The price of lumber is typically a nonlinear distribution. Here are the current prices at a popular home improvement store for 2” x 4” lumber in different lengths.

length – feet price

8            $5.11

10            $7.58

12            $9.12

16            $12.87

* Create a scatterplot using this data. Place the explanatory variable on the horizontal axis and response variable on the vertical axis. Be sure to label the axes and scale.


* Determine the exponential regression model for this data. Write the results below:

Equation r2

* Determine the quadratic regression model for this data. Write the result below:

Equation r2

* Use the regression models to make a price chart for some non-standard lengths of 2” x 4” lumber.

Length – feet Exponential Regression Price Quadratic Regression Price

4  

14  

20  

32  

* Write a brief paragraph comparing and contrasting the two regression models. Why do you think the regression model for lumber price is best represented in a nonlinear distribution?