# Question: Suppose that a researcher does a study to see how

Suppose that a researcher does a study to see how level of anxiety (A1 = low, A2 = medium, A3 = high) is used to predict exam performance (Y). Here are hypothetical data for this research situation. Each column represents scores on Y (exam scores).

A1, low Anxiety

A2, low Anxiety

A3, low Anxiety

72

86

65

81

93

79

54

81

74

66

80

80

71

92

74

a. Would it be appropriate to do a Pearson correlation (and/or linear regression) between Anxiety, coded 1, 2, 3 for (low, medium, high) and exam score? Why or why not?

b. Set up orthogonal coded dummy variables (O1, O2) to represent linear and quadratic trend, and run a regression analysis to predict exam scores from O1 and O2. What conclusions can you draw about the nature of the relationship between anxiety and exam performance?

c. Set up dummy coded dummy variables to contrast each of the other groups to Group 2, medium Anxiety; run a regression to predict exam performance (Y) from these dummy coded dummy variables.

d. Run a one way ANOVA on these scores; request contrasts between group 2, medium anxiety, and each of the other groups. Do a point-by-point comparison of the numerical results for your ANOVA printout and the numerical results for the regression in part 2c, pointing out where the results are equivalent.

A1, low Anxiety

A2, low Anxiety

A3, low Anxiety

72

86

65

81

93

79

54

81

74

66

80

80

71

92

74

a. Would it be appropriate to do a Pearson correlation (and/or linear regression) between Anxiety, coded 1, 2, 3 for (low, medium, high) and exam score? Why or why not?

b. Set up orthogonal coded dummy variables (O1, O2) to represent linear and quadratic trend, and run a regression analysis to predict exam scores from O1 and O2. What conclusions can you draw about the nature of the relationship between anxiety and exam performance?

c. Set up dummy coded dummy variables to contrast each of the other groups to Group 2, medium Anxiety; run a regression to predict exam performance (Y) from these dummy coded dummy variables.

d. Run a one way ANOVA on these scores; request contrasts between group 2, medium anxiety, and each of the other groups. Do a point-by-point comparison of the numerical results for your ANOVA printout and the numerical results for the regression in part 2c, pointing out where the results are equivalent.

**View Solution:**## Answer to relevant Questions

Why is it acceptable to use a dichotomous predictor variable in a regression when it is not usually acceptable to use a categorical variable that has more than two values as a predictor in regression? Consider the following actual data from a study by Lyon & Greenberg (1991). The first factor in their factorial ANOVA was family background; female participants were classified into two groups (group 1, “Codependent”, ...How is a weighted average of group means, different from an unweighted average of group means? What is the “weighting” factor? Under what circumstances would each type of mean be preferred? What types of research situations often make use of multiple regression analysis with more than two predictors? Briefly explain how the approach to data analysis differs for these combinations of types of predictor variables In addition, explain what kind of graph(s) can be used to represent the nature of interactions for each of ...Post your question