Specifically, in your model as it stands, the rate of change in Ln when (say) X1 changes (other explanatory variables remaining unchanged) is constant and equal to B1. You can easily find this out by differentiating if your variables are differentiable, if not by using a finite differences approach. In your model - nonlinear in Y - the contribution of any of the explanatory variables does depend upon the value of Y. I assume this is what you mean by decomposing the forecast into the contributions of X1, X2 etc. If your model were linear in Y it would clearly be easy enough to determine the amount by which Y changes if (say) X1 changes by a specified amount and the other explanatory variables don't change - the answer to this is just the coefficient B1 and it doesn't depend on the values of any of the variables in the situation that you wish to forecast. Are you sure your regression model is optimal for the purpose for which you want to use it? It may give you linear unbiased forecasts of Ln but it seems that Ln(Y) isn't really your main aim. Your model won't give you linear unbiased forecasts of Y (unbiased in the sense that the mean or expected value of the difference between the forecast and the eventuating value of Y is zero). For example marketing might contribute 800 dollars of sales, weather 300 dollars, the economy 1000 dollars and the alpha (a) 495 dollars. Now of the 2595 forecast, I want to want to breakdown it's composition in terms of the independent variables, i.e how much does each of the three independent variables contribute to making up the sales forecast. Where X1 = Marketing, X2 = weather, X3 = economy and each B represents the estimated beta coefficient associated with each respective variable: b1=0.5, b2=0.2 and b3=1.3 and a = 1įorecast of actual sales (Y in the orginal series) = 2595
Lets say sales is also a function of other variables, But continuing with your example, here's what I want to do.
Excel linear regression analysis model how to#
This I know how to do as per your example which I agree with. Yes I realise I would need to input the indepentent variables to get the actual forecast whether in log or orginal Y.
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