Using the TI84 Graphing Calculator Data Analysis Using the TI84 Graphing Calculator Data Analysis Using the TI84 Graphing Calculator Section 0.1

Unit Objectives: To learn the five steps involved in the Data Analysis process. To become more familiar using the TI84 graphing calculator. Unit Objectives: To learn the five steps involved in the Data Analysis process. To become more familiar using the TI84 graphing calculator.

5 Steps to Data Analysis: • Create an event • Look up existing data Collect the data Organize the data Display the data Regression model Make predictions • Table • List • Graph • Chart 5 Steps to Data Analysis: Collect the data Organize the data Display the data Regression model Make predictions • Equation of best fit • Use the model to determine past and future events.

I. Collecting the Data: You will identify an independent and dependent variable. Examples: independent variable: x-coordinate, input, domain dependent variable: y-coordinate, output, range I. Collecting the Data: You will identify an independent and dependent variable. Examples: independent variable: x-coordinate, input, domain dependent variable: y-coordinate, output, range

II. Organize the Data The independent (x) and dependent (y) values will be placed into a list, chart or table. (You will be entering the values for x and y into your graphing calculators) II. Organize the Data The independent (x) and dependent (y) values will be placed into a list, chart or table. (You will be entering the values for x and y into your graphing calculators)

Calculator steps for entering data into a list: Use the following data: Number of Students Time in sec. 2 5.34 4 9.03 8 19.06 12 27.07 13 27.16 16 37.32 Calculator steps for entering data into a list: Use the following data: Number of Students Time in sec. 2 5.34 4 9.03 8 19.06 12 27.07 13 27.16 16 37.32

Calculator steps cont… STAT 1 ENTER If there is data in your lists, use the arrow keys to move the curser until the list title (L1) is highlighted. Then Use the keys on your calculator. CLEAR ENTER Calculator steps cont Type in your x values one at a time using the key after each entry to insert it into the list. Repeat this step to enter your y values. ENTER

III. Graphing the Data: 1. Turn on your plotter 2. Use the ZOOM function to automatically adjust the viewing screen to fit your data. III. Graphing the Data: 1. Turn on your plotter 2. Use the ZOOM function to automatically adjust the viewing screen to fit your data.

Calculator steps for graphing data: To turn on the plotter: 2nd y= Enter the number of the plotter you want to turn on. Today we will turn on Plot2 so you will enter . 2

Enter each of the following settings and press to go on to the next. graphing continued… Enter each of the following settings and press to go on to the next. ENTER

graphing continued… ZOOM 9

graphing continued… The graph will now appear in the window. Your x and y axis may not be visible. Remember, the window has been adjusted to fit only the data you entered.

IV. Create a Regression Model Linear equation: straight lines 1. y = kx (parent function) The graph is a line The regression model is y=ax+b 1 when k is positive when k is negative

Regression Model cont… Quadratic equation: forms a curve. 2. y = kx2 (parent function) The graph is a parabola The regression model is y=ax2+bx+c when k is positive when k is negative

Regression Model cont… 3. y = kx3 (parent function) The graph is a cubic curve The regression model is: y=ax3+bx2+cx+d when k is positive when k is negative

Regression Model cont… 4. y = k√x (parent function) The graph is a square root The regression model is: y=axb (b=.5) when k is positive when k is negative

Regression Model cont… 5. y = k(b)x (parent function) The graph is exponential The regression model is: y=a*bx when k is positive when k is negative

Calculator steps to finding a regression model: Input: STAT Move curser over to CALC Calculator display: 4: LinReg 5: QuadReg 6: CubicReg 7: -------- 8: -------- 9: -------- 0: ExpReg A: PwrReg Choose the option based on the shape of your graph.

Calculator steps to finding a regression model: Since your data looked like it was forming a line, we will use option 4, LinReg. The screen will now display: LinReg (ax+b)

Calculator steps to finding a regression model: LinReg (ax+b) 2nd 1 , 2nd 2 , Continue with the following key sequence: Input the title of the list where your x values are stored. Input the title of the list where your y values are stored. VARS move curser over to Y-VARS 1 (Function) 1 (Y1 ) ENTER

Calculator steps to finding a regression model: The equation for the line will be automatically put into y1 so you can graph the equation and your calculator will display the following: LinReg y=ax+b a= b= r2= r= 2.208… .587… .989.. .994…

Calculator steps to finding a regression model: If you do not have r2 and r you need to turn on your "diagnostic" as follows: CATALOG This will open the catalog that Contains all of the commands Available on the TI84 Plus 2nd Sroll down until you highlight the command “DiagnosticOn”. Then press ENTER ENTER

Calculator steps to finding a regression model: To display your regression model again you need to enter the following key sequence: Your screen will display: 2nd ENTER LinReg y=ax+b a= b= r2= r= 2nd ENTER 2.208… ENTER .587… .989.. .994…

Calculator steps to finding a regression model: There are 2 variables listed on your screen that are very important and require some explanation. r = Correlation coefficient: (*Only used for Linear relationships*) Indicates the strength of the relationship and the direction (slope of the line), positive or negative. The closer r is to 1 or -1, the better the fit.

Calculator steps to finding a regression model: There are 2 variables listed on your screen that are very important and require some explanation. r2 = Coefficient of determination: Indicates the percentage of data points that lie on the curve. (Can be used for all regression models.)

Calculator steps to finding a regression model: To superimpose the regression model over the data, you should now press the key to see the “Line of Best Fit”. GRAPH Line of Best Fit: The average of the data points.

What question is really being asked? V. Making Predictions: Now that you have graphed the data and found a regression model, you can use the graph and/or the model to make predictions about past or future events. Make a prediction: . How much time would be needed for 43 students to complete the task? What question is really being asked? What is y when x is 43?

Calculator sequence for making predictions: TBL SET Press: 2nd WINDOW The calculator will display: TBL SET TblStart = ∆Tbl = Enter the x-value you want To jump to on the table. 43 Enter how you want the list to Increment, by 1’s, 2’s, 5’s, or Even by .1, .01, .001, . . . Since x represents the number of students, we won’t need any decimals so we will make this: 1

Calculator sequence for making predictions Go to the table to get your answer: TABLE Press: 2nd GRAPH The calculator will display: 95.544 97.753 Use the arrows to scroll up and down if you want other information, or return to the Table Set.

Now, you try: Your Data: Use the given data and the steps of Data Analysis to: Graph the data Create a regression model. (include values for r and r2) 3. Determine the value of y when x is 53.

You try: Practice Problem y-axis x-axis 2 10 14 4 6 8 12 16 18 20 22 24 26 28 30 40 50 60 70 80 You try: x-axis

2. Regression Model: y = 3.268x – 4.439 r = .965 r2 = .931 You try: 2. Regression Model: y = 3.268x – 4.439 r = .965 r2 = .931 3. Make a prediction: If x = 53, then y = 168.78