Breusch-Pagan Test Error Constancy

This test is best employed when the error terms are not highly serially correlated, either by assuring this with the Durbin-Watson test or after the serial correlation has been corrected. It is best used when the sample size is large, assuring normality of the data. 

The equation implies that sj increases or decreases with x,, depending on the sign ( + or —of/i. If/i = —, the s values decrease with x,. If fi = +, the sf values increase with x,-. If/i 0, then the variance is constant. The hypothesis is  

The n must be relatively large, say, n 30, and the c, values normally distributed. 

For one jc, predictor variable, in cases of simple linear regression, ej equals the squared residual (j, — y), as always. Let SSr, equal the sum of squares regression on the ej vs. the x,-. That is, the value, (y, - y) — ej, is used as the y, or predictor value in this test. The e, values are squared, and a simple linear regression is performed to provide the SS/ term. The SSg term is the sum of squares error of the original equation, where ef is not used as the dependent variable. The Chi-Square test statistic tabled value, o degree of 

We will use the data from Example 8.2 and do the test using x, again, or y where x = month and y = potency%. 

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