This document discusses using linear regression in Desmos to analyze the relationship between advertising spending (x) and sales (y) for a company. It provides sample advertising spending and sales data for 6 months. It then shows how to enter this data into Desmos, use the regression operator "~" to calculate the linear regression equation, and plot the regression line to visualize the relationship between x and y. The regression line can then be used to predict expected sales for different advertising spending amounts.

1. Linear Regression
with Desmos
Colleen Young

2. Example
A company carries out some research into the effect of
spending money on advertising. In one month they spend x (in
thousands of pounds) and record the sales, y (also in
thousands of pounds in the following month. The procedure is
repeated every three months, each time with a different
value of x. The procedure is repeated six times with the
following results. Calculate the equation of the regression
line of y on x x y
5 160
9 205
13 229
7 185
11 225
3 136

3. Check with Desmos
Enter the data into
Excel

4. Paste the data into Desmos

5. Add an item and choose expression

6. Use the ~ character for regression.
Desmos calculates the constants and plots the regression line

7. Note you can choose to plot
the residuals

8. We could now add the regression line and...

9. Edit the list
Enter the regession
line and convert to a
table
Change the x values to
see the values
predicted by the
model

10. Select image to see graph on Desmos

11. Colleen Young
Mathematics, Learning & Technology
Mathematics for Students