Q1: Even before looking at his data file, what is the major problem with your friend’s write up above? Multivariate Analysis does not indicate causality.
Q2: How would you interpret the effect size for the predictability of physical health symptoms on mental health visits? Moderate. R squared rule of thumb – Small = 1%, Moderate = 9%, Strong = 25%
Because of what you have been taught about regression in Stats I and II you know that there may be some underlying issues with your friend’s interpretation of the results. After asking to see his dataset you notice that two more variables were not used in your friend’s original regression model; visits to health professionals (timedrs) and the number of mental health symptoms (menhel). Being the good friend that you are, you decide to run an atheoretical regression analysis on your friend’s data.
Instructions: run a standard multiple regression analysis on all the data. Be sure that you use physical health symptoms as the dependent variable and answer the next several questions.
Q3. Is there any evidence that suggests violations of assumption for multiple regressions analysis (eg Independence of Observations, linearity, homoscedasticity, multicollinearity, outlier, normality, etc…)? Please explain (write in APA format).
There was independence of residuals, as assessed by a Durbin-Watson statistic of 1.957. There was linearity and homoscedasticity, as assessed by visual inspection of a plot of studentized residuals versus unstandardized predicted values. There was no evidence of multicollinearity, as assessed by VIF values greater than 10 thus no transformation of variables. There were 6 studentized deleted residuals greater than ±3 standard deviations, however, these cases remained in the final analysis due to no leverage values greater than 0.2, and values for Cook's distance above 1. The assumption of normality was met, as assessed by a Q-Q Plot.
Q4. Examine the model summary and fit. In APA format, explain if the model is a good fit and how much variance it explains if it is.
The multiple regression model statistically significantly predicted physical health symptoms, F(3,461) = 87.107, p < .001, adj. R2 = .36.
Q5. Summarize the coefficients, standard error, and standardized coefficient in an APA formatted summary table (see Standard Multiple Regression, pg 19 in Laerd for example).
Table 1
Multiple Regression results for physical health symptoms
phyheal B 95% CI for B SE B β R2 Adj R2
LL UL
Model .362 .358***
Constant 2.79*** 2.43 3.15
Visits to health Professionals .069*** .053 .086 .009 .318***
Mental Health Symptoms
.227*** .182 .213 .023 .399***
Stressful life events .001 .000 .003 .001 .067
Note. Model = “Enter” method in SPSS Statistics.
*p<.05. **p<.01. ***p<.001
Q6. From the table above, interpret your coefficients. Please write the multiple regression equation.
Phyheal = 2.793 + .069(timedrs) + .227(menheal) + .001(stress)
Q7. Are there any factors that may not be good predictors in the model? Which one and how do you know it is not a good fit?
Stressful life events were not a good predictor of physical health symptoms because p>.05.
After you ran the standard multiple regression model you noticed that one of the factors may not be a good predictor in the model. You have a theory that by itself, the factor in question is a significant predictor of physical health symptoms but as you add other factors it loses its power.
Instructions: Run a hierarchical multiple regression analysis on all the data with physical health symptoms as the dependent variable. Step 1 please use only stress. Step 2 add timedrs. Step 3 add menheal. Please answer the following questions.
Q8. Examine the model summary and fit. In APA format, explain if the model is a good fit and how much variance it explains if it is. Please note how R squared change as you add the multiple factors
The full model of stressful events, visits to health professionals and mental health symptoms to predict physical health symptoms (PHS) (Model 3) was statistically significant, R2 = .362, F(3, 461) = 87.107, p < .0005; adjusted R2 = .358. The initial model for the prediction of (PHS) led to a statistically significant increase in R2 of .093, F(1, 463) = 47.678, p< .001. The addition of visits to health professionals to the prediction of PHS (Model 2) led to a statistically significant increase in R2 of .135, F(1,462) = 80.800, p < .001. The addition of mental health symptoms to the prediction of PHS (Model 3) also led to a statistically significant increase in R2 of .133, F(1, 461) = 96.399, p < .001.
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