Suppose there is a Quadratic relationship between a predictor, which exhibits a trend over time, and the response but we included only a linear term for that predictor in the linear regression model. Which of the following will happen if we use linear model for this regression model?
Will the diagnostics show autocorrelation in the residuals?
Do you think the residuals will add up to 0?
What you will see is a trend in the residuals. That's why it's so important to plot the residuals to know if you have a fit that predicts well or not. A good fit will show random residuals - there will be no clear pattern. But if you have a pattern in the residuals, such as a trend, or periodic spikes, or what have you, that would be a clue that your model is missing something - possibly something important.
