Question

5. Consider the data points (x, y) (10,0.8), (20, 1.6), (30, 2.3), (40, 2.8) (with equal error bars ơi-0-0.06), which have been fitted by the straight line y-0.2 + 0.067x using a least squares method. (a) (4 pts.) Find the value of x2 for the data. (b) (4 pts) Is it possible to assert, with 95% confidence, that a straight line is a good fit for the data? Explain why or why not Hint: Once you have set up the required matrices, you may use a calculator] for the matrix operations, just mention where you used a calculator. 1If you don't have a calculator that handles matrices, a website like www.wolframalpha.com may help. either the instructor nor the T.A. will provide assistance in using calculators, software, or websites.

Answer 1

here we use chi-square test and chi-square=Sum((O-E)²/E)=0.0139 with k-1=4-1=3 df

with null hypothesis H0: observed value =expected value ( line is good fit)

alternate hypothesis Ha: observed value not =expected value ( line is not good fit)

(a) chi-square=0.0139

(b) the critical chi-square(0.05,3)= 7.8147 is the more than calculated chi-square=0.0139, so we fail to reject H0 and conclude that straight line is good fit

following calcualtion has been done for answering this question

x	y(observed)	y(expected)	O-E	(O-E)2/E
10	0.8	0.87	-0.07	0.0056
20	1.6	1.54	0.06	0.0023
30	2.3	2.21	0.09	0.0037
40	2.8	2.88	-0.08	0.0022
sum	7.5	7.5	-1.1E-15	0.0139

O=observed

E=Expected