Question

For the following bivariate data obtain the equation of regression line of Y on X.

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

Answer 1

X = xi	Y = yi	`bb("x"_"i"^2)`	`bb("y"_"i"^2)`	xiyi
1	5	1	25	5
2	7	4	49	14
3	9	9	81	27
4	11	16	121	44
5	13	25	169	65
15	45	55	445	155

From the table, we have

n = 5, ∑ x_i = 15, ∑ y_i = 45, `sum x_i^2 = 55`, `sum y_i^2 = 445`,  ∑ x_i y_i = 155

`bar x = (sum x_i)/n`

= `15/5`

= 3

`bar y = (sum y_i)/n`

= `45/5`

= 9

Now, for regression equation of Y on X,

`"b"_"YX" = (sumx_i y_i − n bar x bar y)/(sum x_i^2 − n barx^2)`

`= (155 − 5 xx 3 xx 9)/(55 − 5(3)^2)`

= `(155 − 135)/(55 − 45)`

= `20/10`

= 2

Also, `a = bar y − b_(XY) xx bar x` 

= 9 − 2(3)

= 9 − 6

= 3

The regression analysis of Y on X is

Y = a + b_YX X

∴ Y = 3 + 2X