Common Hypotheses
H0 : β = 0 Ha : β ≠ 0
H0 : β = 0 Ha : β < 0
H0 : β = 0 Ha : β > 0
Assumptions
Sample are randomly selected or a randomized experiment.
Sampling with replacement (or sample size < 10% N)
The true relationship between x and y is linear.
The standard deviation for y does not vary with x.
sample size n > 30 or distribution of residuals does not show strong skewness
Sampling Distribution
Student's t (if σ unknown)
Scatter plot
SPSS: Graphs -> Legacy Dialogs -> Scatter/Dot...
Pearson Correlation
Analyze -> Correlate -> Bivariate...
Analyze -> Regression -> Linear...
Residual Plot
Step 1: Analyze -> Regression -> Linear...
Step 2: Save...
Step 3: Check Residuals Unstandardized
Step 4: Plot X vs RES_1