Light through the water Some college students collected data on the intensity of light at various depths in a lake. Here are their data:

Depth (m) Light intensity (lumens)

5 168.00 6 120.42 7 86.31 8 61.87 9 44.34 10 31.78 11 22.78

(a) Make a reasonably accurate scatterplot of the data by hand, using depth as the explanatory variable.

Describe what you see.

(b) A scatterplot of the natural logarithm of light intensity versus depth is shown below. Based on this graph, explain why it would be reasonable to use an exponential model to describe the relationship between light intensity and depth.

(c) Minitab output from a linear regression analysis on the transformed data is shown below.
Predictor Coef SE Coef T P Constant 6.78910 0.00009 78575.46 0.000 Depth (m) -0.333021 0.000010 -31783.44 0.000 S = 0.000055 R-Sq = 100.0% R-Sq(adj) = 100.0%

Give the equation of the least-squares regression line.
Be sure to define any variables you use.

(d) Use your model to predict the light intensity at a depth of 12 meters. Show your work.

Transcribed Image Text:

In(intensity) 5.0- 4.5- 4.0- 3.5 3.0- 5 6 7 8 Depth (m) 9 10 11