Goldfield-Quandt

**Step 1:**

Get the data.

**Step 2:**

Second step involves **arranging the X1 values from lowest to highest order. Then, divide the series into two groups, n1 and n2 and remember n1, and n2 must less than N/2. n1,n2 being the size of first and second group respectively and N is the size of the original group. **Here, N= 30, n1 and n2 = 13.

**Step 3:**

Run two regression using the values from the two groups. Check for their **Residual Sum of Squares (RSS)** and find out the ratios between them.

The ratio ** = 1328.9651/ 353.411 = 3.760**

**Step 4:**

Compare the calculated F-Statistics(F-Cal) with critical F-value(F-Crit) with the degrees of freedom and significance level.

**Step 5: Decision Rules**

If F-Cal > F-Crit,

If F-Cal < F-Crit

**This calculated value is larger than the critical F – value at 11 degrees of freedom with a 5 % level of significance. **Reject the null hypothesis.

**White Test**

**Step 1:**

Run regression using the above model. Get the residuals and squared residuals.

**Step 2:**

Run an auxiliary regression using the following model:

**Step 3:**

Find the R-square from this auxiliary regression. Then, use it to compare with the following formula.

**Step 4:**

**Decision Rules:**

If Chi-Cal < Chi-Crit

If Chi-Cal > Chi-Crit

**Step 5:**

If the Chi-Cal value is greater than the Chi-Crit value then reject the null hypothesis.

**Similarities**

Both used for testing heteroscedasticity.

**Differences**

For G-Q test, its necessary to rearrange the X values and know the X having the most impact on the dependent variable. While its not necessary for white test. Assumption of normality is necessary for both.