Lesson 21: Cautions about Correlation and Regression

November 11, 2025

Review:

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

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 studies = following a sample population over time and studying behaviors possibly linked to likelihood of an outcome
  • Video

Demonstration in Sheets:

Now, here’s some real data, gathered 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.

Water Year	Snowpack (x)	Streamflow (y)
2018	20.4	577.5
2019	28.1	1599.3
2020	20.2	901.0
2021	15.5	659.4
2022	17.6	730.4
2023	17.1	1016.0
2024	22.2	1455.7

• We did this manually last time
  • Calculate Sum of Squares, the Linear Equation, the Pearson Correlation Coefficient and R^2.
  • Using the regression equation, estimate Streamflow for 2025 assuming Snowpack x=18.2.
• This time…
  • Use Sheets to produce the regression equation and point estimate for 2025.
  • Check your answer from last week.

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