Results

Linear Regression

Parenting style, b^= 0.062, 𝛽^= 0.194, t = 5.057, p < 0.001, significantly predicted aggression. The beta value indicates that as parenting increases (i.e. as bad practices increase), aggression increases also. Sibling aggression ( b^ = 0.093, 𝛽^= 0.096, t = 2.491, p = 0.013) significantly predicted aggression. The beta value indicates that as sibling aggression increases (became more aggressive), aggression increases also. Computer games (b^ = 0.126, 𝛽^ = 0.134, t= 3.433, p < .001) significantly predicted aggression. The beta value indicates that as the time spent playing computer games increases, aggression increases also. Good diet ( b^ = –0.112, 𝛽^ = –0.118, t = –2.947, p = 0.003) significantly predicted aggression. The beta value indicates that as the diet improved, aggression decreased. The only factor not to predict aggression significantly was television use, b^ if entered = 0.033, t = 0.715, p = 0.475. Based on the standardized beta values, the most substantive predictor of aggression was parenting style, followed by computer games, diet and then sibling aggression.

𝑅2 is the squared correlation between the observed values of aggression and the values of aggression predicted by the model. The values in this output tell us that sibling aggression and parenting style in combination explain 5.3% of the variance in aggression. When computer game use is factored in as well, 7% of variance in aggression is explained (i.e. an additional 1.7%). Finally, when diet is added to the model, 8.2% of the variance in aggression is explained (an additional 1.2%). With all four of these predictors in the model still less than half of the variance in aggression can be explained.

Model Summary - aggression
Model R R² Adjusted R² RMSE
M₀ 0.231 0.053 0.050 0.311
M₁ 0.264 0.070 0.066 0.309
M₂ 0.286 0.082 0.076 0.307
M₃ 0.287 0.083 0.076 0.307
Note.  M₀ includes parenting_style, sibling_aggression
Note.  M₁ includes parenting_style, sibling_aggression, computer_games
Note.  M₂ includes parenting_style, sibling_aggression, computer_games, diet
Note.  M₃ includes parenting_style, sibling_aggression, computer_games, diet, television
ANOVA
Model   Sum of Squares df Mean Square F p
M₀ Regression 3.612 2 1.806 18.644 < .001
  Residual 64.230 663 0.097  
  Total 67.842 665  
M₁ Regression 4.736 3 1.579 16.561 < .001
  Residual 63.106 662 0.095  
  Total 67.842 665  
M₂ Regression 5.554 4 1.389 14.735 < .001
  Residual 62.288 661 0.094  
  Total 67.842 665  
M₃ Regression 5.602 5 1.120 11.882 < .001
  Residual 62.240 660 0.094  
  Total 67.842 665  
Note.  M₀ includes parenting_style, sibling_aggression
Note.  M₁ includes parenting_style, sibling_aggression, computer_games
Note.  M₂ includes parenting_style, sibling_aggression, computer_games, diet
Note.  M₃ includes parenting_style, sibling_aggression, computer_games, diet, television
Coefficients
Collinearity Statistics
Model   Unstandardized Standard Error Standardized t p Tolerance VIF
M₀ (Intercept) -0.006 0.012 -0.479 0.632  
  parenting_style 0.062 0.012 0.194 5.057 < .001 0.970 1.031
  sibling_aggression 0.093 0.038 0.096 2.491 0.013 0.970 1.031
M₁ (Intercept) -0.007 0.012 -0.574 0.566  
  parenting_style 0.054 0.012 0.170 4.385 < .001 0.937 1.067
  sibling_aggression 0.068 0.038 0.070 1.793 0.073 0.933 1.072
  computer_games 0.126 0.037 0.134 3.433 < .001 0.918 1.090
M₂ (Intercept) -0.006 0.012 -0.497 0.619  
  parenting_style 0.062 0.013 0.194 4.925 < .001 0.897 1.115
  sibling_aggression 0.086 0.038 0.088 2.258 0.024 0.908 1.101
  computer_games 0.143 0.037 0.153 3.891 < .001 0.893 1.120
  diet -0.112 0.038 -0.118 -2.947 0.003 0.870 1.150
M₃ (Intercept) -0.005 0.012 -0.416 0.677  
  parenting_style 0.057 0.015 0.177 3.891 < .001 0.669 1.494
  sibling_aggression 0.082 0.039 0.084 2.106 0.036 0.883 1.133
  computer_games 0.142 0.037 0.152 3.851 < .001 0.891 1.123
  diet -0.109 0.038 -0.115 -2.864 0.004 0.862 1.160
  television 0.033 0.046 0.032 0.715 0.475 0.697 1.436

Residuals vs. Predicted

Q-Q Plot Standardized Residuals

The Q-Q plot shown above suggests that errors are (approximately) normally distributed. The Residuals vs. Predicted scatterplot helps us to assess both homoscedasticity and independence of errors. The scatterplot does not show a random pattern and so indicates no violation of the independence of errors assumption. Also, the errors on the scatterplot do not funnel out, indicating homoscedasticity of errors, thus no violations of these assumptions.