Question

a	income	consumption
1	556	2760
2	1622	1930
3	2664	2740
4	3587	3515
5	4535	4350
6	5538	5320
7	6585	6250
8	8582	7460
9	14033	11500

How do I complete the Breusch-Pagan test to test the residuals @ the 5-percent level?

Answer 1

we are doing Breusch-Pagan test to check whether the residuals obtained after linear regression of consumption (dependent variable) on income( independent variable) have constant variances .ie, homoscedasticity,

we use R software to do the needful.

first we fit linear regression

and then apply Breusch-Pagan test on the fit at 5 % level of significance.

Null hypothesis: homoscedastic(constant variance)

Alternate : heteroscedastic( variance differs )

R code:

install.packages("lmtest")
library(lmtest)
x <- c(556,1622,2664,3587,4535,5538,6585,8582,14033)
y<- c(2760,1930,2740,3515,4350,5320,6250,7460,11500)
fit <- lm(y~x) #regression
bptest(fit)

#pvalue = 0.08344 which is greater than 0.05 ( 5%) , so we fail to reject or accept null hypothesis and conclude on the given data that residuals have constant variances or  homoscedastic.