LSRLs and Residuals
ŷ = a + bx
MANATEE POWERBOAT DATA
Interpreting Slope
Interpreting Slope
"On average, for each additional 1000 powerboats, the predicted number of manatees killed increases by 0.13"
Extrapolation
Extrapolation
The use of a regression line for a prediction far outside the interval of values of the explanatory variable x used to obtain the line. Such predictions are often inaccurate
Residuals
Residuals
Distance from data point to line
actual - predicted → y - ŷ
sum of residuals is 0 (and so is the mean)
Coefficient of Determination (r²)
Coefficient of Determination (r²)
The percentage of variability in y that is explained by the LSRL of y on x
[0,1] the closer to 1, the stronger the correlation
"90.82% of variability in manatees killed is explained by the LSRL of manatees killed on boats in thousands"
Standard Deviation of Residuals
Standard Deviation of Residuals
This value gives the approximate size of a "typical" prediction error (residual)
