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That concludes today’s post and I hope you found all the details that you were looking for. Remember to share this post with your friends.Q: Linear regression with multiple predictors I’m trying to develop a predictive model that will forecast a value given multiple environmental predictors (x,y,z). I need to estimate the model parameter b0, b1, b2, and b3 and a model’s goodness of fit. I found that a proper candidate for best model would be a linear regression model, as there should be a linear relationship between y (the predicted value) and predictors x,y,z. After predicting the values based on these predictors, I can then take the residuals (the difference between predicted and actual values). I can estimate these parameters by t-test. I tested the relationship between residuals and predictors and the results are fairly strong and significant. I would be interested to know if my approach is more than a red herring. If there are other statistical approaches to create such a model please mention them. A: Let me first answer the OP’s question: I can estimate these parameters by t-test. I don’t know where this t-test comes from, and I suspect it’s a Student’s t-test of the difference between actual and predicted. This is known as an “ANOVA” regression. If the error term is normally distributed, the “F” statistic for this model is just the total sum of squares divided by the error term sum of squares. The test in the O.P. is simply looking at whether a point $lpha = 0$ has “more” residuals than points $lpha > 0$.