Regression and Correlation

Regression analysis examines the relationship between a dependent variable (Y) and one or more independent variables (X). Simple linear regression uses the equation Y = a + bX, where b is the slope and a is the intercept. The coefficient of determination (R²) indicates the proportion of variance explained by the model. Correlation (r) measures the strength and direction of a linear relationship, ranging from -1 to +1.

Governing Formulab = Σ[(X_i - x̄)(Y_i - ȳ)] / Σ[(X_i - x̄)²], r = Σ[(X_i - x̄)(Y_i - ȳ)] / √[Σ(X_i - x̄)² × Σ(Y_i - ȳ)²]

Knowledge Check

10 Questions

1.A regression equation is Y = 2 + 3X. What is the predicted Y when X = 5?

2.The correlation coefficient (r) ranges from:

3.If r = 0.85, what is the coefficient of determination (R²)?

4.In simple linear regression, the slope (b) is calculated as:

5.A correlation coefficient of r = 0 indicates:

6.What is the intercept in the regression equation Y = 3 + 2.5X?

7.The standard error of the estimate in regression measures:

8.If the slope b = 0 in a regression model, then:

9.What is the residual in regression analysis?

10.Multiple linear regression involves: