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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 your .sav file.

***.SAV FILE INCLUDED AND TEMPLATE ATTACHED AS WELL (APA TEMPLATE FOR ASSIGNMENT PAPER).

MLR ANALYSIS AND APPLICATION

Instructions

Provide a context of the data set in the supplied .sav file. Specifically, imagine that you are a teacher studying how well scores on Quiz 1 (X1), GPA (X2), and the total points in the course (X3) predict the final grade in the course (Y). Identify your predictor variables, the outcome variable, and the scales of measurement for each variable. Specify the sample size of the data set.

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.

Test the four assumptions of multiple regression. Begin with SPSS output of the four histograms on X1, X2, X3, 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’s 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.

Begin with a brief statement reviewing assumptions. Next, paste the SPSS output for the Model Summary. Report R and R2 in correct APA format; interpret R2 effect size. Next, paste the SPSS ANOVA output. Report the F test for p value and interpret them against the null hypothesis. Next, paste the SPSS Coefficients output. For each predictor, report the b coefficient and 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 9.2 of your Field text, generate a table of results for the .sav file that summarizes:

The means and standard deviations of each variable in the regression equation.

The zero-order (Pearson’s 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.

Next, rerun the regression analysis choosing Backward rather than entry. Report which variable or variables were entered into the equation and which were removed from the equation. Report the R, R squared, adjusted R squared, F test, and p value of the final model that best predicts the variance in the outcome variable.

Discuss your conclusions of the multiple regression as they relate 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.

Additional Requirements

Your assignment should also meet the following requirements:

Written communication: Should be free of errors that detract from the overall message.

APA formatting: References and citations are formatted according to current APA style guidelines. Refer to Evidence and APA for more information on how to cite your sources.

Length: 8–10 double-spaced pages, in addition to the title page and references page.