# Week 6 Multiple Regression Discussion

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**Week 6 Multiple Regression Discussion**

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Please read all of this post:

This week (6) and in Week 7, you will be studying multiple regression, which is an extension of simple (bivariate) correlation and regression that you learned in RSCH8200, or your Statistics 101 class in college. Because RSCH8200 is the prerequisite for this class, it is assumed that you are proficient with simple correlation (Pearson’s r) and simple Regression analysis (which involves a single X (predictor or IV) and a single Y (outcome or DV) variable – where Y – a + bX. Correlation and Regression was covered in Week 10 in RSCH8200. As you know, in week one I asked you to review simple correlation and regression during weeks 1 and 2, and to ask questions on anything that you did not understand. At this point, I have to assume that you would have complied with these instructions. You’ve all had to opportunity to ask question based on your review of simple correlation and regression during weeks one and two.

Multiple Correlation and Regression (MCR) is an extension of simple correlation and regression. The difference is that MCR involves two or more IVs (predictors) that are used to predict a single DV (outcome). Note: IVs and DVs occur in the context of an experiment. In survey/correlational research the researcher does not manipulate any conditions, so the variables are referred to as the predictors (X1, X2, X3….) and the outcome measure (Y).

MCR allows the researcher to assess the overall relationship between a set of predictors (IVs) and a single DV. This is accomplished through the computation of Multiple R (correlations) R-square, and an ANOVA. Follow-up tests examine the impact of each of the IVs, after controlling for the other IVs in the model; to determine which IVs (predictors) are the significant predictors of the DV (outcome). The Regression part attempts to predict Y (the DV or outcome) from the IVs.

You must read all of Chapter 8 in the Andy Field text, and you must ask questions on any statistics, assumptions, or concepts that you do not fully understand. Along with your question include the page(s) and concept that you are struggling with.

There are instructional Video’s on Regression in the Week 6 Resource Page, and in the Week 7 Resource Page. All of these videos have text notes.

The Video in the Week 6 Resource Page is a review of Simple Correlation and Regression. You study this video in RSCH8200. Watch it, read the text notes, and Ask questions in the Discussion Board.

There are Two Videos in the Week 7 Resources Page (Multiple Correlation – Conceptual and Multiple Regression – Applied). Watch the Videos, read the notes, and posts question in the Discussion Board on any part that you don’t understand.

Please DO NOT e-mail me questions about the instructional material, SPSS, or assignment requirements. Post your questions in the Discussion Board. If you do e-mail me a question, I will ask you to post it in the Statistics-Week 6 Discussion Board so that all students can see the question and my response. If a classmate ask a question in the discussion board, and you know the answer, or where they can find the answer, please respond to them

YOU MUST ALSO READ MY SAMPLE SUMMARY.

You must also read all of my posts within this discussion board.

This week you are also required to submit the Journal Critique Assignment. Instructions for the Journal Critique Assignment appear in the Week 6 Resources Pages above. I’ll also post those instructions below.

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**Effect size R2 and sr2**

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The effect size for the overall model is *R*^{2}

The effect size conventions for *R*^{2 }are as follows:

*R*^{2} =.01 – Small

*R*^{2} =.06 – Medium

*R*^{2} =.14 – Large

.

The effect sizes for the predictors in the regression model are the squared semi-partial correlation coefficients – represented as *sr*^{2}. SPSS does not compute *sr*^{2}. It does compute the semi-partial correlation which is labeled Part Correlation. All you need to do is to square the part correlation coefficient to produce *sr2*. I also explain this and how to compute *sr*2 in my sample summary.

.

Here are some guidelines for interpreting *sr*^{2}

Effect size *sr*^{2}

Small 0.01

Medium 0.09

Large 0.25

.

Example: In the SPSS output below, the variable NHP (Negligent Health Practices) is a significant predictor of Illness (β = .592, *t* = 6.38, *p* < .001, *sr*^{2} = .252). Note that I squared Part Correlation, so (.505)^{2} = .252, and this would represent a large effect size.

.

Coefficients^{a} |
||||||||

Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | Correlations | |||

B | Std. Error | Beta | Zero-order | Partial | Part | |||

(Constant) | 1.308 | 2.224 | 0.59 | 0.56 | ||||

Stress | 0.135 | 0.092 | 0.137 | 1.47 | 0.15 | 0.446 | 0.156 | 0.117 |

NHP | 0.302 | 0.047 | 0.592 | 6.38 | 0 | 0.664 | 0.564 | 0.505 |

a. Dependent Variable: Illness Score |

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**Regresion Instructional Videos**

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**Video Series on Multiple Regression**

Andy Field’s video Lectures (Part I and Part II) on Multiple Regression can be viewed at the following website. Each Video is approximately 60 minutes

Field provides a more advanced lecture on Moderation and Categorical Predictors can be viewed at:

Dr. Dawg created the Following Websites, a series of seven video lectures, on Multiple Regression by Dr. Dawg.Each is about 7 minutes.

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**Effect size R2 and sr2**

Top of Form

The effect size for the overall model is *R*^{2}

The effect size conventions for *R*^{2 }are as follows:

*R*^{2} =.01 – Small

*R*^{2} =.06 – Medium

*R*^{2} =.14 – Large

.

The effect sizes for the predictors in the regression model are the squared semi-partial correlation coefficients – represented as *sr*^{2}. SPSS does not compute *sr*^{2}. It does compute the semi-partial correlation which is labeled Part Correlation. All you need to do is to square the part correlation coefficient to produce *sr2*. I also explain this and how to compute *sr*2 in my sample summary.

.

Here are some guidelines for interpreting *sr*^{2}

Effect size *sr*^{2}

Small 0.01

Medium 0.09

Large 0.25

.

Example: In the SPSS output below, the variable NHP (Negligent Health Practices) is a significant predictor of Illness (β = .592, *t* = 6.38, *p* < .001, *sr*^{2} = .252). Note that I squared Part Correlation, so (.505)^{2} = .252, and this would represent a large effect size.

.

Coefficients^{a} |
||||||||

Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | Correlations | |||

B | Std. Error | Beta | Zero-order | Partial | Part | |||

(Constant) | 1.308 | 2.224 | 0.59 | 0.56 | ||||

Stress | 0.135 | 0.092 | 0.137 | 1.47 | 0.15 | 0.446 | 0.156 | 0.117 |

NHP | 0.302 | 0.047 | 0.592 | 6.38 | 0 | 0.664 | 0.564 | 0.505 |

a. Dependent Variable: Illness Score |

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**SPSS Assignment Requirements & Sample APA Style Summary**** **

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Dear Stat Cats:

Attached is a Sample Summary for Multiple Correlation and Regression Analysis. You must read it; and you must ask questions on any parts that you do not fully understand. You should model your summary after mine, because I’m showing you what to report and how to report it.

In your assignment be sure to:

1) Describe and test the assumptions of multiple correlation – report both in the summary.

2) Create the null and alternative hypotheses..

3a) Correctly Report (in APA style) and summarize the results for the overall model (R, R-square, it’s *F*-test, *p*-value).

3b) Then summarize and explain the results for each significant (where *p* ≤ .05) predictor variable (of salary), report Beta (standardized regression coefficient), *t*-test for *b* (unstandardized regression coefficient) along with it’s *p*-value (sig.)

3c) Report the effect sizes – squared semi-partial correlation (*sr*^{2}) for all variables. Interpret *sr*^{2} for all significant predictors.

4) Include the appropriate tables (see sample summary)

5) Be sure to attach the spss output with syntax in a separate file.

WHAT QUESTIONS DO YOU HAVE?

-Dr. Napoli

APA Summary for Multiple Regression.pdf (297.387 KB)

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**Pearson’s r**

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The guidelines for interpreting Pearson’s *r* as an effect size (which was covered in RSCH8200), are presented on pages 82 of the Field textbook are as follows:

r (+/-) .10 small

r (+/-) .30 medium

r (+/-) .50 Large

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