Regression analysis

Question 1

What is the main objective of simple linear regression?

Answer 1

To fit a linear equation that relates the dependent variable with the independent variable.

Question 2

What are the four assumptions of a simple regression model?

Answer 2

• The two variables X and Y should both be continuous.
• The relationship between X and Y must be linear.
• For each X-value, Y is a random variable having a normal (bell-shaped) distribution.
• All these Y distributions have the same variance.

Question 3

What is the equation of the regression line in the population?

Answer 3

Y = β0 + β1 X, where β0 and β1 are parameters to be estimated from the sample data

Question 4

What is the coefficient of determination or R2?

Answer 4

R2 is the proportion of variation in the dependent variable that is explained by the regression model. It always lies in the range 0 ≤ R2 ≤ 1.

Question 5

How do we test for a statistically significant regression?

Answer 5

We use an F test to compare the explained (SSR) and unexplained (SSE) sums of squares. The null hypothesis is that there is no relationship between X and Y, and the alternative hypothesis is that there is a relationship between X and Y.

Question 6

How do we test for a significant linear correlation between two variables?

Answer 6

We use a t test to compare the sample correlation coefficient r with the null hypothesis that there is no correlation in the population (ρ = 0). The test statistic is t = r * sqrt(n-2) / sqrt(1-r^2), where n is the sample size. We compare this t value with a critical value from the t table with n-2 degrees of freedom and a desired level of significance (α).