significant.

20. In SPSS, how is statistical significance indicated?

A. An examination of the p value will indicate any statistical significance.

B. An examination of α will indicate statistical significance.

C. An examination of β will indicate statistical significance.

D. Dividing the standard error by the sampling distribution differences of the mean will provide statistical significance.

21. In the SPSS regression output box, the symbol ______ indicates the unstandardized slope coefficients.

A. P

B. R

C. r

D. B

22. In the SPSS regression output box, what word indicates the y intercept?

A. constant

B. consistent

C. node

D. intercept

23. In multiple regression, what represents the multiple coefficient of determination in the SPSS regression output?

A. P

B. r

C. R²

D. B

24. The measure that reports the proportion of variance in a dependent variable that is attributable to the impact of two or more independent variables operating jointly is referred to as what?

A. partial slope coefficients

B. multiple coefficient of determination

C. multiple correlation

D. bivariate coefficient

25. The slope coefficients in multiple regression are called______, reflecting the fact that each one is calculated while holding the others constant.

A. bivariate coefficients

B. multiple coefficient of determination

C. multiple correlation

D. partial slope coefficients

26. Which type of regression analysis is used when the dependent variable is continuous and normally distributed?

A. ordinary least squares regression

B. binary logistic regression

C. multinomial logistic regression

D. Poisson regression

27. Which type of regression analysis is used when the dependent variable is dichotomous?

A. ordinary least squares regression

B. binary logistic regression

C. multinomial logistic regression

D. Poisson regression

28. Which type of regression analysis is used when the dependent variable is nominal and has three or more classes?

A. ordinary least squares regression

B. binary logistic regression

C. multinomial logistic regression

D. Poisson regression

29. Which type of regression analysis is used when the dependent variable is count-based?

A. ordinary least squares regression

B. binary logistic regression

C. multinomial logistic regression

D. Poisson regression

30. Which type of regression analysis is used when there are multiple dependent variables?

A. ordinary least squares regression

B. binary logistic regression

C. structural equation modeling

D. multilevel modeling

31. Which type of regression analysis is used when the data are measured at two units of analysis?

A. ordinary least squares regression

B. binary logistic regression

C. structural equation modeling

D. multilevel modeling

32. What kind of analysis is an extension of the bivariate correlation?

A. ordinary least squares regression

B. binary logistic regression

C. bivariate regression

D. multilevel modeling

33. When examining the relationship between employment and crime, a β weight of 0.20 is produced. What is the magnitude of this correlation?

A. weak

B. moderate

C. large

D. extra large

34. When examining the relationship between neighborhood disadvantage and crime, a β weight of 0.35 is produced. What is the magnitude of this correlation?

A. weak

B. moderate

C. strong

D. very strong

35. When examining the relationship between delinquent peers and crime, a β weight of 0.60 is produced. What is the magnitude of this correlation?

A. weak

B. moderate

C. strong

D. very strong

1. Regression analysis is a method of prediction often used in criminal justice research.

2. There are two fundamental types of regression analyses: bivariate and multiple.

3. In inferential regression analysis, the distribution centers on zero because the null hypothesis predicts that the variables are not related.

4. Bivariate regression is an extension of bivariate correlation.

5. If the independent variable is a good predictor of the dependent variable, the empirical scores and the predicted values will be very similar to one another.

6. In inferential regression analysis, the standard error of a slope coefficient is of little importance.

7. It is an unfortunate fact of reality that in inferential regression analysis. There is no viable method of determining the slope coefficient’s magnitude.

8. In inferential regression analysis, if the null hypothesis is retained, it is an indication that the slope coefficient is statistically significant.

9. In the context of inferential regression analysis, a rejected null hypothesis indicates that the independent variable exerts some level of predictive power over the dependent variable.

10. In multiple regression, a significant F statistic is a necessary but insufficient condition for a good regression model.

11. The multiple coefficient of determination is similar to the bivariate coefficient of determination except it measures the impact of several independent variables instead of just one.

12. The use of several independent variables in multiple regression helps prevent the omitted variable bias.

13. In multiple regression, the coefficient of determination addresses the statistical significance of the y intercepts.

14. Ordinary Least Squares, or OLS, regression is the fundamental form of regression and the default procedure used in much criminal justice research.

15. The y intercept in the regression line is symbolized as “a.”

16. The slope of the regression line conveys information about the steepness of the line.

17. Bivariate regression is a form of regression analysis that uses one independent and one dependent variable.

18. In inferential regression analysis, a large standard deviation means that there is substantial uncertainty as to the accuracy of the sample slope coefficient as an estimate of the population slope.

19. The standardized slope coefficient used to determine the slope coefficient’s magnitude is symbolized by β.

20. In inferential regression analysis, β weights are standardized estimates that range from −1.00 to 1.00.

1. Write the equation for a basic regression line and identify each component.

2. Write the equation for the slope and y intercept below and identify each component.

= the mean of the dependent variable

b = the slope coefficient

= the mean of the independent variable

Cognitive Domain: Application

Answer Location: One Independent Variable and One Dependent Variable: Bivariate Regression

Difficulty Level: Medium

3. The professor described in Question 48 has decided to add to her database and wishes to explore the nature of larceny. She has two variables, age and larceny arrests. Use the data below, and calculate the y intercept and slope of the regression line.

Age No. of Arrests for Larceny

19 5

20 5

25 3

30 4

35 3

36 2

4. Now use the same data from above, plug the slope and y intercept values into the equation, and write the regression line.

5. The essence of regression analysis is prediction. Use the regression line written in Question 50, and predict the number of larceny arrests for an individual who is 40 years of age.