Exam Questions - Regression

Exam Questions - Regression

Regression Questions Structure

  • Introduction: Regression problems usually begin by providing the dataset comprising of two or more variables. This could be presented in a table or graph format.

  • Identification: The question will thereby prompt to identify the dependent and independent variables. The dependent variable is usually what you’re asked to predict or estimate, while the independent variable is used to make the prediction.

  • Equation Required: The task will specify to devise the regression equation which includes determining the slope and the y-intercept. Remember, the regression equation is of the format y = a + bx.

Strategy for Solving Regression Questions

  • Identify Variables: Begin by identifying the independent and dependent variables. Typically, the dependent variable is the one that you are trying to forecast or estimate.

  • Calculate Slope & y-intercept: Use the formulas for ‘b’ and ‘a’ to determine the slope and the y-intercept respectively. Make sure to accurately calculate the mean of the x and y values.

  • Formulate Equation: Using the values of ‘a’ and ‘b’, formulate the regression equation. It’s essential to place these values accurately in the model y = a + bx.

  • Interpret Results: Typically, the question will ask to interpret the slope, y-intercept, and possibly the R squared value. This requires a clear understanding of what each of these represents.

Pitfalls to Avoid

  • Accuracy: Ensure you accurately calculate the mean values and correctly substitute them in the formulas for ‘b’ and ‘a’.

  • Overfitting: Avoid forcing the regression model to fit all points. Aim for a model with the least residual sum of squares (RSS).

  • Interpretation: Be careful while interpreting the slope and y-intercept. Remember the slope indicates how much ‘y’ changes for each unit change in ‘x’, while the y-intercept is the estimation of ‘y’ when ‘x’ is zero.

Types of Regression Questions

  • Prediction: These questions ask to forecast future values using the regression equation.

  • Interpretation: These questions involve interpreting the regression output, specifically the slope, y-intercept, and the coefficient of determination.

  • Calculation: These questions ask to calculate the line of best fit and the residual sum of squares.

Always remember, practise is crucial, so make sure you work on a variety of different regression questions to strengthen your understanding.