Suppose we have two independent samples from one population: Global Sample(Xg,Yg) and Local Sample(Xl,Yl)

And we have a linear regression model derived from global sample which I call it: GR(X).

We are asked to calibrate the global regression model by local sample using a calibration factor. In order to do that we need to calculate the regression models prediction for local values:

Yp = GR(Xl) (note that we have used the regression model derived from the global sample to predict the values from local sample)

Calibration factor is defined as:

Cr = (summation of Yl) / (summation of Yp)

What is the variance of Cr?

(we need the variance to define interval estimates of Cr)

Thanks for your help!