Asked by Dejim Edolsa on Jun 09, 2024
Verified
If a simple linear regression model is developed based on a sample where the independent and dependent variables are known to be negatively related, then the sum of squares for error will be negative also.
Sum of Squares
A statistical measure used to describe the dispersion of data points. It calculates the sum of the squared differences from the mean.
Simple Linear Regression
A technique in statistics that estimates the association between an independent variable and a dependent variable using a straight line.
Negatively Related
A term describing the relationship between two variables where an increase in one variable is associated with a decrease in the other.
- Grasp the concept of sum of squares in regression analysis and its implications.
Verified Answer
HP
Heather PowersJun 14, 2024
Final Answer :
False
Explanation :
The sum of squares for error cannot be negative by definition. It is the sum of the squared differences between the actual values and the predicted values, and these differences cannot be negative. If the regression model is developed based on a sample where the independent and dependent variables are known to be negatively related, then the slope coefficient of the regression line will be negative and the sum of squares for error will be positive.
Learning Objectives
- Grasp the concept of sum of squares in regression analysis and its implications.