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In the linear simple regression model, If R^2=0 does it necessarily mean that the estimate of...

In the linear simple regression model, If R^2=0 does it necessarily mean that the estimate of B1 equal 0? Can you explained this please.

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Answer #1

R^2 is known as the coefficient of determination or, more precisely, the coefficient of multiple determination for multiple regression. It is used to measure the percentage of variation in the dependent variable that can be explained due to the multiple linear regression. It measures how much close the data are to the fitted regression model.

If R^2 = 0, it only means that 0% of the variation of the dependent variable can be explained due to the linear regression model that has been fitted. The regression coefficient B1 (of the independent variable) is not equal = 0, but it cannot explain any of the variation of the dependent variable.

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