Question

2. Theory gives you the following relationship between variables x and y, y = β0 + β1x + u. You collect a sample of data on n = 4 sample members. The data are : {x1, y1} = {3, 8},{x2, y2} = {2, 7},{x3, y3} = {1, 6},{x4, y4} = {3, 4}

a. State the minimization problem that you need to derive the OLS estimators

b. Estimate the relationship between x and y using this sample. What is your estimate of β0 and β1 ?

c. What is your prediction for y when x =10 ? (i.e. Find by when x = 10 )

Answer 1

Please give ratings it will be appreciable, for any query please comment, Thank you

Solution,

Solution b).

x	y	xi-x(bar)	yi - y(bar)	(xi - x(bar))*(yi - y(bar))	(xi - x(bar))2
3	8	0.75	1.75	1.3125	0.5625
2	7	-0.25	0.75	-0.1875	0.0625
1	6	-1.25	-0.25	0.3125	1.5625
3	4	0.75	-2.25	-1.6875	0.5625
9	25			-0.25	2.75