TI-83 Calculator Help in MATH 166

Finding the Intersection Point of Two Lines

Graph the two functions by entering the slope-intercept form of the lines into Y1 and Y2. These are located under the Y= button.
Go to CALC which is found by pressing 2nd TRACE.
Select option 5:intersect.
The calculator will prompt you for the first and second curves you want to intersect. The cursor will blink on a function and show the function name in the upper left corner of the screen. When it blinks on Y1, press ENTER & when it blinks on Y2, press ENTER.
The calculator will then ask you to guess where the intersection point is located. Use your right and left arrow keys to move to the intersection point and press ENTER.
The intersection point will appear at the bottom of the screen.

Linear Regression

Enter your x and y values into lists. To do this, hit STAT and select 1:Edit.... If you have anything in L1 or L2, cursor up to the name of the list, hit CLEAR and ENTER. Now just enter in your values one at a time by pressing ENTER after each number.
To find the regression equation, first hit STAT, cursor right to CALC and select option 4:LinReg(ax+b). Now press 2nd 1 , 2nd 2 , to specify the x list and y list. (REMEMBER THE COMMAS!) Hit VARS, cursor right to Y-VARS, select 1:Function... and Y1 (or whichever function you would like) to specify where the regession equation will be saved. You should now see the following on your home screen:
LinReg(ax+b) L1, L2, Y1
Now, press ENTER. The following should appear on your screen:
LinReg(ax+b)
y=ax+b
a=....
b=....
r^2=....
r=....

Your regression line is the equation now saved under Y1. If you don't have the r stuff, then you need to turn your diagnostics on. To do this, hit 2nd 0, and cursor down to select DiagnosticOn. When this comes up on your home screen, press ENTER and it should say Done.
To graph the regression line with the data points, first make sure your stat plot is turned on. To do this, hit 2nd Y= and select 1.... by pressing ENTER. You can then highlight any of the options you would like. Now just hit GRAPH. If you don't see anything, adjust your window size under WINDOW and ZOOM.
To find a y value from your regression line when given an x value, go to CALC (2nd TRACE) and select option 1:value. Then just enter the value for x.
To find an x value from your regression line when given a y value, enter the y value under Y2 and then find the intersection point between Y1 (your regression line) and Y2.

Matrices
If you have a TI-83 Plus, when you see directions to hit the MATRX button, you need to hit 2nd x^(-1).

Entering a Matrix
1. Hit MATRX.
2. Cursor right two places to EDIT and hit ENTER.
3. Enter the size of the matrix. (ROW NUMBER FIRST, COLUMN NUMBER SECOND!!!)
4. Enter the matrix elements. If you enter the elements and press ENTER after each element, the cursor will move left to right across the rows and then down to the next row and continue in the same fashion until you reach the last element of the matrix. You can always move around to different elements with your cursor keys, too.
Calling a Matrix for Computation
1. Make sure you are on the home screen before you begin. To do this, hit 2nd MODE to quit.
2. Press MATRX and cursor down under the NAMES list until you get to the matrix you want and hit ENTER. The name of the matrix you need to do computations with will now be on your homescreen.
Matrix Transpose
1. Call the matrix you would like to transpose from the home screen.
2. Hit MATRX, cursor right to MATH and select option 2:T.
3. You should now see the symbolic representation of transposing your matrix. To actually see the transpose, hit ENTER.
Square Matrix Inverses
1. Enter the matrix for which you would like to find the inverse.
2. Call that matrix from your home screen.
3. Hit the x inverse button (x^-1) which is directly below the MATH key and press ENTER.
Fast RREF (This only works when the #rows is less than or equal to #columns)
1. Enter the matrix you want to reduce.
2. Go to your home screen.
3. Press MATRX, cursor right to MATH, and select B:rref.
4. Call the matrix you want to reduce and hit ENTER.

Counting

Factorials
1. Enter n on your home screen.
2. Press MATH, cursor over to PRB, and down to 4:!.
3. Press ENTER.
Permutations
1. Enter n on your home screen.
2. Press MATH, cursor over to PRB, and down to 2:nPr.
3. Enter r.
4. Press ENTER
Combinations
1. Enter n on your home screen.
2. Press MATH, cursor over to PRB, and down to 3:nCr.
3. Enter r.
4. Press ENTER

Statistics

Histograms
1. Enter Data into Lists. Your random variable(X) values should be entered into L1 and the corresponding probabilities should be entered into L2.
2. Turn on Stat Plot. Press 2nd Y= and choose which plot you want. In class I used the first one. When on the Stat Plot screen, highlight the following options:
  On
  Histogram (Bar Graph) picture - the last picture in the top row
  Xlist: L1
  Freq: L2
  
  NOTE: Once you've done this the plot will be turned ON until you turn it OFF.
3. Set Window. Use X values to choose Xmin and Xmax. Set Y values between 0 and 1 and choose Yscl by looking at your data.
4. Graph. (Make sure you don't have anything entered on Y= screen.)
Expected Value/Standard Deviation/Variance
1. Enter data into L1 and L2 as in the above.
2. Press STAT cursor right to CALC and down to 1: 1-Var Stats.
3. When you see 1-Var Stats on your home screen, add L1,L2 so that your screen reads 1-Var Stats L1,L2 and press ENTER.
4. The expected value is the first number listed : x bar.
5. The standard deviation is the fifth number listed: sigma x.
6. To find the variance, use the standard deviation. Press VARS, cursor down to 5:Statistics, and down again to 4:sigma x. Then press the x-squared key and hit ENTER.
Probability Distributions
- Binomial probability P(n,r)
  1. Press DIST (2nd Vars) .
  2. Cursor down to 0:binompdf(. Hit ENTER.
  3. Enter n, probability of success p, and r. Don't forget the commas!
- Cumulative binomial distribution P(X < b)
  1. Press DIST (2nd Vars) .
  2. Cursor down to A:binomcdf(. Hit ENTER.
  3. Enter n, probability of success p, and b. Don't forget the commas!
- Normal distribution P(Z < a)
  1. Press DIST (2nd Vars) .
  2. Cursor to 2:normalcdf(. Hit ENTER.
  3. Enter -1e99, ((-) 1 2nd , 9 9),a, mean , and standard deviation. Don't forget the commas!
- Cumulative normal distribution P(a< Z < b)
  1. Press DIST (2nd Vars) .
  2. Cursor to 2:normalcdf(. Hit ENTER.
  3. Enter a, b, mean , and standard deviation. Don't forget the commas!
- Inversion of normal distribution - how to find the a value given the probability P(Z < a) = p
  1. Press DIST (2nd Vars) .
  2. Cursor to 3:invNorm(. Hit ENTER.
  3. Enter probability value p, mean , and standard deviation. Don't forget the commas!
Compound Interest and Effective Rates of Interest for Non-Continually Compounded Accounts
For both of these types of problems, go to FINANCE on your calculator. If you have the regular TI-83, this is found by hitting 2nd x^(-1). If you have the TI-83 Plus, this is found by hitting the blue APPS button and selecting option 1:Finance....
- Compound Interest
  1. Select option 1:TVMSolver. You should have the following on your screen:
    N =
    I%=
    PV=
    PMT=
    FV=
    P/Y=
    C/Y=
  2. If you are making payments, make sure that END is highlighted at the bottom of the screen.
  3. Fill in all but one of the above options (the one you are trying to solve for) as follows: N = the total number of times compounded (the number of times compounded per year times the number of years), I% = interest rate (not in decimal form), PV = present value (the amount you invest), PMT = value of payments (0 if you are not making any payments), FV = future value (the amount of money you have at the end of your investment), P/Y = the number of payments per year (the number of times compounded per year if you are not making any payments), C/Y = the number of times compounded per year. If you fill in PV and FV, one must be negative in order for your calculator to find an answer. (Simulating the flow of money between you and the bank.) Make sure you have some kind of value entered in the spot for whichever variable you are solving for or else the calculator will not let you proceed to input values for the rest of the variables.
  4. Move your cursor to the value you are solving for and hit ALPHA and then ENTER.
- Effective Rates of Interest
  1. Select option C:Eff(.
  2. Input the nominal interest rate (not in decimal form) followed by a comma and then the number of times the account is compunded per year.
  3. Hit ENTER.