Question

We want to investigate the causal relationship between the dependent variable Y and independent variable x.

X	Y
1	2
2	2
3	4
4	4
5	8

A) Calculate the ?₀ hat and ?₁ hat (show the steps)

B) Calculate SSE, S², and S

C) Calculate the t-statistics for ?₁ hat

Answer 1

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	1	2	1	4	2
	2	2	4	4	4
	3	4	9	16	12
	4	4	16	16	16
	5	8	25	64	40
Total	15	20	55	104	74

Sample size: n=5

Now,

A)

Slope of the regression equation is

and intercept of the equation will be

So the regression equation will be

y'=-0.2 +1.4x

B)

Let us find SSE first :

The S^2 is

So standard error of estimate will be

C)

The standard error of slope is

T-statistics is