|
ObservedValue
|
CalculatedValue
|
ObservedValue
|
CalculatedValue
|
|
0.33
|
0.36
|
0.74
|
0.78
|
|
0.36
|
0.36
|
0.79
|
0.86
|
|
0.54
|
0.58
|
0.97
|
0.97
|
|
0.56
|
0.64
|
1.03
|
1.11
|
|
0.66
|
0.64
|
1.10
|
1.06
|
|
0.66
|
0.67
|
1.13
|
1.08
|
|
0.74
|
0.58
|
1.14
|
1.17
|
The article "Polyhedral Distortions in Tourmaline" (A. Ertl, J. Hughes, et al., Canadian Mineralogist, 2002:153-162) presents a model for calculating bond- length distortion in vanadium-bearing tourmaline. To check the accuracy of the model, several calculated values (x ) were compared with directly observed values (y). The results (read from a graph) are presented in the following table.
a. Compute the least-squares line y = βˆ0 + βˆ1 x .
b. Predict the value y when the calculated value is x = 1.0.
c. For which values of x will the predicted value y be less than the calculated value x ?