Lesson 6-2 explained: Use and Evaluation of Regression Analysis

Lesson summary

Regression analysis expresses the relationship between an explanatory variable (the input used to make the prediction) and a response variable (the result) as a model — a line y = ax + b for simple regression, or a sum of weighted variables for multiple regression. Judge the model with R2, RMSE, and MAE, and never mistake a good fit for proof of causation.

Takeaway: Regression predicts a response variable from one (simple, y = ax + b) or several (multiple) explanatory variables, fitted by least-squares. Judge it with R2, RMSE, and MAE together — and never read a good fit as proof of cause.

Key terms

• Regression analysis
• Response variable
• Explanatory variable
• R2
• RMSE
• MAE
• Coefficient
• Intercept
• Confounder

Textbook page: Arabic book 34 · English book 39

Free questions on this lesson

From the textbook question bank. Think of the answer first, then open it.

1. 1. What is regression analysis?

   • A method that expresses the relationship between variables as an equation used for prediction
   • A method for drawing data with colors only
   • A method for deleting missing values from a table
   • A method for picking a random sample from a population
   Answer

   Correct answer: A method that expresses the relationship between variables as an equation used for prediction

   Regression analysis writes the relationship between variables as an equation (a model) used to explain or predict.

   1. The Regression Analysis Stage · page 40

2. 2. Why does multiple regression often suit realistic prediction?

   • It needs no data at all
   • It proves causation automatically
   • It always gives an R² of 1
   • Results in real data are rarely decided by a single cause
   Answer

   Correct answer: Results in real data are rarely decided by a single cause

   Real results depend on several factors, and multiple regression can consider several at once.

   2. Multiple regression · page 41

3. 3. In data with a few very large outliers, which error measure is less swayed by them?

   • The number of variables
   • MAE
   • RMSE
   • R²
   Answer

   Correct answer: MAE

   MAE averages the gaps without squaring them, so it is less affected by outliers.

   3. Evaluation Indicators for Models · page 41

Lessons in this chapter 6: Analysis and Communication

1. 6-1 Statistical Inference
2. 6-2 Use and Evaluation of Regression Analysis
3. 6-3 Data Visualization and Communication