Name:
___________________
Solution
______________
Problem #1
(20 points total) A company is evaluating the ultimate strength (Su) of two types of
cement as it cures over time.
Consider the raw data, the bestfit lines, and the rsquared values
determined using the method of leastsquares for Cement A (A) and Cement B (B) below.
Su = 0.0386*Time + 2.0571
0
1
2
3
4
0
1
2
3
4
5
6
Curing Time (h)
Ultimate Strength, Su (GPa)
Su = 0.6671*Time + 0.5821
0
1
2
3
4
0
1
2
3
4
5
6
Curing Time (h)
Ultimate Strength, Su (GPa)
Cement A:
2
2.25 and
0.388
Su
r
=
=
Cement B:
2
2.25 and
0.949
Su
r
=
=
1.1 (4 points) The computed rsquared value for A is much less than that of B because:
(Clearly circle
one
response.)
a.
The Sum of Squares of Errors (SSE) for A is considerably less than for B
b.
The Sum of Squares of Errors (SSE) for A is considerably greater than for B
c.
The Sum of Squares of Deviations (SST) for A is considerably less than for B
d.
The Sum of Squares of Deviations (SST) for A is considerably greater than for B
e.
Both B and C
1.2 (8 points) Which of the following statements is/are true? (Circle
all
that are true.)
a.
The slope of the regression line for B is greater than the slope of the regression line for A.
b.
The “goodness of fit” (as measured by r
2
) of the regression line for B is greater than
“goodness of fit” of the regression line for A.
c.
The value of intercept of the regression line for A is greater than the value of the intercept
of the regression line for B.
d.
The mean Su value for A is equal to the mean Su value for B.
1.3 (4 points) The intercept for Cement B is: (Clearly circle
one
response)
a.
0.75
b.
0.5821
c.
0.6671
d.
0
1.4 (2 points) The r
2
value of B is 0.949. This means that 94.9% of the variation of the data
around the regression line is due to unexplained error.
(Clearly circle
one
response)
True
False
1.5 (2 points) By comparing A and B, we can tell that the regression line for A fits the data for A
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 Fall '08
 Oakes
 Regression Analysis, regression line

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