Simple Linear Regression

Question 1

Residuals

Answer 1

• Difference between observed value (data points) and values predicted by the model (i.e. regression line)
• Residual = (observed value) - (predicted value)

Question 2

Residual sum of squares SS_R

Answer 2

Square residuals and sum them

Question 3

How to determine the line of best fit

Answer 3

• Ordinary least squares (OLS) method: line with smallest SS_R (error)

Question 4

R-squared R² in regression

Answer 4

• Proportion of variance accounted for by the regression model
• In simple (one predictor) regression, this is the same as the shared variance
• R² = SS_M/SS_T
  
  • SS_T = Total variability: variability between the scores and the mean
  • SS_M: Model variability: difference between the model (line) and the mean

Question 5

R² SPSS output

Answer 5

Question 6

ANOVA (F)

Answer 6

• Whether the regression line is a significantly bettwe fit to the data than chance (using the mean as our best guess)

Question 7

ANOVA (F) SPSS output

Answer 7

Question 8

Model parameters

Answer 8

Equation for a straight line is y = b₀ + b₁x

• b_<em>0</em> is the constant and the y-intercept
• b₁ is the gradient of the line
• y is the outcome variable (DV)
• x is predictor (IV)

Question 9

Model parameter SPSS output

Answer 9