This section ties in heavily with the notes for a statistics class. In particular, look at the Introduction to Statistics and Lists on the TI82 and Scatter Plots and Regression Lines on the TI82. With that said, I will try to convey most of that information here, also.
I don't normally do the TI85, but the statistics mode on it is fairly difficult to grasp. I do not have notes on how to use any of the other calculators, like the Casio or Sharp.
The Linear Correlation Coefficient (r) is a measure of the strength and direction of a relationship between two variables. If the y gets larger when the x gets larger, the coefficient is positive and if the y gets smaller when the x gets larger, the coefficient is negative. If there is no linear relationship between the two variables, then the coefficient is zero. If all the data exactly lies on a line, then it is called perfect correlation and the value will either be 1 or -1. The closer the value is to 1 or -1, the closer the points are to the line and the stronger the linear relationship. The same concept applies for other types of regression (the TI82, TI83, and TI85 will do linear, logarithmic, exponential, power, quadratic, cubic, and quartic regression).
The Regression Equation or Regression Line is the equation of the line which best fits the data.
One of the uses of regression is to see if there is a correlation between the two variables. This is indicated by the value of the correlation coefficient r. Another use of regression is to predict values.
I'm going to assume that you're putting the x-coordinates into xStat and the y-coordinates into yStat. Make appropriate modifications to the instructions if you use different lists.
With the TI85, you enter pairs of x-coordinates and y-coordinates. If you have just cleared out your data, skip steps 1 through 3 and begin on step 4.
On the TI85, you must set up the viewing window before you view the scatter plot. Also, the ZoomFit option does not work to automatically set the window for the data. However, the TI85 does provide an easier way to graph the regression equation
It will be difficult to see the dots on the scatter plot because they are just individual pixels, not boxes or crosses like with the TI82 or TI83.
The least squares regression model is the line which minimizes the variation. Ok, if you really want to know, take a statistics class. In general terms it is the line that best fits the data. That is why it is sometimes called the best fit line.
Warning! The TI85 returns the regression equation y=a+bx. The book and the other TI calculators will be using y=ax+b instead. Be sure to adjust appropriately.
If you have just plotted your scatter plot, then skip to step 2.
You must compute the regression equation before doing this. If you just computed the regression equation, skip to step 2
One of the uses of the regression equation is to predict values.
You must have computed the regression equation, but you do not have to graph it to use this. If you have just completed the Linear Regression, then skip to step 2.
The TI85 can be used to find the values of x that give a particular value of y. To do that, enter the value for y, position the cursor on the x= line and hit solve.
You don't have to do anything special. The statistical plots and y= plots are kept separate from each other. If you want to, however, you may clear your drawing
Alternatively, and probably quicker ...