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`	xi yi
1	5	1	5
2	7	4	8
3	9	9	27
4	11	16	64
5	13	25	125
15	45	55	229

From the table, we have,

n = 3, ∑ x_i = 15, ∑ y_i = 45, `sum x_i^2 = 55`, ∑ x_i y_i = 229

`barx = (sum x_i)/n 15/3 = 5`

`bary = (sum y_i)/n = 45/3 = 15`

Now, `b_YX = (sumx_i y_i - n bar x bar y)/(sum x_i^2 - n barx^2)`

`= (229 - 3xx5xx15)/(55 -  3(5)^2)`

= `(229 - 225)/(55 - 75)`

= `4/-20`

∴ b_YX = − 0.2

Also, `a' = bary - b_YX  barx`

= 15 − (− 0.2) (5)

 = 15 + 1.0

= 1.5

∴ The regression equation of Y on X is

Y = a' + b_YX X

∴ Y = 1.5 - 0.2 X