Consider the data set shown below. Find the 95% confidence interval for the slope of the regression line.
y 0 3 2 3 8 10 11
x -2 0 2 4 6 8 10
9) A) 0.94643 ± 0.27603 B) 0.94643 ± 0.33306 C) 0.94643 ± 0.28377 D) 0.94643 ± 0.36203
Answer:-
Given That:-
Consider the data set shown below. Find the 95% confidence interval for the slope of the regression line.
y 0 3 2 3 8 10 11
x -2 0 2 4 6 8 10
Given,
-2 | 0 | 4 | 0 | 0 | -0.3927 | at x = -2 | 0.3927 |
0 | 3 | 0 | 9 | 0 | 1.5001 | at x = 0 | 1.4999 |
2 | 2 | 4 | 4 | 4 | 3.3929 | at x = 2 | -1.3929 |
4 | 3 | 16 | 9 | 12 | 5.2857 | at x = 4 | -2.2857 |
6 | 8 | 36 | 64 | 49 | 7.1785 | at x = 6 | 0.8215 |
8 | 10 | 64 | 100 | 80 | 9.0713 | at x = 8 | 0.9287 |
10 | 11 | 100 | 121 | 110 | 10.9641 | at x =10 | 0.0359 |
= 28/7
= 4
= 37/7
= 5.2857
= 106.0004/112
= 0.9464
= 5.2857 - 0.9464 * 4
= 1.5001
Simple linear regression model
= 11.1072/7-2
= 2.2213
= 224 - 7*4 *4
= 112
100(1 - )% confidence interval for is
i.e,
0.9464 0.3619968
0.9464 0.36200
Here I take , Take and perfrom calculation then you will get exact 0.9463 0.36203 95% confidence interval.
The correct answer is option (D)
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