This (-.81) seems like a pretty substantial correlation to me! Nonetheless, it would not hurt to take a look at the scatterplot to check for potential non-linearity. Also, if you have other variables that should also be related to the DV in theory, you could add them to the model.

In most context the .66 would be considered high, particular it either (or both) of the variables are measured with error. Perhaps you can provide more context to say why this is considered low in your context. (and of course this is the equivalent value in magnitude to the r, so why you consider that high).

Daniel Wright so to give some context, im trying to see if there is a relationship between the mass of a club and the distance travelled by the golf ball. I used Irons 3 to 9 and did 8 trials and then took the mean of these 8 trials for the distance travelled by the golf ball for each club. I plotted a scatter plot of the average distance travelled (Y) against the mass of the club (X). I calculated r and that came out to around -0.81, squaring that gave me the coefficient of determination which came to around 0.661. Now, from this what i understand is that while these 2 have a strong negative correlation, the value of r-squared, led me to believe that independent variable is only able to account for 66.1% of the variation in the dependent variable. Looking at the scatter plot, I seemed to me that trend, however, doesn't appear to be quite linear. It appears as if the relationship is slightly curved. Now, the part where Im facing trouble is whether I go ahead see if a polynomial fits the data better or do I add another independent variable and do a MLR ? From the scatter I have attached below, trying to fit a quadratic gives me a r-squared of 0.839 which is pretty high increase in the r-squared value. Adding another independent variable, the loft angle of the club, I observed that the adjusted r-squared value increases from 0.592 to 0.886

@Dhruv, First, I am not so impressed with the multivariable models. Adding predictors always increases R**2. Second if you thought the additional predictors were important they should have been in the original model model. Further if you are going to approach things this way I would suggest comparing models by AIC NOT R**2. NOTE that AIC is equivalent to Mallows Cp which I believe is optimal for OLS regression. I am attaching a paper with good references on many of these topics but the paper itself uses logistic regression. Of course your problem is a prediction problem so adaptive lasso as used in the paper is still the optimal model for OLS as well. I'd recommend investigating that method for your problem. Best wishes and Good luck. David Booth

@Dhru, I'm adding a Google search that contains some advice and an R program which you may find helpful should you wish to try adaptive lasso. Best wishes David Booth

Are you not interested in the variability of the lengths? Just wondering why you take the mean of these and not model the individual lengths. I think golfers will be interested in the consistency of the lengths from clubs.