- Understand linear regression and describe a case study
- Compute and interpret coefficients in a linear regression analysis in R.
- Interpolate regression model in R to produce a raster layer.

May 12 2021

- Understand linear regression and describe a case study
- Compute and interpret coefficients in a linear regression analysis in R.
- Interpolate regression model in R to produce a raster layer.

What are we doing?

- Explain
- Predict

Why is it windy in Iowa?

- Missouri sucks and Minnesota blows
- No connection

Where do babies come from?

- Storks deliver babies
- No connection

Why are basements in Iowa full of cracks?

- Soils in Iowa contain high amounts of shrink-swell clays
- Connection

Predictions

- None of us will report to work on Sunday
- The average price of a gallon of gas in the US will be $100.00 on January 1

Predicting with a function

- \[y= \beta_0 + \beta_1x + \epsilon\]

- Linear
- Independent
- Homoscedastic
- Normal

- Ordinary Least Squares
- \[\beta_1= \frac{\sum(x_i - \bar x) (y_i - \bar y)} {\sum(x_i - \bar x)^2}\]
- \[\beta_0= \bar y - \beta_1 \times \bar x\]

Wills et al., 2013

Carbon equivalent correction regression factor: \[OC_{dc}= 0.25 + 0.86(OC_{wc})\] where

\(OC_{dc}=\) organic carbon by dry combustion (%)

\(OC_{wc}=\) organic carbon by wet combustion (%)