Question 2.139

2.139 Wood products

A wood product manufacturer is interested in replacing solid-wood building material by less-expensive products made from wood flakes.27 The company collected the following data to examine the relationship between the length (in inches) and the strength (in pounds per square inch) of beams made from wood flakes:

wood

Length 5 6 7 8 9 10 11 12 13 14
Strength 446 371 334 296 249 254 244 246 239 234
  1. Make a scatterplot that shows how the length of a beam affects its strength.
  2. Describe the overall pattern of the plot. Are there any outliers?
  3. Fit a least-squares line to the entire set of data. Graph the line on your scatterplot. Does a straight line adequately describe these data?
  4. The scatterplot suggests that the relation between length and strength can be described by two straight lines, one for lengths of 5 to 9 inches and another for lengths of 9 to 14 inches. Fit least-squares lines to these two subsets of the data, and draw the lines on your plot. Do they describe the data adequately? What question would you now ask the wood experts?

2.139

(b) The strength decreases with length until 9 inches then levels off. There are no outliers. (c) The line does not adequately describe the relationship because the relationship changes after length 9 inches. (d) The two lines adequately explain the data. Ask the wood expert what happens at 10 inches.