Here is a good way to remember the assumptions/conditions for a

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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?

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