Exercise 1:
Following are measurements of tensile strength in ksi (x) and Brinell hardness (y) for 10 specimens of cold drawn copper. Assume that tensile strength and Brinell hardness follow a bivariate normal distribution.
|
x
|
y
|
|
106.2
|
35
|
|
106.3
|
37.2
|
|
105.3
|
39.8
|
|
106.1
|
35.8
|
|
105.4
|
41.3
|
|
106.3
|
40.7
|
|
104.7
|
38.7
|
|
105.4
|
40.2
|
|
105.5
|
38.1
|
|
105.1
|
41.6
|
a) Find a 95% confidence interval for ρ, the population correlation between tensile strength and Brinell hardness.
b) Can you conclude that ρ <0.3?
c) Can you conclude that ρ ≠0?
Exercise 2
The article "Optimization of Medium Composition for Lipase Production by Candida rugosa NCIM 3462 Using Response Surface Methodology" describes a series of experiments in which lipase was produced from a bacterial culture. In each experiment, the rate of lipase production (in μ mol per ml enzyme per minute) and the cell mass (in g/L) were measured. The results are presented in the following table:
|
Cell mass (x)
|
Lipase (y)
|
Cell mass (x)
|
Lipase (y)
|
Cell mass (x)
|
Lipase (y)
|
Cell mass (x)
|
Lipase (y)
|
|
4.5
|
2.06
|
3.98
|
2.1
|
3.65
|
2.2
|
4.15
|
3.75
|
|
4.68
|
2.1
|
4.72
|
2.75
|
4.23
|
2.3
|
4.3
|
3.15
|
|
5.4
|
3.15
|
3.41
|
2.8
|
4.1
|
2.4
|
4.9
|
5.1
|
|
5.45
|
4.1
|
4.8
|
4.6
|
5.03
|
4.75
|
5.23
|
5.04
|
|
4.2
|
2.2
|
3.6
|
2.5
|
4.19
|
3.15
|
5.4
|
4.96
|
|
4.12
|
3.2
|
4.95
|
4.1
|
4.4
|
3.9
|
4.85
|
5
|
|
4
|
2.85
|
3.25
|
2.15
|
3.92
|
3.2
|
5.1
|
4.92
|
|
4.41
|
4.5
|
4.4
|
4.4
|
3.5
|
2.1
|
4.94
|
4.98
|
Using SAS, create a scatter plot, find the least squares line (prediction line), Pearson's correlation coefficient (explain), complete a test of linearity based on your SAS output, and find/explain the coefficient of determination. Note: Print out of SAS code and output is needed.