Multiple linear regression is a statistical technique used to predict the value of a dependent variable based on several independent variables. This regression provides a way to understand and measure the influence of independent variables on the dependent variable.
The general equation of multiple linear regression is as follows:
Y = bo+b1X1+b2X2+…+bnXn+e
Where:
Y is the dependent variable
X1, X2, …, Xn are the independent variables
bo is the intercept
b1, b2, …,bn are the regression coefficients
e is the error term
In a previous article, I wrote about the assumptions of multiple linear regression on time series data. Continuing from that article, this time Kanda Data will discuss the assumption tests for multiple linear regression on cross-section data.
Cross-section data is data collected at a single point in time from various individuals or entities. Examples of cross-section data include family income data for a particular year, student height data at a school on a specific day, or household electricity consumption data for a particular month. This data is used to analyze the relationships between variables at a specific point in time.
Assumption of Data Normality
The normality assumption requires that the distribution of residuals in the regression model follows a normal distribution. Residual normality is important for the validity of hypothesis testing and the formation of confidence intervals in regression analysis.
Residual normality can be tested using statistical tests such as the Kolmogorov-Smirnov test or the Shapiro-Wilk test. If the statistical tests show a p-value greater than the significance level (e.g., 0.05), the null hypothesis that the residuals are normally distributed cannot be rejected.
Assumption of Homoscedasticity
Homoscedasticity is the assumption that the variance of residuals is constant across all predicted values of the independent variables. If the variance of residuals is not constant (heteroscedasticity), this can lead to inefficient estimates of the regression coefficients.
To detect heteroscedasticity, the Breusch-Pagan test can be used. If the Breusch-Pagan test results show a p-value greater than 0.05, the null hypothesis that the model has homoscedasticity cannot be rejected.
Assumption of No Multicollinearity
Multicollinearity occurs when there is a high correlation between two or more independent variables. This can disrupt the accurate estimation of regression coefficients because it becomes difficult to determine the individual influence of each independent variable.
The Variance Inflation Factor (VIF) is a commonly used method to measure multicollinearity. A VIF value above 10 indicates significant multicollinearity.
Conclusion
Testing the assumptions of multiple linear regression on cross-section data is crucial to ensure the validity and reliability of the resulting model. The assumptions of residual normality, homoscedasticity, and no multicollinearity must be tested to ensure the regression model provides accurate and useful results.
By conducting these assumption tests, we can ensure that the regression model yields the Best Linear Unbiased Estimator (BLUE). This concludes the article that Kanda Data can write at this time, and I hope it is useful. Stay tuned for updates from Kanda Data in the next opportunity.
