i have been trying to run a multiple regression in SPSS package, where i have 10 variables of which one variable is DV and the remaining 9 are IVs. when linear regression was run it shows a perfect fit. the value of R-square is 1.00 and so also the adjusted R-square is 1.00, hence the influence statistics can not be computed. My question is how to determine the variation in the variables between the DV and IVs?
How many data points do you have? If less than 10, it sounds like your software is choking on an inadequate data set. If you have a large data set, R =1 should not happen. (With a large dataset, if you had R = 1, likely you overfit your model to the extreme.) Perhaps you could write to SPSS and ask them what is happening.
Graphing y on the y-axis, and predicted-y on the x-axis might be informative for you. But if you do not have a positive number of degrees of freedom, you aren't going to be able to estimate variance. - Cheers!
I don't know what you mean by DV and IV. But, as said by James, it's probably due to over fitting. For my point of view, a better indicator of the quality of the model is the prediction R². It is calculated by predR²=1-PRESS/SS, where PRESS is obtained by cross validation (Leave-One-Out).
If you have 10 variables in your problem, I think that, in a first time, you have to select the most important ones. Then, depending of the structure of your data (what type of DOE?), you may include interaction effects and conclude after examining of residuals.
Pierre Chagnon
DV=dependent variable, IV=independent variable
You either have a mistake, or you have over fitted your model (as James suggested). You can get a perfect fit when the number of variables equals or exceeds the number of data points.
A mistake can take many forms. You could have copied one variable such that you have a model DV=DV. You could have a strange transformation that (when written out carefully) proves that 1=1 with an R2 of 1. I tried this once. You could have a deterministic process. I am trying to model the quantity of pesticide applied through a boom sprayer to a field (DV) using several independent variables. I happen to choose the number of droplets, tractor speed, the diameter of droplets, pressure of the pump, and the concentration of pesticide in the spray tank as the IVs. However, 4/3*pi*r3 converts droplet radius to volume, multiplied by the number of droplets gives total applied volume which can be multiplied by the concentration to give total applied dose. Knowing the tractor speed determines the spread of this dose per unit area. The R2 from this model should be 1 if everything was measured accurately.
Further to Pierre Chagnon's reply, DV and IV respectively mean Dependent Variable and Independent Variable. H. Abdi in http://www.utdallas.edu/~herve/abdi-wireCS-PLS2010.pdf also recommends to use the prediction indicator R2
for preventing overfitting.
Additional useful references:
- http://blog.minitab.com/blog/adventures-in-statistics-2/multiple-regession-analysis-use-adjusted-r-squared-and-predicted-r-squared-to-include-the-correct-number-of-variables
- http://blog.minitab.com/blog/adventures-in-statistics-2/the-danger-of-overfitting-regression-models
- http://blog.minitab.com/blog/adventures-in-statistics-2/beware-of-phantom-degrees-of-freedom-that-haunt-your-regression-models
- http://blog.minitab.com/blog/adventures-in-statistics-2/how-to-choose-the-best-regression-model
Another simple explanation could be that the DV is calculated directly from the IVs, e.g. Profit=Income-Expenditure. In that case R-square will be 1.
- Badges
- Science topic
- Similar topics
- Mathematical Sciences
- Statistics
- Statistical Software
- SPSS