AP Statistics
Chapter 15 – Inference for Regression
Mr. Dooley
Here is a good way to remember the assumptions/conditions for inference for the slope of the true LSRL.
L – The mean response 𝜇 𝑦
has a straight L ine relationship with x . 𝜇 𝑦
= 𝛼 + 𝛽𝑥 The slope β and intercept α are unknown parameters.
I – Repeated responses y are I ndependent of each other.
N – residuals have approximately N ormal distribution
E – residuals have E qual variance
This is an example of data that satisfy the conditions for regression inference well:
15.3 One of nature’s patterns connects the percent of adult birds in a colony that return from the previous year and the number of new adults that join the colony. Here are the data for 13 unrelated colonies of sparrowhawks: x = percent of adult sparrowhawks returning x y
74
5
66
6
81
8
52
11
73
12
62
15 y = number of new adult sparrowhawks
52
16
45
17
62
18
46
18
60
19
46
20
38
20
(a) Independent Observations . Can we assume the 13 observations are independent?
(b) Linear Relationship.
Make a residual plot. Does the plot show any systematic deviation from a roughly linear pattern?
(c) Spread about the line stays the same.
Does your residual plot show any systematic change in spread as x changes?
(d) Normal variation about the line.
Make a histogram of the residuals. With only 13 observations, no clear shape emerges. Do strong skewness or outliers suggest lack of Normality?