Week 1 (9/13) P-value and Breusch-Pagan Test

What is the P-value ?

The p-value is a measure of the observed value of the test or evidence against the null hypothesis

To calculate the P value
Ho : µ = µo
Ha : µ > µo

The smaller the p-value, the greater the evidence against the NULL hypothesis

If we have a significance level of alpha
We can reject Ho if the P-value is ≤ alpha

If we do not have a given significant level, then we cannot reject null hypothesis

In short

  • P-value < 0.01
    Very strong evidence against Ho
  • 0.01 < P-value < 0.05
    Strong evidence against Ho
  • 0.05 < P-value < 0.1
    weak evidence against Ho
  • P-value > 0.1
    little or less evidence against the Ho Heteroscedasticity Breusch-Pagan Test

On linear regression, the residuals are distributed with equal variance at each level of the dependent variable Y

So Heteroscedasticity means the Differently scattered or the spread of the residual over the range is More and Homoscedasticity means the Same scatter

The Breusch-Pagan Test, in which the null hypothesis is that Homoscedasticity is present and against the alternative Heteroscedasticity is present

Ho : Homoscedasticity is present (Error on variance are all Equal)

Ha : Heteroscedasticity is present (Error on variance are NOT Equal)

how do we calculate or compare

1. Get the residual
2. Square the residual and calculate Pearson’s R2
3. Calculate the probability P for the Chi-Squared distribution

If P is small Reject the hypothesis meaning
If the calculated chi-square exceeds the critical value or significant value

which helps us to conclude Heteroscedasticity is present in the model

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