Overview
This lecture explains how to compute, display, and interpret the least squares regression line using a TI-83/84 calculator.
Entering Data
- Enter explanatory (X) values in list L1 and response (Y) values in list L2 via STAT > EDIT.
- Ensure all data points are correctly entered into L1 and L2.
Enabling Diagnostics
- Access the catalog by pressing 2nd > CATALOG.
- Select "DiagnosticsOn" and press ENTER to enable regression statistics.
Calculating the Regression Line
- Go to STAT > CALC and choose option 4 (LinReg(ax+b)).
- The calculator outputs the regression equation in the form y = ax + b, where a is the slope and b is the intercept.
- Results are displayed to four decimal places.
Creating a Scatter Plot
- Press 2nd > Y= (STAT PLOT) and select Plot 1.
- Turn the plot ON and choose the scatter plot type.
- Set Xlist to L1 and Ylist to L2 using ALPHA and the L1/L2 keys.
Displaying the Plot and Regression Line
- Press ZOOM and select option 9 (ZoomStat) to fit the plot to the data.
- To graph the regression line, enter its equation into Y=.
- You can type in the regression parameters directly or use VARS > Statistics > EQ to insert exact values for a (slope) and b (intercept).
- Graphing displays the regression line over the scatter plot for comparison and analysis.
Interpreting the Graph
- Visually check how well the line fits the data by matching plotted points to the regression line.
Key Terms & Definitions
- Least Squares Regression Line — The line that minimizes the sum of squared residuals for best fit.
- Slope (a) — Indicates how much Y changes for each unit increase in X.
- Intercept (b) — The predicted value of Y when X is zero.
- Scatter Plot — A graph that displays individual data points using Cartesian coordinates.
Action Items / Next Steps
- Practice entering data and calculating a regression line on your calculator.
- Review how to use VARS > Statistics > EQ for regression parameters.
- Attempt similar problems to reinforce these calculator skills.