Multiple regression P

multiple linear regression

Y = a + b1X1 + b2X2 + ... bkXk + e

slope in multiple regression

represents the predictive relationship between an independent variable X with the dependent variable Y, while holding all other independent variables constant, or controlling for their effects

Which variable is most important in predicting the number of items recalled?

comparison of the standardized coefficients

• the larger the absolute value of the standardized coefficient, the greater the impact the corresponding predictor has on the dependent variable

delta r-squared

measures the increase in explained variance

model comparison

this test evaluates whether there is a significant difference between the two models in the amount of variance explained

multiple regression - assumptions

• the dependent variable: quantitative

• the independent variable: quantitative/categorical

• a linear relationship

• no outliers

• no multicollinearity

• the residuals are normally distributed

• ohmoscedasticity of the residuals

• residuals are independent

checking for outliers 

Cook’s distance - presence of multivariate outliers 

• >1 - presence of outliers

checking multicollinearity

1. the correlation between pairs of independent variables and verifying that they are not strong

2. Tolerance >0.2 - no multicollinearity

3. Variance Inflation Factor - should be low

checking for normal distribution of the residuals

1. Shapiro-Wilk test - statistic close to 1

2. Q-Q plot of the residuals - point lie along reference line

checking if residuals are independent - no autocorrelation

Durbin-Watson test for autocorrelation - p>0.05

• around 2d

checking for homescedasticity of the residuals

residuals scatterplots