# 2.6 - Exploring Data: Linear Models and Scatter Plots (TI85)

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.

## Correlation and Regression

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.

## Clearing Existing Data in the Calculator

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.

1. Hit the [Stat] key.
2. Choose Edit [F2]
3. [Enter] twice to accept the lists xStat and yStat (you can change names if you want to).
4. Choose CLRxy [F5]

## Entering Data into the Calculator

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.

1. Hit the [Stat] key.
2. Choose Edit [F2]
3. [Enter] twice to accept the lists xStat and yStat (you can change names if you want to).
4. Enter the x-coordinate of the first point and hit [Enter]
5. Enter the y-coordinate of the second point and hit [Enter]
6. Repeat steps 4 and 5 for each additional point
7. [Exit] twice to get back to the main screen.

## Scatter Plots

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

1. Turn off all regular y= plots by going [Graph], y(x) [F1] and either clearing or deleting the functions. You may also choose to leave the graphs but turn them all off by using [More] and All- [F2]
2. Set your viewing window by choosing Range [F2]
3. Set the values so that all the data values are displayed.
4. Hit [Stat]
5. Choose Draw [F3]
6. Choose Scatter Plot [F2]

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.

## Least Squares Regression Line

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.

1. Hit [Stat]
2. Choose Calc [F1]
3. Hit [Enter] twice to accept the lists containing your data
4. Choose Linear Regression [F2]
5. The calculator will return the y-intercept (a), slope (b), and the correlation coefficient r (corr). The TI85 also returns the number of values (n).

## Drawing the Regression Line on the Scatter Plot

You must compute the regression equation before doing this. If you just computed the regression equation, skip to step 2

1. Hit [Stat]
2. Choose Draw [F3]
3. Choose Draw Regression Equation (DDREG) [F4]

## Predicting Values

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.

1. Hit [Stat]
2. Choose Forecast (FCST) [F4]
3. Enter the value for x you wish to use and press [Enter].
4. With the cursor sitting on the y= line, press Solve [F5]

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.

## When you're all done

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

1. Hit [Graph], [More]
2. Choose Draw [F2]
3. Hit [More] ClrDrw [F5]

Alternatively, and probably quicker ...

1. Hit [Stat]
2. Choose Draw [F3]
3. Choose ClrDrw [F5]