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The TI-85 analyses one-variable and two-variable statistical data. Statistical data is stored in lists, and there are seven types of regression analyses available to analyse the data.
The STAT menu accesses the statistical capabilities and features of the TI-85. From this menu the user can enter and analyse data. To select the STAT menu:
where:
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CALC : |
a menu which provides numerical descriptive measures and calculates regression coefficients. | ||||||
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EDIT : |
a menu that allows the user to enter, edit, sort, and clear numerical information. | ||||||
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DRAW : |
a menu which provides access to four built-in statistical graphs, and allows the user to store and recall graphic objects to the screen. | ||||||
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FCST : |
a menu which provides the predicted x or y values for regression analysis. | ||||||
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VARS : |
a menu that gives access to summary statistics and regression variables. | ||||||
The data must be entered into the TI-85 before any of the statistical functions can be implemented. There are three ways of entering, storing and manipulating statistical data, namely:
1. Enter data in the form of a list and store/use from a command line on the home screen.
2. Enter, edit and store data in the LIST editor element by element, or
3. Enter and edit the data as a pair of lists in the STAT editor as data points.
We shall illustrate the three methods of entering the list with the following example:
A lecturer of an introduction to computer science class is interested in the relationship between time spent using the computer system (x) and the final exam mark (y). Data collected for a sample of 10 students who took the class in the second semester are presented, in table 3.2.1, below:
To enter the data in the form of a list, ie by method 1, we follow procedure below:
1. Access the LIST menu by pressing [2nd] [-], and the following menu appears:
2. Begin the list with [{ ], select this by pressing [F1]
3. We shall now enter the x-data:
[45] [ , ] [30] [ , ] [90] [ , ] etc.
4. End the list with [ }], select this by pressing [F2]
Store the list to a name by pressing [STO>] [HOURS] [ENTER]
Note that list names can be up to 8 characters in length, and by selecting [NAMES] from the LIST menu, ie by pressing [F3], we see that ‘HOURS’ now appears in the list menu.
To check that the correct number of elements have been entered in the list:
Now we shall enter the y-data as a list in the list editor:
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1. |
Press [2nd] [-] to access the LIST menu | ||||||||||||||||||
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2. |
Press [F4] to access the EDIT menu | ||||||||||||||||||
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3. |
Enter [GRADE] at the prompt "Name=". Note that all
previous entered lists are shown at the bottom of the
screen. | ||||||||||||||||||
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4. |
[ENTER | ||||||||||||||||||
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5. |
We now enter the data values one by one.
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6. |
[EXIT] | ||||||||||||||||||
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7. |
To verify that the GRADE data has been entered
successfully, press NAMES in the LIST menu and see that
GRADE is included in the menu items. | ||||||||||||||||||
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8. |
[EXIT] [EXIT] returns you to the home screen. | ||||||||||||||||||
To enter the data as a pair of lists of data points in the STAT menu follow the procedure below (assuming that the lists HOURS and GRADES are not already entered):
1. Press [STAT] [F2] (for EDIT)
2. xlist = [HOURS] [ENTER]
3. ylist = [GRADE] [ENTER]
The menu at the bottom of the display screen contains xstat, ystat, and the lists, in alphabetical order, that have been assigned names.
4. Now enter the elements as shown below:
After entering the data using the three methods we see that the last method is the best for entering our data.
Lists of the same length may be added, subtracted, multiplied, divided and compared term by term, using MATH functions.
If an incorrect value is noticed we can edit the list by using:
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LIST EDIT |
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or |
STAT EDIT |
To delete a data value:
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1. |
[2nd] [-] to access the LIST menu | ||||||||||||||||||
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2. |
[F4] to access the EDIT menu | ||||||||||||||||||
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3. |
Select the list you wish to edit, [ENTER] | ||||||||||||||||||
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4. |
Position the cursor at the element you wish to delete | ||||||||||||||||||
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5. |
Press [F2] to select [DELi], this deletes the value at the cursor and the remaining values shift up one position. | ||||||||||||||||||
To insert a data value follow the same steps replace step 5 with
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5. |
Press [F1] to select [INSi], this inserts a value at the cursor position and the remaining values shift down one position. | ||||||||||||||||||
In the STAT menu select EDIT and then the pair of lists which you wish to edit.
To delete a pair of values:
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1. |
Position the cursor on the x or y value of the data point, | ||||||||||||||||||
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2. |
Press [F2] to select [DELi]. The pair of data values are removed from the data set and the remaining pairs shift up one position. | ||||||||||||||||||
To insert a pair of values:
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1. |
Position the cursor where you want to insert the data point, | ||||||||||||||||||
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2. |
Press [F1] to select [INSi]. A prompt appears for an additional pair of data values and the remaining pairs shift down one position. | ||||||||||||||||||
Now that the data has been entered we can investigate the relationship between the number of hours spent using the computer system (x) and the final exam grade (y).
Our first stage of the analysis is to draw a scattergram plot of HOURS against GRADE to see if there exists a linear relationship between x and y.
1) Set the RANGE
Select [GRAPH] [RANGE]
Enter the range for viewing the scattergram, for example:
2) [EXIT]
3) In the STAT menu choose which values you wish to plot:
[F1] [ENTER] to select the CALC menu
xlist Name = [HOURS] [ENTER]
ylist Name = [GRADE] [ENTER]
[EXIT]
4) Now plot:
[F3] to select the [DRAW] menu
[F2] to select the [SCAT] plot
From this scattergram we can draw some preliminary conclusions:
Now that the data values have been successfully entered we can access the statistical functions within the STAT menu:
1. Press [F1] for the CALC menu
2. Enter the name of the xlist, in this case [HOURS] [ENTER]
3. Enter the name of the ylist, in this case [GRADE] [ENTER]
The function [LINR] performs a linear regression of the form y=a+bx on the lists which we have selected. For regression analysis the TI-85 uses a least squares fit to calculate the regression line.
1) [F2] to select [LINR]
This computes the following
Therefore the estimated regression line (to 2 decimal places) using the least squares fit is
GRADE = 5.83 + 0.83(HOURS)
The correlation coefficient, corr, measures the fit of the above equation with the data points. In general the nearer the modulus of corr to 1, the better the fit, and if corr = 0 this implies that x and y are completely independent. The value of 0.94 can be interpreted as meaning the fit of this regression equation with the data points of GRADE and HOUR is a good fit.
The TI-85 updates the statistical result variables when a one-variable of two-variable (but not polynomial) analysis is performed, and these values can be recalled by using either the STAT VARS menu, or the VARS STATS menu.
To access the statistical variables used in the above calculation:
1) Press [2nd] [ 3 ] to access the [VARS] menu which is a list of variables
2) [MORE] [MORE] [F3] to access the list of statistical variables
3) Use the cursor to select which variable you wish to view, say Sxy
4) [ENTER] the variable appears on the home screen
5) [ENTER] the variable value is given on the home screen
To plot the current regression equation we use the command [DRREG] (draw regression) in the [DRAW] menu:
1) Press [F4] to select DRREG
The following should now be plotted:
Note that to clear a drawing use the command [CLDRW] in the [DRAW] menu
To delete a list you no longer require:
1) Press [2nd] [+] to access the MEM menu
2) Press [F2] to select [DELET]
3) Press [F4] to select [LIST]
4) Position the arrow cursor by the list you wish to delete
5) [ENTER]
6) [EXIT]
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