Consider x to be the number of years after 1900. Compare the graphs of both regressions. Notice that you do not have enough data to made a cubic regression.
Linear Model: y=5.8x-379.6666667 Quadratic Model: y=0.8x^2-146.2x+6827 Best Fit: The quadratic model fits the data set better.
Practice makes perfect
To know which models to use to approximate the data, we will begin by plotting the values using our graphic calculator. Let's consider x to be the number of years after 1900 and y to be the Average Sale Price (thousands $).
x
Average Sale Price (y)
90
149
95
158
100
207
Now we push STAT, choose Edit, and enter these values.
Once the values have been entered we can plot them by pushing 2nd and Y= and choosing one of the plots in the list. Make sure you turn the plot ON, choose scatterplot as the type, and use L1 and L2 as XList and YList. Finally, you can pick whatever mark you want.
By pushing GRAPH the calculator will plot the data set. A standard viewing window might not show the data points, so we can change it if necessary.
Let's try to approximate the average sale price of homes sold in the United States either by using a linear or a quadratic regression.
Performing Regressions
By pressing STAT we can find the linear regression under the CALC menu. If we choose LinReg the calculator performs a linear regression test. One line below in the list, we can find QuadReg, which performs a quadratic regression.
Which Model is Best?
To determine which model is best, we will plot the results we got and examine how they fit the data.
We can see that the quadratic regression fits the data set much better. Therefore, we will choose the quadratic model as the one that represents the data set.
Extra
Note
Here we didn't try to make a cubic regression, because we have less data than is necessary.
