Review of Part II
161
Review of Part II – Exploring Relationships Between Variables
1. College.
% over 50:
r
= 0.69
The only moderate, positive correlation in the list.
% under 20:
r
= –0.71
Moderate, negative correlation (–0.98 is too strong)
% Fulltime Fac.:
r
=
0.09
No correlation.
% Gr. on time:
r
=
–0.51
Moderate, negative correlation (not as strong as %under 20)
2. Togetherness.
a)
If no meals are eaten together, the model predicts a GPA of 2.73.
b)
For an increase of one meal per week eaten together, the model predicts an increase of 0.11
in GPA.
c)
The model will predict the mean GPA for the mean number of meals, 3.78.
GPA
Meals
GPA
GPA
ˆ
..
()
ˆ
(
.
)
ˆ
.
=+
=
273 011
273 011378
315
d)
A negative residual means that the student’s actual GPA was lower than the GPA
predicted by the model.
The model overpredicted the student’s GPA.
e)
Although there is evidence of an association between GPA and number of meals eaten
together per week, this is not necessarily a causeandeffect relationship.
There may be
other variables that are related to GPA and meals, such as parental involvement and family
income.
3. Vineyards.
a)
There does not appear to be an association between ages of vineyards and the cost of
products.
rR
==
=
2
0 027
0 164
, indicating a very weak association, at best.
The model
only explains 2.7% of the variability in case price.
Furthermore, the regression equation
appears to be influenced by two outliers, products from vineyards over 30 years old, with
relatively high case prices.
b)
This analysis tells us nothing about vineyards worldwide.
There is no reason to believe
that the results for the Finger Lakes region are representative of the vineyards of the world.
c)
The linear equation used to predict case price from age of the vineyard is:
CasePrice
Years
ˆ
..(
)
92 765
0 567284
d)
This model is not useful because only 2.7% of the variability in case price is accounted for
by the ages of the vineyards.
Furthermore, the slope of the regression line seems
influenced by the presence of two outliers, products from vineyards over 30 years old, with
relatively high case prices.
4. Vineyards again.
a)
There is no evidence of an association between size of the vineyard and case price.
The mean GPA is 3.15.
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Part II
Exploring Relationships Between Variables
b)
One vineyard is approximately 250 acres, with a relatively low case price.
This point has
high leverage.
c)
If the point were removed, the correlation would be expected to increase, from a slightly
negative correlation, to a correlation that is slightly positive.
The point is an outlier in the
x
direction and low in the
y
direction.
It is giving the association the artificial appearance
of a slightly negative relationship.
d)
If the point were removed, the slope would be expected to increase, from slightly negative
to slightly positive.
The point is “pulling” the regression line down.
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 Spring '08
 WEINSTEIN
 Regression Analysis

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