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Block 2 Unit 4 Bivariate and Multiple Regression

For Numericals, check the questions and examples in your study material.

1) What is the fundamental goal of regression analysis?

Regression analysis aims to predict the value of a dependent variable (Y) based on the value of one or more independent variables (X). It establishes a mathematical relationship between the variables, enabling us to estimate or forecast the outcome variable based on the predictor variable(s).

2) Explain the difference between bivariate and multiple regression.

• Bivariate Regression: Involves one predictor variable (X) and one outcome variable (Y).
• Multiple Regression: Incorporates two or more predictor variables (X1, X2, ... Xk) to predict a single outcome variable (Y).

3) How is the regression line determined?

The regression line is the line of best fit that minimizes the sum of the squared differences between the observed data points and the predicted values on the line. This method is called ordinary least squares (OLS).

4) What are the key components of a regression equation?

A typical regression equation has the form: Y = a + bX + e, where:

• Y: Dependent variable or outcome variable.
• X: Independent variable or predictor variable.
• a: Intercept, representing the predicted value of Y when X is 0.
• b: Slope, indicating the change in Y for every one-unit change in X.
• e: Error term, representing the difference between the observed and predicted values of Y.

5) What is the coefficient of determination (R2) and how is it interpreted?

The coefficient of determination, denoted as R2, measures the proportion of variance in the dependent variable (Y) that is explained by the independent variable(s) (X). It ranges from 0 to 1, with higher values indicating a stronger relationship.

For example, an R2 of 0.60 suggests that 60% of the variation in Y is accounted for by the predictor(s).

6) How is the significance of a regression coefficient tested?

The significance of a regression coefficient (b) is assessed using a t-test. The null hypothesis states that the coefficient is equal to 0 (no relationship). If the p-value associated with the t-test is below a predetermined significance level (e.g., 0.05), the null hypothesis is rejected, suggesting a statistically significant relationship between the variables.

7) What are some key assumptions of regression analysis?

Regression analysis relies on certain assumptions, including:

• Linearity: The relationship between the variables should be linear.
• Independence: The observations should be independent of each other.
• Homoscedasticity: The variance of the errors should be constant across all levels of the predictor variable(s).
• Normality: The errors should be normally distributed.

Violations of these assumptions can affect the validity and reliability of the regression results.