Basics of Multiple Regression and Underlying Assumptions

Multiple regression is a statistical technique used to analyze the relationship between a dependent variable and two or more independent variables. It is an extension of simple linear regression and allows for the examination of how multiple factors simultaneously influence an outcome.

Importance of Multiple Regression:
1. Helps identify the most significant predictors of a dependent variable.
2. Allows for the control of confounding variables.
3. Enables the development of predictive models for decision-making.

How Multiple Regression Works:
1. Collect data on the dependent variable and independent variables.
2. Estimate the regression coefficients using the least-squares method.
3. Assess the model's goodness of fit and the significance of the coefficients.
4. Interpret the results and make predictions.

Underlying Assumptions of Multiple Regression:
1. Linearity: The relationship between the dependent and independent variables is linear.
2. Independence: The observations are independent of each other.
3. Homoscedasticity: The variance of the residuals is constant across all levels of the independent variables.
4. Normality: The residuals are normally distributed.
5. No multicollinearity: The independent variables are not highly correlated with each other.

Exam Tips: Answering Questions on Basics of Multiple Regression and Underlying Assumptions
1. Identify the dependent and independent variables in the question.
2. Recognize the assumptions being tested and the consequences of their violation.
3. Interpret the regression coefficients and their statistical significance.
4. Assess the overall model fit using the R-squared and adjusted R-squared values.
5. Apply the results to make predictions or draw conclusions based on the given scenario.