Lesson 20: Cautions about Correlation and Regression

April 13, 2026

Review:

• Pearson Correlation Coefficient
• R-Squared
• Schedule
  • Finish Simple Regression this week
  • Review and Exam 3 next week

Presentation:

• Cautions about Correlation and Regression
  • Influential Observations
    • Outliers
  • Lurking Variables
    • Explanatory variables not included
    • Beyond scope
  • Extrapolation
    • Use of regression for prediction far outside the range of the explanatory variable
    • Predictions outside the range are unreliable
    • Further outside the range = less reliable predictions
  • The Question of Causation
    • Correlation does not imply causation
    • Spurious Correlations
    • Retrospective study = looking back to find possible causes for an established outcome among a sample population
    • Prospective study = following a sample population over time and studying behaviors possibly linked to likelihood of an outcome
  • Video

Demonstration in Sheets:

Last week we gathered data from USDA National Water and Climate Center and the USGS Water Data Center. The snowpack data (snow-water equivalent inches) is for the Freemont Pass location. The streamflow data (ft^3/SEC) is for the Arkansas River station in Pueblo. Today, let’s look at the data in Sheets to produce the regression equation and point estimate for 2026

Activity/Assignment:

• Use Sheets (or Excel) to solve the problems from last week (see below)
• Use Sheets to find the regression equation for this larger real estate data set

Problem 1. A small coffee shop tracks daily high temperature (°F) and the number of iced coffees sold. Calculate Sum of Squares and the equation of the regression line.

Day	Temp (x)	Iced Coffees Sold (y)
1	60	42
2	65	48
3	70	52
4	75	61
5	80	65

Problem 2. A local brewery tracks weekly social media ad spending and kegs sold. Calculate Sum of Squares and the equation of the regression line.

Week	Ad Spend (x, $100’s)	Kegs Sold (y)
1	2	11
2	3	15
3	4	17
4	5	20
5	7	26
6	9	30

Problem 3. A realtor wants to estimate the relationship between square footage (x) and listing price (y in $1000s). Calculate Sum of Squares and the equation of the regression line.

House	Sq Ft (x)	Listing Price (y)
A	1,600	315
B	1,850	344
C	2,000	365
D	2,300	399
E	2,500	425