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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.