Question

Compute the appropriate regression equation for the following data:

X	1	2	3	4	5
Y	5	7	9	11	13

X is the independent variable and Y is the dependent variable.

Answer 1

Since X is an independent variable and Y is a dependent variable, we find the regression equation of Y on X.

X = xi	Y = yi	`x_i^2`	xiyi
1	5	1	5
2	7	4	14
3	9	9	27
4	11	16	44
5	13	25	65
15	45	55	155

From the table, we have,

n = 3, ∑X = 15, ∑Y = 45, ∑X² = 55, ∑XY = 155

`bar x = (sum X)/n 15/5` = 3

`bar y = (sum Y)/n = 45/5` = 9

Now, b_YX = `n((sum X Y) - n(sum X)(sum Y))/(n(sum X^2) - (sum X)^2)`

= `(5(155) - (15)(45))/(5(55) - (15)^2)`

= `(775 - 675)/(275 - 225)`

= `100/50`

∴ b = 2

The formula for the Y-intercept, a, is:

a = `bar Y - b bar X`

= 9 − 2(3)

 = 9 − 6

= 3

∴ The regression equation of Y on X is

Y = a + bX

∴ Y = 3 − 2 X