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Linear regression

(a) In this question, A,B, and C are random variables with means µA,µB, and µC respectively, and a common variance σ
2
. An independent random sample of size 10 is
taken from each of these random variables, with the following results:
a¯ = 49.617 ∑
10
i=1
a
2
i = 24635.30 ∑
10
i=1
(ai −a¯)
2 = 16.832
b¯ = 48.526 ∑
10
i=1
b
2
i = 23583.16 ∑
10
i=1
(bi −b¯)
2 = 35.438
c¯ = 51.031 ∑
10
i=1
c
2
i = 26100.33 ∑
10
i=1
(ci −c¯)
2 = 58.704
i) Explain what assumptions on A,B, andC are required in order to perform a oneway ANOVA test of the null hypothesis µA = µB = µC against the alternative that
this is false. [2 marks]
ii) Given that those assumptions hold, perform the ANOVA test at the 0.05 significance level. [5 marks]
iii) Let SSw denote the total sum of squares random variables in this ANOVA set-up.
What is the distribution of SSw/σ
2? [3 marks]
iv) Derive a 95% confidence interval for σ
2
.

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