Question

1. Explain an example of the Breusch-Pagan test.

Answer 1

let us consider the data

MPG	HORSE POWER
43.1	48
19.9	110
19.2	105
17.7	165
18.1	139
20.3	103
21.5	115
16.9	155
15.5	142
18.5	150
27.2	71
41.5	76
46.6	65
23.7	100
27.2	84
39.1	58
28	88
24	92
20.2	139
20.5	95
28	90
34.7	63
36.1	66
35.7	80
20.2	85
23.9	90
29.9	65
30.4	67
36	74
22.6	110
36.4	67
27.5	95
33.7	75
44.6	67
32.9	100
38	67
24.2	120
38.1	60
39.4	70
25.4	116
31.3	75
34.1	68
34	88
31	82
27.4	80
22.3	88
28	79
17.6	85
34.4	65
20.6	105

using excel>data>data analysis>Rehression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.788177
R Square	0.621224
Adjusted R Square	0.613333
Standard Error	5.081207
Observations	50
ANOVA
	df	SS	MS	F	Significance F
Regression	1	2032.546	2032.546	78.72388	1.09E-11
Residual	48	1239.296	25.81867
Total	49	3271.842
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	50.00521	2.523506	19.81577	9.42E-25	44.93136	55.07905
HORSE POWER	-0.23627	0.02663	-8.87265	1.09E-11	-0.28982	-0.18273

the vakue of R2 = 0.6212

n = 50

let us consider the null and alternative hypothesis is

Ho:there is homoskedicity present between the MPG and Horsepower

Ha::there is no homoskedicity present between the MPG and Horsepower

using Breuch Pegan test

= 50*0.6212 = 31.06

the tabulated value of at 0.05 with 49 df is 66.34

since 31.06 < 66.34 so we do not reject Ho and conclude that there is homoskedicity present between the MPG and Horsepower