Regression
The Casio makes regression analysis easy. First, one enters the data set. We illustrate with an example of linear regression. Nonlinear regression is done in a similar way. Consult TechSkills 2: Regression for further details.
Linear Regression
Linear regression is the process of fitting a straight line to a data set. A linear function has the form y = ax + b. The task of linear regression is to determine values for a and b that create the straight line that best fits the given data. For example, consider the following data set^{1}.
Plot |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
Fertilizer, X (lbs/100ft^{2}) |
0 |
0 |
5 |
5 |
10 |
10 |
15 |
15 |
20 |
20 |
25 |
25 |
Yield, Y (bushels) |
4 |
6 |
10 |
7 |
12 |
10 |
15 |
17 |
18 |
21 |
23 |
22 |
Our first task is to enter the data set into the Casio. Press the MENU key to display the MAIN MENU. Press 2 to select the STAT menu. A spreadsheet is displayed. Enter the fertilizer amounts in List 1 and the yield data in List 2. Use the thumb pad to navigate from List 1 to List 2.
After the data set is entered and checked for accuracy, we are ready to see a plot of the data. Press F1 to access the GRAPH menu. Press 1 to select 1:S-Grph1, statistical graph 1. A graph of the data set appears.
Notice that it looks reasonable to fit a straight line through the displayed data points. A regression analysis is done as follows.
Press F4 to select CALC. Press 2 to select 2:Linear. The screen now displays the values for the linear form y=ax+b for the straight line of best fit. Here, to three decimal places, the linear equation of best fit is y = .717x + 4.786.
Press F5 to select COPY to copy the linear regression equation into the Graph Func editor.
Press EXE to return to the LinearReg screen.
Press F6 to select DRAW. The Casio then displays the linear regression line superimposed on the data.
Of course there are other functional relationships besides linear. The Casio supports a handy suite of choices, including linear, quadratic, cubic, quartic, logarithmic, exponential, sinusoidal and logistic.
^{1 }Sullivan and Sullivan, Precalculus enhanced with graphing utilities, Second Edition, page 112, Example 3, Prentice Hall.