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Is A Linear Model Appropriate?

Example:  The data in the table below represent the closing price of Harley Davidson stock at the end of each year from 1994 through 2001.  Determine whether the relation between the closing price and the year is linear.

Using the data in table above, enter the X-values into L1 and the Y-values into L2. (Note: You may notice that the values displayed in L2 are rounded values. These rounded values are for display purposes only; the actual values are still stored in the calculator.) Press STAT , highlight CALC and select 4:LinReg (ax +b) and press ENTER.

To plot the residuals, first make sure that there is nothing stored in the Y-registers. Press Y= and check the Y-registers. If any of them contain a function, move the cursor to that Y-register and press CLEAR.

Press 2^nd , select 1:Plot 1, turn ON plot 1 and press ENTER. For Type of graph, select the scatter plot which is the first selection. Press ENTER. Enter L1 for Xlist. Move the cursor to Ylist. Press 2^nd and select 7:Resid. Highlight the first selection, the small square, for the type of Mark. Press ENTER. Press ZOOM and 9 to select ZoomStat.

This graph of the residuals vs. the predictor variable (years) shows a U-shaped pattern, which indicates that the linear model is not appropriate.