R-squared values?

Question

If a high R-squared value tells you the "best fit" trendline that your data is following, is the converse also true? That is, does a low R-squared value tell you which simple average (horizontal line) that your data is most closely following?

Yes, R-squared, at its most basic level tells you how well variations in X explain variations in Y, but the practical definition, at least in my mind, is that R-squared is a statistical measure of how well a regression line approximates real data points; an R-squared of 1.0 (100%) indicates a perfect fit and a R-squared value of 0 indicates that a regression line for that particular time period is no better than a horizontal line. Hence, my question.

I should have also probably mentioned that my X value is time, in days.

Answer 1

Nope.

I don't quite get the horizontal line reference. Are you (in a roundabout way) trying to say if y=mx+b is not a good fit, use y=y-bar?

Anyway, r^2=% variationof y that can be accounted by variationin x. So if r^2 is low, it just means that the variation in ycan not be accountable by variation in x.

One option is "perhaps a different model" like exponential or power or log............

Answer 2

The coefficient of determination R^2, is the percentage of the variation in y, explained by the variation in x.

R^2 is not really the best measure of fit. A better measure is the standard error of the regression line which takes into account the number of data points.

Answer 3

The R squared values indicates how closely your "best fit" line matches your data. A low R squared value indicates low accuracy, so your data is not reliable because it's less accurate. Usually an R squared value of .97 or higher is considered a good fit.

Answer 4

R Squared Value

Answer 5

Are you sure a high r-squared value tells you that? My understanding is that r-squared is a measure of the degree to which you can feel confident one variable is predictable of the other.

The square of of r squared, of the Pearson product-moment correlation, is a measure of how strong the association between your two variables is. A low r value would suggest that the points are not closely related. If points aren't closely related, they don't follow any kind of a trend. They are essentially independent of each other.

In short, the answer to your question is no.

Answer 6

i thought r squared told you the % of variation of the DV that is accounted for by the IV... ? a low r2 tells you that the DV doesn't really vary due to the IV.

The sum of squares for the residuals is all the deviation of actual scores from predicted scores. if you divide that by N and take the square root, you get the standard error which is i think what u want?