We have two variables X and Y. Analysis of different regression models shows that polynomial quadratic equation provides the best fit for Y with respect to X.
Say, the equation is y = -0.0055x² + 2x - 20 and R² is 0.98.
What will be the preliminary interpretation about relation between X and Y? Also, how can one use R² to bolster this observation?
Best.
Hi
The R-Square is the measure of good ness of fit of the estimated model so the percentage 0.98 is excellant where that is mean the variable x in general linear terms is very good to interpretation variation in dependnt variable, but also you need the F value and associated p value.
what are the standard deviations of x and x^2 coeffs ? what is the correlation between them ?
I would say the preliminary interpretation about the relationship between X and Y is that it is not a straight line relationship, but rather a curve, which you can plot based on that equation given. If you compare this R² to the R² for the regression equation when you force the relationship to be a straight line (x coefficient only, drop x² from the model), then I think that could bolster the argument, as I suspect R² for the straight line relationship would be smaller.
Suggest you look at the attached book. Plotting the data is always the first step. What makes you think that the model is quadratic? David Booth
Hi
The R-Square is the measure of good ness of fit of the estimated model so the percentage 0.98 is excellant where that is mean the variable x in general linear terms is very good to interpretation variation in dependnt variable, but also you need the F value and associated p value.
Dear Hasnahana,
IMHO, previous contributions address your question, in particular the ones from Ashley Franklin and David Eugene Booth .
The more parameters you add to your model the larger R2 will be (up to a certain point and then it will not increase anymore).
In you particular case the X2 coefficient is roughly 400-fold smaller than the coefficient for X. Is it significant?
Just because R2 is larger, does not mean the "higher order" models are better or are the right ones as R2 it is not a measure of the goodness of fit of the model!
It tells you the amount of the observed variation that is explained by your model, and in your case, that 98% of the observed change in the Y variable is explained by the Y=a+bx+cx^2 model. The "missing" 2%, not explained by the model, may be due to the variability of the (experimental) observed data or to a true lack-of-fit of the model (meaning that you are fitting a "wrong" model to your data).
Kind regards, Luis
R² is usually tagged as coefficient of efficiency (COE). So, the closer its value to one (1), the better the fitted model (y = -0.0055x² + 2x - 20) to the original data, and verse versa. In other words, the closer the value of R² is to one (1), the better the fitted model (y = -0.0055x² + 2x - 20) to the original data.
http://home.iitk.ac.in/~shalab/regression/Chapter12-Regression-PolynomialRegression.pdf
This may help in a very simple manner. However, model validity has to be tested before interpreting any regression model.
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