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