Based on the estimated linear trend model from part (c) of Exercise 13.33, obtain the residuals and plot them as a time series. Describe the pattern in the residuals.
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Now consider a quadratic trend model. Fit a regression model based on two explanatory variables: and where . Report the estimated model.
Based on the estimated quadratic trend model, compute the residuals and plot them as a time series. Is there a pattern in the residuals?
Superimpose the fitted quadratic trend model on the data series. Explain in what way the quadratic fit is an improvement over the linear trend fit of Exercise 13.33.