MTH205 Introduction to Statistical Methods
Tutorial 7
Based on Chapter 7
1. You are given the following data
x y
0.0 10.9
0.0 10.6
0.0 10.8
0.0 9.8
0.0 9.0
2.3 11.0
2.3 11.3
2.3 9.9
2.3 9.2
2.3 10.1
4.6 10.6
4.6 10.4
4.6 8.8
4.6 11.1
4.6 8.4
9.2 9.7
9.2 7.8
9.2 9.0
9.2 8.2
9.2 2.3
18.4 2.9
18.4 2.2
18.4 3.4
18.4 5.4
18.4 8.2
with Sxx = 1058, Syy = 198.76 and Sxy = −363.63. Using the simple linear regression model
Yi = β0 + β1xi + ; i = 1, 2,..., 25
where the are independent and normally distributed with zero means and equal variances σ2, obtain the least squares estimates of β0 and β1. Carry out a lack-of-fit test to determine the adequacy of the simple linear regression model at the 5% level of significance. Interpret the results.