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I had a large data set but extracted three factors from the original data set through factor analysis. I then used the extracted factors as my independent variables to develop a regression model for predicting the dependent variable. After obtaining the regression model, I'm now in the dark on the following. How will I know the values of the new variables given that the original values were provided?

As an illustration, suppose the original regression model is $y=3+2x1+4x2+7x3$ and for prediction $x1=3$, $x2=4$ and $x3=9$. Now suppose after extraction we get a regression model of the form $y=3+4R1+2R2$. How will I figure out the values of $R1$ and $R2$ when I need to predict? Is there a solid relationship between original variables and extracted variables?

Jeremy Miles
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Ben
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    I suppose R's are factor scores. Factor analysis was done on some variables X. If you get new cases Yi and Xi, you can compute Ri from Xi, using the [factor score coefficient matrix](http://stats.stackexchange.com/q/126885/3277) left from your factor analysis. Ask your program - it must keep the matrix somewhere. – ttnphns Nov 30 '16 at 23:41
  • Highly appreciate that ttnphns – Ben Dec 01 '16 at 00:27
  • Hi @ttnphns. I have found the component score coefficient matrix. I hope it is the same as factor score coefficient matrix. However, it is displaying all original variables only this time there are three components to each. Which of this variables am I supposed to use? – Ben Dec 01 '16 at 15:41

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