Choose the correct answer from the options given below:

​​Which of the following are not true about the differences between simple regression and multiple regression?

A. The number of predictors

B. The number of criteria

C. Coefficient of determination

D. Sample size

Correct option is C

• The primary difference between simple regression and multiple regression is the number of predictors (A).
• Simple regression has only one independent variable, whereas multiple regression involves two or more independent variables predicting the dependent variable.
• Since option A is a true difference, it cannot be part of the correct answer.

Now, let's examine the remaining options:

• B (Number of criteria):
• The number of dependent variables (criteria) remains the same in both simple and multiple regression.
• Both models have only one dependent variable.
• Since this is not a true difference, it is part of the correct answer.
• C (Coefficient of determination - R²):
• R² measures how well the independent variables explain the variability of the dependent variable.
• Both simple and multiple regression use R², making it not a distinguishing factor.
• Hence, this is part of the correct answer.
• D (Sample size):
• Multiple regression generally requires a larger sample size due to the increased number of predictors.
• However, sample size is not a defining difference between simple and multiple regression.
• This makes D part of the correct answer.

Information Booster:

Simple vs. Multiple Regression Key Differences

1. Simple Regression:
• 1 independent variable predicts 1 dependent variable.
• Equation:
2. Multiple Regression:

   

• 2 or more independent variables predict 1 dependent variable.
• Example: "How do study time, sleep hours, and motivation predict exam scores?"
• Equation:

  

Additional Knowledge:

• B (Number of Criteria):
• Both types of regression models have one dependent variable (criterion).
• If there were multiple dependent variables, it would be a multivariate regression, not a simple or multiple regression.
• C (Coefficient of Determination - R²):
• R² is used in both simple and multiple regression to explain variance in the dependent variable.
• Since R² is common to both, it is not a unique difference between them.
• D (Sample Size Consideration):
• Multiple regression generally requires a larger sample size to maintain statistical power and avoid overfitting.
• However, this is a practical requirement, not a conceptual difference between the two models.