Question

Question text Suppose that you have a five-point sample data set; the observations of (x, y) are given by (8, 3), (10, 3), (6, 2), (2, 0), and (2, 1).

Fit a simple linear regression model to this data by first computing the least squares estimate of the slope parameter.

Which of the following is the most accurate? Select one:

a. 0.3438

b. 0.4728

d. 0.6712

Answer 1

The following data are passed:

X	Y
8	3
10	3
6	2
2	0
2	1

The independent variable is X, and the dependent variable is Y. In order to compute the regression coefficients, the following table needs to be used:

	X	Y	X*Y	X2	Y2
	8	3	24	64	9
	10	3	30	100	9
	6	2	12	36	4
	2	0	0	4	0
	2	1	2	4	1
Sum =	28	9	68	208	23

Based on the above table, the following is calculated:

Therefore, based on the above calculations, the regression coefficients (the slope m, and the y-intercept n) are obtained as follows:

OPTION A is correct

Also

Therefore, we find that the regression equation is:

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