LAB 8: Graphing Calculator: Applying Linear and Median Regression

New Concept

The graphing calculator can be used to calculate and plot a line of best fit using linear and median regression.

Why it matters

Real-world data rarely fits a perfect equation, but algebra provides the tools to find the underlying trends. Mastering regression allows you to model complex systems, from predicting market behavior to analyzing scientific experiments, turning noisy data into clear insights.

What’s next

Next, you’ll use your graphing calculator to find the line of best fit for a given data set.

Property

A linear regression line is the straight line that best represents a set of data points. Your calculator finds this line using the LinReg(ax+b) function from the CALC menu. You must specify L1 for your x-values and L2 for your y-values. It then calculates the optimal slope a and y-intercept b for the equation $y = ax + b$.

To calculate: Press [STAT] → [CALC] → [4:LinReg(ax+b)].
To specify lists: After selecting LinReg, enter [2nd] [1] [,] [2nd] [2] to use data from L1 and L2.
If the output is a=-1.05 and b=8.8, the line's equation is $y = -1.05x + 8.8$.

Think of drawing one straight line through a cloud of points. The calculator's LinReg function is a genius tool that finds the perfect line that gets closest to all those points at once, giving you the best possible fit!

Property

After calculating a regression line, the calculator stores the equation in a special variable called RegEQ. To plot it, go to the Y= editor, press [VARS], navigate to 5:Statistics..., then open the EQ menu and select 1:RegEQ. This pastes the equation into Y₁ so you can graph it over your data points without manual entry.

In the [Y=] editor: Press [VARS] → [5:Statistics...] → [EQ] → [1:RegEQ] to paste the equation.
With the equation in Y₁, press [GRAPH] to draw the best-fit line over your scatter plot.
To compare lines, paste one into Y₁ and a second (like Med-Med) into Y₂.

Your calculator already did the hard math! Instead of retyping the equation, just tell the Y= editor to grab the RegEQ variable. It's a fantastic shortcut that prevents typos and saves you a ton of time!

Property

The Median-Median line is an alternative best-fit line that is less sensitive to outliers. It is found using the Med-Med function in the CALC menu. This method divides the data into three groups and uses their medians to build the line. The resulting equation for $y = ax + b$ is also stored in the RegEQ variable.

To calculate: Press [STAT] → [CALC] → [3:Med-Med].
After selecting, specify your lists: [2nd] [1] [,] [2nd] [2] for data in L1 and L2.
After calculating, paste the new RegEQ into Y₂ to compare it with the linear line in Y₁.

Meet the cool cousin of linear regression! The Median-Median line is not swayed by wild outlier points. It gives you a fit based on the solid middle of your data, creating a more robust and often more realistic trend line.