How To Find Line Of Best Fit On Ti 84

A line of best fit is a straight line that summarizes the overall relationship between two variables. Learning how to find the line of best fit on a TI-84 helps you calculate its equation, display it on a scatter plot, evaluate how well it represents your data, and make informed predictions.

Introduction: What Is a Line of Best Fit?

A line of best fit, also called a linear regression line, passes as closely as possible to a group of data points. The TI-84 uses the least-squares method, which finds the line that minimizes the total of the squared vertical distances between the points and the line.

For data arranged as pairs such as (2, 7), (4, 11), (6, 15), the calculator treats the first values as x and the second values as y. Its standard linear equation is:

**y =

… mx + b, where m is the slope and b is the y‑intercept. The TI‑84 computes these coefficients automatically and also reports the correlation coefficient r (and r²) to gauge how tightly the points cluster around the line.

Step‑by‑Step Procedure on the TI‑84

1. Enter the data

   • Press [STAT] → select 1:Edit….
   • Clear any existing contents in L1 and L2 (highlight the list name, press [CLEAR] then [ENTER]).
   • Input the x values in L1 and the corresponding y values in L2, pressing [ENTER] after each entry.

2. Calculate the linear regression

   • Press [STAT], arrow right to CALC, then choose 4:LinReg(ax+b) (or 8:LinReg(a+bx) if you prefer the y = a + bx format).
   • Ensure the command reads LinReg(ax+b) L1, L2, Y1 (the last argument stores the equation in Y1 for easy graphing).
   • Press [ENTER]. The screen will display:
     • a (slope)
     • b (y‑intercept)
     • r (correlation coefficient)
     • r² (coefficient of determination)

3. View the regression equation

   • The calculator now holds the equation y = ax + b in Y1.
   • Press [Y=] to confirm that Y1 shows the expression (e.g., Y1 = 2.5X + 0.3).

4. Plot the scatter diagram and the line

   • Press [2nd] then [Y=] to access STAT PLOT.
   • Turn Plot1 On, set the Type to the first scatter‑plot icon, Xlist to L1, Ylist to L2, and choose a mark style.
   • Press [ZOOM] and select 9:ZoomStat to automatically scale the axes to fit the data.
   • Press [GRAPH]; you will see the points superimposed with the regression line drawn from Y1.

5. Assess the fit

   • The value of r ranges from –1 to 1. Values near ±1 indicate a strong linear relationship; values near 0 suggest little linear association.
   • r² expresses the proportion of variance in y explained by the line (e.g., r² = 0.84 means 84 % of the variability is captured).
   • For a residual check, go to [STAT] → EDIT, highlight L3, enter L2 – Y1(L1), and press [ENTER]. Then plot L1 vs. L3 (using another STAT PLOT) to see if residuals are randomly scattered around zero.

6. Make predictions

   • To predict y for a given x, press [VARS], arrow right to Y‑VARS, select 1:Function…, then 1:Y1, and input the desired x value (e.g., Y1(7)) followed by [ENTER].
   • Alternatively, use the [TABLE] feature: press [2nd] then [GRAPH], scroll to the x of interest, and read the corresponding y from Y1.

Practical Tips

• Clear old equations before storing a new regression to avoid overlapping graphs (press [Y=], highlight each unwanted line, and press [CLEAR]).
• If your data suggests a non‑linear trend, explore other regression options in the CALC menu (QuadReg, ExpReg, etc.) and compare their r² values.
• Always label your axes and include a title when copying the graph for a report; the TI‑84’s [DRAW] menu lets you add text directly on the screen.

Conclusion
Mastering the line‑of‑best‑fit on a TI‑84 transforms raw data into actionable insight. By entering paired observations into lists, invoking the LinReg(ax+b) command, and graphing the resulting equation alongside a scatter plot, you obtain both the predictive model (slope *