Two radon detectors were placed in different locations in the basement of a home. Each provided an hourly measurement of the radon concentration, in units of pCi/L. The data are presented in the following table.
|
R1
|
R2
|
R1
|
R2
|
R1
|
R2
|
R1
|
R2
|
|
1.2
|
1.2
|
3.4
|
2.0
|
4.0
|
2.6
|
5.5
|
3.6
|
|
1.3
|
1.5
|
3.5
|
2.0
|
4.0
|
2.7
|
5.8
|
3.6
|
|
1.3
|
1.6
|
3.6
|
2.1
|
4.3
|
2.7
|
5.9
|
3.9
|
|
1.3
|
1.7
|
3.6
|
2.1
|
4.3
|
2.8
|
6.0
|
4.0
|
|
1.5
|
1.7
|
3.7
|
2.1
|
4.4
|
2.9
|
6.0
|
4.2
|
|
1.5
|
1.7
|
3.8
|
2.2
|
4.4
|
3.0
|
6.1
|
4.4
|
|
1.6
|
1.8
|
3.8
|
2.2
|
4.7
|
3.1
|
6.2
|
4.4
|
|
2.0
|
1.8
|
3.8
|
2.3
|
4.7
|
3.2
|
6.5
|
4.4
|
|
2.0
|
1.9
|
3.9
|
2.3
|
4.8
|
3.2
|
6.6
|
4.4
|
|
2.4
|
1.9
|
3.9
|
2.4
|
4.8
|
3.5
|
6.9
|
4.7
|
|
2.9
|
1.9
|
3.9
|
2.4
|
4.9
|
3.5
|
7.0
|
4.8
|
|
3.0
|
2.0
|
3.9
|
2.4
|
5.4
|
3.5
|
a. Compute the least-squares line for predicting the radon concentration at location 2 from the concentration at location 1.
b. Plot the residuals versus the fitted values. Does the linear model seem appropriate?
c. Divide the data into two groups: points where R1 4 in one group, points where R1 ≥ 4 in the other. Compute the least-squares line and the residual plot for each group. Does the line describe either group well? Which one?
d. Explain why it might be a good idea to fit a linear model to part of these data, and a nonlinear model to the other.