OLS a Y write the estimated b s c SEbeta1 If x 15 y Sol

OLS a) Y^ = (write the estimated b) s = c) SE_beta1 = If x = 15, y^ =

Solution

Regression E1n:

-15

Mean of X = X / n =    5
Mean of Y = Y / n =   4
(Xi - Mean)^2 =   20
(Yi - Mean)^2 =   70
(Xi-Mean)*(Yi-Mean) =   -29
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2    
b1 = -29 / 20 = -1.45  
bo = Y / n - b1 * X / n  
bo = 4 - -1.45*5 = 11.25  
  
Y = bo + b1 X  
  
Y\'=11.25-1.45*X  

[ANSWERS]
1.Y\'=11.25-1.45*X
2. Slope = -1.45
3. When X = 15, y= 11.25-1.45*(15) = -10.5
X=-8 => Y = 1.25-1.45*(15) = -10.5
X=-8 => Y = -10.5

Line of Regression Y on X i.e Y = bo + b1 X
Xi	Yi	(Xi - Mean)^2	(Yi - Mean)^2	(Xi-Mean)*(Yi-Mean)
8	2	9	4	-6
6	-2	1	36	-6
5	5	0	1	0
4	6	1	4	-2
2	9	9	25	-15