Linear: y = 2.082999x-2.475234 Quadratic: y=0.086232x^2+0.008929x+5.963724 Cubic: y=-0.002554x^3+0.178307x-0.913645x+8.205128
Cubic is best fit since r^2=1.
Practice makes perfect
We will use a graphing calculator to plot the points, perform the three regressions, and compare the models to the data points. Let's begin by pushing STAT, choosing Edit, and entering the data.
Once the data has been entered, we can plot it by pushing 2nd and Y= and choosing one of the plots in the list. We will choose scatter plot as the type, and use L1 and L2 as XList and YList. Finally, we can pick whatever mark we want. Be sure to turn the plot ON!
By pushing GRAPH the calculator will plot the dataset. A standard viewing window might not show the data points, so we can change it by pressing WINDOW.
By pressing STAT, we can find the different regression types under the CALC menu. If we choose LinReg the calculator performs a linear regression test.
Let's write the linear function for this fit. We will round a and b to 6 decimals.
y = 2.082999x-2.475234
Next, we will do a quadratic regression by choosing QuadReg.
We will write the quadratic function for this fit while rounding a, b, and c to 6 decimals.
y=0.086232x^2+0.008929x+5.963724
Finally, we do a cubic regression by choosing CubicReg.
Let's write the cubic function for this fit. Once more, we will round a, b, c, and d to 6 decimals.
y=-0.002554x^3+0.178307x-0.913645x+8.205128
Choosing the Best Model
Let's plot the results we got and examine how they fit the data! We can plot all three graphs at the same time.
All three graphs fit the data set very well. However, if we look at the r^2 value, we see that it is 1 for the cubic regression. This means that it fits the data set perfectly. Therefore, we will choose the cubic model as the best fit.
