In a simple linear regression model,if the plots on a scatter diagram lie on a straight line,which of the following is the coefficient of determination?
A) -1
B) 0
C) +1
D) Infinity

Question

Quizplus · Accepted Answer

When the plots on a scatter diagram lie on a straight line, it means that the relationship between the variables is perfectly explained with a linear equation. In other words, all the data points fall exactly on the line, leading to a perfect fit. The coefficient of determination, or R-squared, measures the proportion of variation in the dependent variable that is explained by the independent variable(s). Since the data points fit perfectly on the line, there is no unexplained variation, and the coefficient of determination is +1. Therefore, choice C is correct.

In a Simple Linear Regression Model,if the Plots on a Scatter