Question

X	Y
0	22.1
1	24.5
2	26
3	26.8
4	28.2
5	28.9
6	30
7	30.4
8	31.4
0	21.9
2	26.1
4	28.5
6	30.3
8	31.5
10	33.1
0	22.8
3	27.3
6	29.8
9	31.8

Answer 1

We use minitab to solve this question.
The null and alternative hypothesis are,
Ho : There is no lack of fit in the simple linear regression model.
Ha : There is lack of fit in the simple linear regression model
Minitab Output
Regression Analysis: Y versus X

Analysis of Variance

Source         DF   Adj SS   Adj MS F-Value P-Value
Regression      1 195.243 195.243   359.28    0.000
X             1 195.243 195.243   359.28    0.000
Error          17    9.238    0.543
Lack-of-Fit   9    8.485    0.943    10.01    0.002
Pure Error    8    0.753    0.094
Total          18 204.481

F statistic is 10.1 and it's corresponding p-value is 0.002 which is smaller than the significance level alpha =0.05 therefore their is sufficient evidence to conclude that there is lack of fit in simple linear regression model
______________________________________________________________________________________________
Ho : There is no lack of fit in the simple linear regression model.
Ha : There is lack of fit in the simple linear regression model

Regression Analysis: Y versus X, x2

Analysis of Variance

Source         DF   Adj SS   Adj MS F-Value P-Value
Regression      2 201.994 100.997   649.87    0.000
X             1   44.161   44.161   284.15    0.000
x2            1    6.752    6.752    43.44    0.000
Error          16    2.487    0.155
Lack-of-Fit   8    1.733    0.217     2.30    0.130
Pure Error    8    0.753    0.094
Total          18 204.481

F statistic is 2.30 and it's corresponding p-value is 0.130 which is greater than the significance level alpha =0.05 therefore their is sufficient evidence to conclude that there is lack of fit in simple linear regression model.

In second model their is absence of lack of fit while in the first model their is presence of lack of fit therefore we prefer second model.