Data Analysis and Application
This assignment will help you understand proper reporting and interpretation of multiple regression. You will use the IBM SPSS Linear Regression procedure to accurately compute a multiple regression with the u07a1data.sav file located below in Resources. Use the Data Analysis and Application (DAA) Template located in Resources to write up your assignment. The deadline for submitting your work is 11:59 PM CST on Sunday of Week 7.
Step 1. Write Section 1 of the DAA. Provide a context of the u07a1data.sav data set. Specifically, imagine that you are a health researcher studying how well a measure of anxiety ( X1) and weight ( X2) predict systolic blood pressure ( Y) . In Section 1 of the DAA, articulate your predictor variables, the outcome variable, and the scales of measurement for each variable. Specify the sample size of the data set.
Step 2. Write Section 2 of the DAA. Test the four assumptions of multiple regression. Begin with SPSS output of the three histograms on X1, X 2, and Y and provide visual interpretations of normality. Next, paste the SPSS output of the scatter plot matrix and interpret it in terms of linearity and bivariate outliers. Next, paste SPSS output of the zero-order correlations (Pearson r) and interpret it to check the multicollinearity assumption. Note: to test this assumption in SPSS, use Analyze… Correlate… Bivariate Correlations to generate a two-tailed test; do not use the default one-tailed test output from the Linear Regression procedure. Finally, paste the SPSS plot of standardized residuals (ZPRED = x-axis; ZRESID = y-axis) and interpret it to check the homoscedasticity assumption.
Step 3. Write Section 3 of the DAA. Specify a research question for the overall regression model. Articulate a null hypothesis and alternative hypothesis for the overall regression model. Specify a research question for each predictor. Articulate the null hypothesis and alternative hypothesis for each predictor. Specify the alpha level.
Step 4. Write Section 4 of the DAA. Begin with a brief statement reviewing assumptions. Next, paste the SPSS output for the Model Summary. Report R and R2; interpret R2 effect size. Next, paste the SPSS ANOVA output. Report the F test for R and interpret it against the null hypothesis. Next, paste the SPSS Coefficients output. For each predictor, report the b coefficient, the t test results, including interpretation against the null hypothesis, the semipartial squared correlation effect size, and the interpretation of effect size. In your Interpretation section, following Table 11.1 on page 460 of your Warner text, generate a table of Results for the u07a1data.sav file that summarizes:
- The means and standard deviations of each variable in the regression equation.
- The zero-order (Pearson r) correlations among variables.
- The y-intercept.
- The b coefficients of each predictor with notation of calculated p-values for rejecting the null hypothesis.
- The β coefficients of each predictor.
- The squared semipartial correlations of each predictor.
- The values of R, R2, and adjusted R2 with notation of p-values for rejecting the null hypothesis.
Step 5. Write Section 5 of the DAA. Discuss your conclusions of the multiple regression as it relates to your stated research questions for the overall regression model and the individual predictors. Conclude with an analysis of the strengths and limitations of multiple regression.