Answered: How do you calculate the coefficient of…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter4: Linear Functions

Section: Chapter Questions

Problem 8PT: Does Table 1 represent a linear function? If so, finda linear equation that models the data.

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Question

How do you calculate the coefficient of determination (R^2) in a simple linear regression model?

Expert Solution

Step 1

Introduction :The coefficient of determination, denoted by R^2, is a statistical measure used in regression analysis to assess the goodness of fit of a regression model. It provides a summary of the proportion of variability in the response variable that is explained by the predictor variable(s). In simple linear regression, the coefficient of determination can be calculated by dividing the sum of squared errors (SSE) by the total sum of squares (SST). The resulting value ranges from 0 to 1, with a value of 1 indicating that the regression line perfectly fits the data, and a value close to 0 indicating that the regression line does not fit the data well.