Question

6. The value of the residuals for a linear regression model with six observations is given in the table below.

Observation number 1, 2, 3, 4, 5, 6

Residual (ei) 1.1, 4.2, -0.5, -3.7, 2.3, -1.9

(a) Compute the value of the residual variance for this sample.

(b) Compute the value of the residual standard error for this sample.

(c) Explain why the residual variance is useful in hypothesis tests for the slope and the intercept.

Answer 1

	Residuals( e)	e^2
	1.1	1.21
	4.2	17.64
	-0.5	0.25
	-3.7	13.69
	2.3	5.29
	-1.9	3.61
Total	SSE =	41.69	SUM(e^2)
	n =	6
Se^2 =	MSE =	4.948333	SSE/n-2
	Se =	2.224485	SQRT(MSE)

a)

the value of the residual variance for this sample = Se^2 = 4.948

b)

the value of the residual standard error for this sample = Se = 2.224

c)

t stat for intercept and slope

t = bi/Sbi

Sb0 = Se * (1/n+Xbar^2/SSxx)^2

Sb1 = Se/SQRT(SSxx)

Standard error of slope or intercept is directly proportional to the standard error of regression

Standard error of regression is used to find slope and intercept standard errors