Q1. Perform and Interpret a Bivariate Linear Regression (9 points total)
Q1Q2 data set contains cognitive function scores and demographics from a group of older adults. The focus of this question set is the executive function (Executive). Create an SPSS data file by importing the Q1Q2 data. Configure the “measure” for each variable.
A . Perform exploratory bivariate correlations in SPSS.
1. Perform bivariate (Pearson’s) correlations among all the variables in the data set. Paste the correlation matrix (table) here. Hint: Enter all the variables in the same correlation analysis. (1 point for the table)
2. Report the correlation result in APA format (including r and p) for each of the following pairs of variables: (1.5 points: .5 for each correlation, both r and p must be correct to earn .5 point)
Education and Executive:
MMSE and Executive:
Age and Executive:
B. Perform a bivariate (simple) linear regression.
The regression model should contain the following:
Outcome variable – Executive
Predictor – Variable with the strongest correlation with Executive (regardless of direction)
1. Create a scatter plot between the predictor variable (X axis) and outcome variable (Y axis). Make sure the scatter plot has labels for the X and Y axes. Paste the scatter plot here.
(1 point: Deduct .5 for each error up to a total of 1.)
2. Perform the bivariate regression analysis in SPSS. Report the omnibus test result in APA style on the regression model, including F, p, and adjusted R2. Be sure to paste the relevant output tables (Model Summary and ANOVA tables) here to support your answer. (1.5 points: .5 for each error in value or format up to 1.5 total. No credit is earned if no table is pasted.)
3. Discuss the regression result. Is the null hypothesis rejected? What does the result mean?
Hint: Think about the null hypothesis being tested here and form your answer based on whether the null hypothesis is rejected or not.
(1 point: .5 for each answer)
4. Report the coefficient test on the predictor variable in APA format, including , t and p. Be sure to paste the relevant output table (Coefficients table) if they have not been pasted above.
(1 point: .5 for any error in value or format, up to 1 total. No point is earned if the table is not included here)
5. Explain the coefficient test result. Is the null hypothesis rejected? What does that mean?
(1 point: .5 for each answer)
6. How much of the variance in the outcome variable can be predicted by the predictor variable? (1 point)
Q2. Perform and Interpret a Multiple Linear Regression (8 points total)
In Q1 above, we examined the relationship between executive function and one predictor variable. Here we are interested in how multiple predictors may be combined to predict executive function even better. Specifically, we would like to build a regression model for executive function with two predictor variables that have the highest and second highest correlations with Executive.
A. Perform a multiple linear regression with Executive as the outcome variable and the two variables with the highest and second highest correlations with Executive as the predictors in the regression model. Use “ENTER” (the default in SPSS) as the method of adding the predictor variables to the regression model.
1. Report the omnibus F test result for the regression model, in APA format, including F, p, and adjusted R2. Be sure to paste the relevant tables (Model Summary and ANOVA tables) here to support your answers. (1.5 points total: .5 for any error in value or format up to 1.5 total. No credit is earned if no relevant table is pasted.)
2. Interpret the test result by answer the following questions: (2 points total: .5 for each question)
a. What was the null hypothesis (in words) tested by this multiple regression analysis?
b. What was the hypothesis test result? (Do you reject or fail to reject the null hypothesis?)
c. What is the effect size of this regression model?
d. What does the effect size mean? The answer should clearly indicate the predictor variables and the outcome variable. Hint: Think about the extent that the predictors can collectively predict the outcome variable.
3. Report the statistics on each predictor variable in APA format, including , t, and p. Paste the relevant table (Coefficients table) here to support your answers.
(2 points total. .5 for each error in value or format, up to 2 total. No point is earned if the relevant table is not pasted here.)
4. Discuss the relative contributions of the predictors in the model. (1.5 points total: .5 for each question)
a. Which is the strongest predictor?
b. How did you know which predictor is the strongest?
c. Is the strongest predictor statistically significant?
B. Compare this current multiple regression model with the bivariate (simple) regression model in Q1. Does the model with two predictors predict the outcome variable better than the model with only one predictor? How do you know? (1 point. .5 for each answer.)
Q3. Perform and Interpret a Bivariate Linear Regression (9.5 points total)
This analysis will be performed on a data set collected by a national company on their 27 chain stores. The marketing department would like to know how various factors contribute to the net sales (Netsales) amount for a chain store. Create an SPSS data file by importing the Q3Q4 data. Configure the “measure” for each variable.
A . Perform exploratory bivariate correlations in SPSS.
1. Perform bivariate (Pearson’s) correlations among all the variables in the data set. Paste the correlation matrix (table) here. Hint: Enter all the variables in the same correlation analysis. (1 point for the table)
2. Report the correlation result in APA format (including r and p) for each of the following pairs of variables: (2 points: .5 for each correlation, both r and p must be correct to earn .5 point)
Storesize and Netsales:
Adcost and Netsales:
Area and Netsales:
Competitor and Netsales:
B. Perform a bivariate (simple) linear regression.
The regression model should contain the following:
Outcome variable – Netsales
Predictor – Variable with the strongest correlation with Netsales (regardless of direction)
1. Create a scatter plot between the predictor variable (X axis) and outcome variable (Y axis). Make sure the scatter plot has labels for the X and Y axes. Paste the scatter plot here.
(1 point: Deduct .5 for each error up to a total of 1.)
2. Perform the bivariate regression analysis in SPSS. Report the omnibus test result in APA style on the regression model, including F, p, and adjusted R2. Be sure to paste the relevant output tables (Model Summary and ANOVA tables) here to support your answer. (1.5 points: .5 for each statistic, both value and APA format must be correct to earn the credit for each statistic. No credit is earned if no table is pasted.)
3. Discuss the regression result. Is the null hypothesis rejected? What does the result mean?
Hint: Think about the null hypothesis being tested here and form your answer based on whether the null hypothesis is rejected or not.
(1 point: .5 for each answer)
4. Report the coefficient test on the predictor variable in APA format, including t and p. Be sure to paste the relevant output table (Coefficients table) if they have not been pasted above.
(1 point: .5 for each statistic, both value and APA format must be correct to earn the credit for each statistic)
5. Explain the coefficient test result. Is the null hypothesis rejected? What does that mean?
(1 point: .5 for each answer)
6. How much of the variance in the outcome variable can be predicted by the predictor variable? (1 point)
Q4. Perform and Interpret a Multiple Linear Regression (8.5 points total)
In Q3 above, we examined the relationship between Netsales and one predictor variable. Here we are interested in how multiple predictors may be combined to predict Netsales even better. Specifically, we would like to build a regression model for Netsales with four predictor variables: Storesize, Adcost, Area, Competitor.
A. Perform a multiple linear regression according to the research question above and answer the following questions. Use “ENTER” (the default in SPSS) as the method of adding the predictor variables to the regression model.
1. Report the omnibus F test result for the regression model, in APA format, including F, p, and adjusted R2. Be sure to paste the relevant tables (Module Summary and ANOVA tables) here to support your answers.
(1.5 points total. .5 for each statistic. Both value and format must be correct to earn the point. No credit is earned if no relevant table is pasted.)
2. Interpret the test result by answer the following questions: (2 points total: .5 for each question)
a. What was the null hypothesis (in words) tested by this multiple regression analysis?
b. What was the hypothesis test result? (Do you reject or fail to reject the null hypothesis?)
c. What is the effect size of this regression model?
d. What does the effect size mean? The answer should clearly indicate the predictor variables and the outcome variable. Hint: Think about the extent that the predictors can collectively predict the outcome variable.
3. Report the statistics on each predictor variable in APA format, including , t, and p. Paste the relevant table (Coefficients table) here to support your answers.
(2 points total. .5 for each error in value or format, up to 2 total. No point is earned if the relevant table is not pasted here.)
4. Discuss the relative contributions of the predictors in the model. (2 points total: .5 for each question)
a. Which is the strongest predictor?
b. Which is the weakest predictor?
c. How do you determine the strength of each predictor?
d. Which variables are significant?
B. Compare this current multiple regression model with the bivariate regression model in Q3. Does the model with four predictors predict the outcome variable better than the model with only one predictor? How do you know? (1 point. .5 for each answer.)