Unit 9: Slopes
L46: CI for slopes
Properties
Mean of the sampling distribution
Std. dev. of the sampling distribution
σ can be estimated using the std. dev. of residuals
Conditions
Linearity: no pattern or fanning in scatterplot of residuals
Independence: population size 10x larger
Normality: no strong skew or outliers in scatterplot of residuals or n >= 30
Equal variance: std. dev. of y doesn't vary with x
Randomness: random assignment or randomized experiement
Margin of error for the slope
Point estimate of a regression model: β
Variables for population/sample
DF: n-2
Use one-sample t-interval for slope (quantitative data)
Interpretation of slope: mean/average increase (of ...) the prediction is always made for the population
Residual plots do NOT indicate independence
L47: Test for slopes
Test statistic for the slope of a regression model:
Testing for linearity:
Testing for another slope value:
H0: β = 0 Ha: β ≠ 0
H0: β = (some value) Ha: β > or < or ≠ the value
Same condition as the CI for slopes
Confidence interval for the slope