Question

ce the given data to find the equation of the regression line. Fill out the table below and show how you calculate each value below. Round the final values of a and b to three decimal places, if necessary. 5) x 0 3 4 5 12 y 8 2 6 9 12 5) X-7 y-y (x-7)(y- 0 3 y 8 2 6 9 4 5 12 12 b=

Answer 1

We are given the following data

x	0	3	4	5	12
y	8	2	6	9	12

$\overline{x}$ = mean of all values of x

= (0 + 3 + 4 + 5 + 12) / 5 = 24/5 = 4.8

= 4.8

$\overline{y}$ = mean of all values of y

= (8 + 2 + 6 + 9 + 12) / 5 = 37/5 = 7.4

T		(2-x)	$(y-\overline{y})$	(2 - -T)	(-1) (2-0)
0	8	-4.8	0.6	23.04	-2.88
3	2	-1.8	-5.4	3.24	9.72
4	6	-0.8	-1.4	0.64	1.12
5	9	0.2	1.6	0.04	0.32
12	12	7.2	4.6	51.84	33.12
Total				78.8	41.4

b = slope of the regression line = S_xy / S_xx =  $\frac{\sum (x-\overline{x})(y-\overline{y})}{\sum (x-\overline{x})^{2}}$

= 41.4 / 78.8

= 0.525

a = intercept on y axis when x = 0

= $\overline{y}-b\overline{x}$

= 7.4 - 0.5253 * 4.8

= 4.878

Regression line , $\widehat{y}$ = 4.878 + 0.525*x

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