Quandt-Goldfeld Test

A statistical method used to check for homoscedasticity (constant variance) in a linear regression model. It assesses whether the variance of the errors is the same across all levels of the independent variable(s). In the context of YouTube analysis you could check if the variance of views remains constant as the number of likes or comments increases. This would deepen your understanding of the reliability of your regression models predictions.

Assumptions

• Constant variance (Homoscedasticity)
• Normal distribution of errors
• Linear relationship among variables
• Independent errors

Hypothesis

• H₀: σ₁² = σ₂² (Homoscedasticity)
• Hₐ: σ₁² ≠ σ₂² (Heteroscedasticity)

Steps

1. The dataset is divided into two groups, usually by sorting the data based on the independent variable
2. The residuals (errors) from the regression model are calculated for both groups, and their variances are estimated
3. An F-statistic is computed by comparing the variances of the two groups. If the ratio of the variances is significantly different from 1, it indicates the presence of heteroscedasticity

Interpretation

If the calculated F-statistic exceeds the critical F-value for the chosen significance level, we reject the null hypothesis of homoscedasticity. This suggests that the variance of errors is not constant across the range of predicted values, which may indicate that the models assumptions are violated and its predictions may be less reliable for certain ranges of the data.