The numerical value of the coefficient does not tell whether the corresponding variable has a big effect on the dependent variable Y. The coefficient of a particular variable in a regression depends on the units used to express that variable. If you change the units by a factor of 10000 (say, convert distance in millimeters to meters by dividing by 10000), the numerical value of the coefficient will be changed without changing its meaning at all. The way to tell whether one independent variable Xi has a big or little effect on the dependent variable Y is the use of the so-called elasticity ratio (assuming the variable starts at its mean value). The elasticity ratio has the advantage that it is dimensionless (units-free).

Neelabha Roy The main rationality and justification of regression analysis is to estimate the parameters of a dependency, not of an interdependency relationship. This is not limited to holistically controlled, fixed variate experiments, the regression model, is limited to good experiments if good results are to be derived. A significantly robust experiment must above all provide as many dimensions of independent variation. You might want to look at the possibility towards the occurrence of multicollinearity which is viewed as an interdependency condition.

You may also want to adopt a stepwise multiple regression, and validate the predictive model by implementing the residual analysis method. The extreme bound analysis (EBA) method could be adopted to determine how robust each of the rework predictors are connected to the predictive model. EBA is a useful technique for quantifying estimates the sensitivity of regression in determining how robustly each influential predictor is related to the predictive model. Hope this helps.

Good luck.

Hello Neelabha,

Yes, the choice of metric for your IVs will affect the value for the estimated regression coefficients. Using a too-small increment scale for an IV can indeed result in a numerically small estimated regression coefficient, even though that regression coefficient might well be significantly different from zero in your model.

Here's a simple example. Among major league baseball players (USA), if one looks at the relationship of salary (in US dollars) as the IV with runs batted in (RBI: a measure of offensive contribution of the player) during the season as the DV, for the 1992 season yields this equation:

Y (estimated) = 24.127 + 0.00001593 * Salary (in USA dollars)

Overall R-squared is .45, and the model is statistically significant, and the contribution of the lone IV (salary) is statistically different from zero. Yet, a lot of people would look at that "tiny" regression coefficient and possibly conclude that salary is not a useful explanatory variable.

Now, let's rescale salary to $100,000 units. The resulting equation becomes:

Y (estimated) = 24.127 + 1.593 * Salary (in $100,000 units)

Same R-squared, same significance all around.

Here, you see that players would be predicted to have about 1.6 additional RBIs per season for a salary difference of $100,000 . So, salary differentials of $1 million would be expected to correspond to about 16 additional RBIs per season. That becomes important to a team's standing in the league.

By the way, in 1992, the salary range for MLB players was from $109,000 to $6,100,000, with a median value of $740,000 and mean value of $1,248,530. Clearly, it's a profession that pays pretty well.

And again, scale matters!

Good luck with your work.

thank you so much, Sir. David Morse