Problem 1 (50 points)
Consider a simple linear regression yi = β0 + β1xi + εi with a sample of size n = 10, which yielded
x 1 1 1 1 1 −1 −1 −1 −1 −1 y 2.5 1.5 1.5 1.5 1.5 −2.5 −1.5 −1.5 −1.5 −2.5
For your convenience,
n ni=1 yi ni=1 xi ni=1 yi2 ni=1 x2i ni=1 xiyi
10 −1 0
34.5 10 18
(a) Find the least-squares estimates βˆ0 and βˆ1. (b) Find an unbiased estimate of variance σ2.
(c) At 5% level, test whether each of β0 and β1 are zero. Show your work. (d) What proportion of variation in y is explained by the regression line?
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