This document contains most (almost all) of the workgroup's important assignments incorporated into an exam guide. The type of question is printed in bold, with the steps below on how to process it in SPSS (to possibly take to your exam, but if you no longer understand the question/no longer know h...
Week 1 | Multiple Regression Analysis (MRA)
When? Independent X1, X2 (INT) + Dependent Y (INT)
Y is always regressed on X
Q: Calculate the Pearson correlations between the five variables.
Analyze > Correlate > Bivariate > insert variables >
Q: What is the sample size N?
Under ‘N’
Q: Does it make sense to perform a linear regression of GPA on IQ, age, gender and/or
self-concept?
Check ‘Correlations’ table and check for each variable the correlation and the significance, if it’s
significant we can say it makes sense or think theoretically
Q: Which variable is likely to be a good predictor of GPA?
Check ‘Correlations’ table and check for each variable the correlation and the significance, if it’s
significant it is likely to be a good predictor
Next, perform a linear regression of GPA on IQ, age, gender and self-concept. In Statistics, ask for
part and partial correlations, and collinearity diagnostics. In Save ask for Cook’s distances and
Leverage values.
Q: Can the null hypothesis of no relationship between GPA and IQ, age, gender and/or
self-concept be rejected?
< Analyze > Regression > Linear > in ‘Statistics’ check ‘part and partial correlations’ and ‘collinearity
diagnostics’ > in ‘Save’ ask for ‘Cook’s distances’ and ‘Leverage values’
H0: none of the predictors are good predictors
Ha: at least some of the predictors are good predictors
• Check ANOVA table > report the F value → e.g. F(dfregression, dfresidual) = value → F(4,73) =
23.117, p<0.001
• If F value is significant, we can reject H0, at least some of the predictors are good predictors
Q: How much variance of GPA is explained by IQ, age, gender and SC together?
• Look at ‘Model Summary’ table > look at R squared > report the value
Q: What predictor explains the most unique variance?
• Look at ‘Coefficients’ table > under ‘correlations’ look at the ‘part’ column > the biggest number
should be squared, that variable explains the most unique variance
Q: Is there evidence of multicollinearity in the predictors?
Test whether we have too much of a dependence between our predictors
• Look at ‘Coefficients’ table and under VIF column > VIF should be below 10 > Tolerance needs to
be bigger than 0.1
,Q: Do Cook’s distances and Leverage values suggest the presence of outliers?
• Formula center leverage value: 3(p+1)/N where p = number of predictors > the value calculated is
the largest value we can have in the centered leverage values > look at ‘Residuals Statistics’ under
‘maximum’ column at ‘centered leverage value’ > determine whether the calculate value is higher
than the maximum value in the table > if value calculated is bigger than given value, it suggests
outliers
• Cook’s distance tells us whether an outlier is influential > look at ‘Residuals Statistics’ > check
Cook’s distance value under ‘minimum’ and ‘maximum’ > should not be higher than 1
Q: If one or more outliers are detected, all previous steps are repeated with exclusion of the
outlier(s). Use Selection to get rid of the outlier(s).
• Look at Data View tab > go to new Cook’s Distance variable > select with right mouse and click
‘sort descending’ > look at which participants have a distance above 1 > don’t delete the participant
> go to ‘Data’ and ‘Select cases’ > click ‘if conditions is satisfied’ and insert criteria of the study (e.g.
participants should be below the age of 14)
Q: Finally, remove the non-significant predictors from the model
• Run the analysis of LRA again > remove Cook’s Distance and Leverage under ‘Save’ > Look at
‘Coefficients’ table and look at whether the variables are significant (<0.05) and determine the ones
that are not significant
Q: Perform a linear regression of GPA on the remaining predictors. In Plots, make a scatter plot
of the standardized predicted values versus the standardized residuals, and ask for the normal
probability plot.
• Run LRA again > remove non-significant predictors > in ‘Plots’ add ZPred to X and ZResid to Y and
check normality probability plot
Q: Is there evidence of non-linearity, heteroscedasticity or non-normality of the residuals?
• Look at ‘Scatterplot’
• Linearity = if one creases the other increases, if one decreases the other one decreases > the plot
should look like there is no relationship (look a bunch of random spots) and if the best description is
a horizontal line there is evidence of non-linearity
• Heteroscedasticity → we want homoscedasticity > so we don’t want differences > check from
value 0 on the Y-axis, if there is approx the same amount of dots on both sides, we don’t violate the
assumption of heteroscedasticity
• Normality → look at ‘Normal P-P Plot of Regression’ > the more the dots are on the line the better
the normality → ??????
Q: What is the estimated regression equation? Interpret the regression coefficients.
• Look at ‘Coefficients’ table > constant = intercept (b0) > b1 = variables > add constant and all
variables in the equation
• ŷ = b0 + b1(var) → use unstandardized
Q: How much variance of GPA is explained by the predictors?
, • Look at ‘Model Summary’ and R squared
Q: What predictor explains the most unique variance?
• Look at ‘Coefficients’ table > look under ‘correlations’ and ‘part’ > report the biggest number and
square it
Hierarchical Regression Analysis
Q: How much variance of VarX is explained by VarY?
• Check ‘Model Summary’ table > check R squared
Q: add VarZ as a predictor in a second block to the linear model. In Statistics, ask for R squared
change
Analyze > Regression > Linear > add predictor to Independent in Next’ Block > in ‘Statistics’ ask for
‘R squared change’ > check the same options under ‘Statistics’
Q: Does adding VarZ significantly improve the linear model?
• Look at the ‘Model Summary’ table > look at R squared change > if the model contributed, the
value under model 2 should be positive (and thus the R square has become higher with model 2 >
report the significaince with F and df
Q: Is there evidence of non-linearity, heteroscedasticity or non-normality of the residuals?
In this example we don’t violate the assumption of linearity, heteroscedasticity, or normality
Q: What is the estimated regression equation? Interpret the regression coefficients.
• Do the same as a normal regression equation, except we now look at the values for model 2
• If everything else remains the same, improving 1 point of the score of VarY (independent), would
make the predicted score of VarX (dependent) … (value of VarY B unstandardized) higher
• If we hold everything else the same, if a participant scores one point higher on VarZ, the predicted
value of VarX (dependent) would become (value of VarZ B unstandardized) higher
Q: How much variance of VarX is explained by VarY and VarZ together?
• Look at ‘Model Summary’ > look at R square model 2 > that would explain the variance
Q: How much variance is uniquely explained by neuroticism?
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