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Multiple Linear Regression and Choosing the Best Statistical Test, Thesis of Management Accounting

University of Phoenix (UOPX)Management Accounting

Practice questions related to multiple linear regression models and choosing the appropriate statistical test for different scenarios. It covers topics such as the use of linear regression models, adjusted and unadjusted regression coefficients, dummy variables, and interaction terms. It also provides a list of scenarios and asks the reader to choose the most appropriate statistical test for each. useful for students studying statistics or data analysis.

Typology: Thesis

2023/2024

Available from 01/13/2024

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C797 Practice Questions
1. Multiple linear regression models are best used with
a. a dichotomous dependent variable.
b. any ratio-level variable.
c. a normally distributed ratio-level variable.
d. all of the above.
2. The unadjusted regression coefficients (bs) in a multiple linear regression model give
information about
a. the strongest predictor of the dependent variable.
b. the change in the dependent variable per unit increase in the independent
variable.
c. the adjusted odds of having the condition represented by the dependent
variable given that the independent variable is present.
d. a and b only.
3. The adjusted regression coefficient in a multiple linear regression contains information
about
a. the strongest predictor of the dependent variable.
b. the change in the dependent variable per unit increase in the independent
variable.
c. the adjusted odds of having the condition represented by the dependent
variable given that the independent variable is present.
d. a and b only.
4. The coefficient of determination in a multiple linear regression contains information
about
a. the strongest predictor of the dependent variable.
b. the change in the dependent variable per unit increase in the independent
variable.
c. the adjusted odds of having the condition represented by the dependent
variable given that the independent variable is present.
d. the amount of variance in the dependent variable explained by the model.
5. Linear regression models describe
a. curvilinear relationships only.
b. linear relationships only.
c. both a and b.
d. none of the above.
6. Dummy variables are used to
a. recode the dependent variable.
b. represent ratio variables in regression models.
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C797 Practice Questions

  1. Multiple linear regression models are best used with a. a dichotomous dependent variable. b. any ratio-level variable. c. a normally distributed ratio-level variable. d. all of the above.
  2. The unadjusted regression coefficients (bs) in a multiple linear regression model give information about a. the strongest predictor of the dependent variable. b. the change in the dependent variable per unit increase in the independent variable. c. the adjusted odds of having the condition represented by the dependent variable given that the independent variable is present. d. a and b only.
  3. The adjusted regression coefficient in a multiple linear regression contains information about a. the strongest predictor of the dependent variable. b. the change in the dependent variable per unit increase in the independent variable. c. the adjusted odds of having the condition represented by the dependent variable given that the independent variable is present. d. a and b only.
  4. The coefficient of determination in a multiple linear regression contains information about a. the strongest predictor of the dependent variable. b. the change in the dependent variable per unit increase in the independent variable. c. the adjusted odds of having the condition represented by the dependent variable given that the independent variable is present. d. the amount of variance in the dependent variable explained by the model.
  5. Linear regression models describe a. curvilinear relationships only. b. linear relationships only. c. both a and b. d. none of the above.
  6. Dummy variables are used to a. recode the dependent variable. b. represent ratio variables in regression models.

c. represent ordinal variables in regression models. d. represent nominal variables in regression models.

  1. Linear regression allows you to test the significance of the following: a. The overall model b. Each regression coefficient c. The risk ratio comparing those with a characteristic to those without d. a and b only
  2. When the outcome is nominal and dichotomous, which form of regression would be appropriate? a. Linear regression b. Logistic regression c. Multinomial or polytomous regression d. All of the above
  3. Multivariate regression models, be they linear, logistic, or any other form, allow us to do which of the following? a. Simultaneously consider the effects of several independent variables on the dependent variable of interest b. Look at the association between two variables of nominal scale c. Minimize the risk of obtaining spurious results d. a and c
  4. Adding an interaction term to the linear regression model allows us to a. interpret the adjusted association between each independent variable and the outcome. b. assess whether there is significant interaction between the two variables used to create the interaction term. c. calculate odds ratios. d. all of the above. Choosing the Best Statistical Test For each of the following scenarios (1 to 10), choose the most appropriate test (a to l).  a. Independent t test  b. Mann-Whitney U -test  c. Paired t test  d. Wilcoxon matched-pairs test  e. Logistic regression  f. McNemar test  g. Linear regression  h. Repeated-measures ANOVA  i. Friedman’s ANOVA by rank  j. Kruskal-Wallis ANOVA

Computational Problems

 1. Consider the following multiple linear regression equation: Y = 2.75 + 13.42 X 1 + .75 X 2 − 4.21 X 3 + 10.30 X 4 Find the predicted value of the dependent variable (ˆY) given the following situations:  a. The values of all the independent variables are equal to 0.  b. X 1 = 2; X 2 = 3; X 3 = 1; X 4 = −  c. X 1 = −1; X 2 = 3; X 3 = −1; X 4 = 8  2. Is BMI associated with eating out in restaurants frequently (more than five times per week on average) after adjusting for gender, age, and race/ethnicity? Use the SPSS data set we used for our example on cholesterol to answer the following questions: o a. First look at a histogram for BMI and decide if you need to log transform the outcome to make it more normal. o b. Next run the linear regression model (make sure to use dummy variables for the race/ethnicity categories) and interpret the results. o c. What is the predicted ln(BMI) of a white woman age 25 who does not eat out often? o d. Is there interaction between gender and eating out often in predicting BMI? ANSWERS

Multiple-Choice Concept Review

1 (c), 2 (b), 3 (a), 4 (d), 5 (b), 6 (d), 7 (d), 8 (b), 9 (d), 10 (b)

Choosing the Best Statistical Test

1 (e), 2 (g), 3 (a or g), 4 (e), 5 (b), 6 (g or k), 7 (g),

8 (c), 9 (j), 10 (l)

Critical Thinking Concept Review

  1. Any three hypotheses that have a ratio-level dependent variable and more than one independent variable are acceptable.

Computational Problems

a. 2. b. −3. c. 78.

a. BMI is somewhat right skewed. After taking the natural log, it seems more normal, so we will use the log-transformed BMI as the outcome in the linear regression model. b. The model explains 9.0% of the variance of BMI and this is statistically significant ( p = .000). Eating out in restaurants frequently is not significantly associated with BMI ( p = .512). However, gender, age, and black race (compared to white) are all significantly positively associated with BMI. c. Predicted ln(BMI) = 3.136 − .015(0) + .016(1) + .003(25)

  • .087(0) − .062(0) + .058(0) = 3.136 + .016 + .075 = 3.227; predicted BMI = e 3.227^ = 25.2.