QuestionQuestion

Transcribed TextTranscribed Text

Question 3 4 Using the sample of 50 students from question #1, the variables of GRE and undergraduate GPA were used to predict graduate GPA. This regression analysis resulted in the following. Multiple R = .750 R Square = .563 Standard Error = .066 The variable of gender was added to this set of predictors and the following resulted: Multiple R = .770 R Square = .593 Standard Error = .064 3a. Did the addition of gender allow for a significant increase in the explained variance in graduate GPA?. Perform the appropriate test to address this question and briefly explain what it means. 3b. Test the overall regression equation (including the variables of GRE, undergraduate GPA, and gender) for statistical significance. Report the F value obtained from this test and briefly explain what it means. Question 4 A researcher had a hypothesis that sense of humor was the key predictor of mental health. However, this researcher also believes that a belief in a team and having a support network also help your mental health. After consultation with the ERMA 7310 class, s/he ran an initial regression analysis and found the following. 1 Model Summary 5 Model R R Square Adjusted R Square Std. Error of the Estimate R Square Change F Change df1 df2 Sig. F Change .975a .951 .945 1.08812 .951 185.690 3 29 .000 a. Predictors: (Constant), satsupport, AUfan, humor Change Statistics ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 659.576 3 219.859 185.690 .000a Residual 34.336 29 1.184 Total 693.912 32 a. Predictors: (Constant), satsupport, AUfan, humor b. Dependent Variable: mental 4a. The null hypothesis is that these three predictors do not relate to the DV of Mental Health. Is there a relationship between these three predictors and the DV of mental health? Provide at least two sources of information to support your decision. 6 Coefficientsa Unstandardize d Coefficients Standardized Coefficients 95.0% Confidence Interval for B Correlations Collinearity Statistics Model Std. B Error Beta t Sig. Lower Bound Upper Bound Zero- order Partial Part .969 .201 .046 .972 .422 .104 .959 .025 .006 Tolerance 1 (Constant) -.368 .902 -.407 .687 1.107 .278 2.507 .018 .134 .894 -2.212 1.477 humor .437 .395 .382 -.371 1.245 .014 69.726 AUfan .378 .151 .562 .070 .686 .034 29.437 satsupport .025 .190 .036 -.363 .414 .024 42.222 a. Dependent Variable: mental VIF 4b. Examine the information summarized in the Coefficients table above. Which predictor variables (IVs) contribute to the prediction of the DV of Mental health? Provide at least three sources of evidence to support your decision. 7 Regression #2 After having the initial analysis reviewed, the researcher was asked by the Board of Trustees and Booster Club to examine the effects of team support above and beyond social support and sense of humor. They wanted to tell alumni that team support was most important in hope that they would get larger alumni donations. The following results were obtained. Model Summary Change Statistics Model 1 2 R .969a .975b Adjusted R R Square Square .940 .936 .951 .945 Std. Error of the Estimate 1.18009 1.08812 R Square Change F Change df1 .940 234.141 .011 6.286 df2 Sig. F Change .000 .018 2 1 30 29 a. Predictors: (Constant), humor, satsupport b. Predictors: (Constant), humor, satsupport, AUfan 4c. Does team support (AUfan) contribute above and beyond humor and social support? 8 Regression #3 Finally, the researcher was asked to just estimate whether being a fan had an effect and predict mental health. The following results emerged. Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate R Square Change F Change df1 df2 Sig. F Change .972a .945 .943 1.11373 .945 528.427 1 31 a. Predictors: (Constant), AUfan Change Statistics .000 1 Coefficientsa Unstandardized Coefficients Standardized Coefficients 95.0% Confidence Interval for B Correlations Zero- order Partial Part .972 .972 .972 Collinearity Statistics Model Std. B Error Beta t Sig. Lower Bound Upper Bound Tolerance 1 (Constant) .955 .211 4.517 .000 22.988 .000 .524 1.387 AUfan .654 .028 .972 .596 .712 1.000 a. Dependent Variable: mental VIF 1.000 4e. What is the predicted mental health score of a person with a team support (AUfan) score of 8? 4d. What is the regression equation that would be used to predict mental health using team support as a predictor?

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

3a. Did the addition of gender allow for a significant increase in the explained variance in graduate GPA?. Perform the appropriate test to address this question and briefly explain what it means.

We can use the R²∆ F-test compare the R² from this model and the full model derived earlier.

where: R²(L) = R² from the larger model = .593
k(L) = number of predictors in larger model = 3
R²(S) = R² from the smaller model = .563
k(S) = number of predictors in smaller model = 2
N = number of subjects 50

F = ((0.593-0.563))/(3-2)/((1-0.593)/(50-3-1)) = 0.030/0.008847826 =3.390663391

looking at an F-table F(1,50, α = .05) = 4.034309707 so, this R²-change is not significant at the .05 level because the F calculated value is smaller than the F tabulated value. It means that the addition of gender variable in the regression model is not needed as it does not help in predicting the dependent variable.

3b. Test the overall regression equation (including the variables of GRE, undergraduate GPA, and gender) for statistical significance. Report the F value obtained from this test and briefly explain what it means.

For overall model, we have

Multiple R = .770
R Square    = .593
Standard Error = .064

R Square    = .593
Regression/Total = 0.593
Regression = 0.593*Total...

By purchasing this solution you'll be able to access the following files:
Solution.docx.

$75.00
for this solution

or FREE if you
register a new account!

PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

Find A Tutor

View available Advanced Statistics Tutors

Get College Homework Help.

Are you sure you don't want to upload any files?

Fast tutor response requires as much info as possible.

Decision:
Upload a file
Continue without uploading

SUBMIT YOUR HOMEWORK
We couldn't find that subject.
Please select the best match from the list below.

We'll send you an email right away. If it's not in your inbox, check your spam folder.

  • 1
  • 2
  • 3
Live Chats