Question

find a linear (regression) equation with following data.

Answer y= ( ) + ( )* x

(X, Y)

(30, 12)

(40, 20)

(50, 24)

(60, 38)

(70, 40)

Answer 1

Solution:
Linear regression equation can be calculated as
Y = a +b*X
Here a is the intercept of the regression line and b is the slope of regression line
slope and intercept can be calculated as

X	Y	X^2	Y^2	XY
30	12	900	144	360
40	20	1600	400	800
50	24	2500	576	1200
60	38	3600	1444	2280
70	40	4900	1600	2800
250	134	13500	4164	7440

Slope = (n*Summation(XY)-Summation(X)*Summation(Y))/(n*summation(X^2)-(Summation(X))^2) = (5*7440 - 250*134)/(5*13500-250*250) = 0.74
Intercept can be calculated as
Intercept = (Summation(Y) - b*Summation(X))/n = (134-0.74*250)/5 = 134-185)/5 = -10.2
So regression equation is
Y = - 10.2 + 0.74*X