A linear regression model with 4 predictors is fitted to a random sample of size
ID: 3174964 • Letter: A
Question
A linear regression model with 4 predictors is fitted to a random sample of size 35. It is found that value of the multiple coefficient of determination is R^2 = 0.35. Test for the overall utility of the model at alpha = 0.05 and identify which of the following statements is the most appropriate. The overall model is significant: hence it is useful to predicting the response with all 4 predictors in the model. The overall model is not significant: hence it is not useful to predicting the response with all 4 predictors in the model. The model is not significant because R^2 = 0.35 is less than 50%. No conclusion can be drawn from the given information.Explanation / Answer
R-squared is a statistical measure of how close the data are to the fitted regression line. It is also known as the coefficient of determination, or the coefficient of multiple determination for multiple regression.
The definition of R-squared is fairly straight-forward; it is the percentage of the response variable variation that is explained by a linear model. Or:
R-squared = Explained variation / Total variation
R-squared is always between 0 and 100%:
In general, the higher the R-squared, the better the model fits your data. However, there are important conditions for this guideline that I’ll talk about both in this post and my next post.
Hence c is right correct answer
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