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Unit 9: Slopes - Coggle Diagram
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
DF: n-2
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
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
Confidence interval for the slope
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