As a part of a task I took a regression equation $y(x)$ for a certain sample (1) and used it with the $x$ values of a different sample (2) to produce a residual plot as shown, for residual-regression value
Next I need to determine whether the regression model is still applicable for sample (2).
I use 2 different approaches to determine it,
- I calculate the regression model for sample 2 and compare it to the regression model of sample 1, if the coefficients are different for the two, I determine it to be non-applicable.
2.The residuals need to be distributed with a constant variance, so if I get a slope in my trendline, as shown here, I determine it to be non-applicable as a result of a non-constant variance.
Are these two approaches in fact correct?
The model has several parts.
First, what you are saying about the residuals having constant variance is part of the model, but the argument you are making is that the residuals do not have mean 0. That is a different assumption in the model. Another assumption is that the residuals are normally distributed. These are 3 different assumptions built into the statement that the residuals are iid normal with mean 0 and constant variance. The test for whether the estimated slope in sample 1 is the same as that in sample 2 is fine by finding the difference in the two estimates and dividing by the square root of the sum of the two standard errors squared. Since the two estimates are independent and approximately normal, this is standard normal if the two have the same slope. If you want to test whether the slope in sample 2 is equal to some fixed value, that is something else. Subtract the fixed value from the estimate and divide by the s.e.