Why not?
What do we look at to answer this question?
11
We have textbook solutions for you!
The document you are viewing contains questions related to this textbook.
The document you are viewing contains questions related to this textbook.
Expert Verified
Thus
jar
we've
found
that both "Training"
and
"Salary" are related to "Performance Rating".
How can we capitalize on both
of
these relationships?
By
building a multiple regression
equation (i.e., using multiple predictor variables in the same equation).
Mtb
Express:
Statistics
Multiple
Regression
Regression Analysis: perform versus training, salary
Model
Summary
s
=
5.947
RSq
=
89.6%
RSq(adj)
=
88.7%
Coefficients
Predictor
coef
SE
Coef
Tvalue
Pvalue
Constant
30.83
10.86
2.84
0.010
training
3.2569
0.3886
8.38
0.000
salary
0 .
06919
0.01471
4.70
0.000
Regression
equation
perform=

30.8
+
3.26
training
+
0.0692
salary
3
0 . 8
This is the average performance rating for those whose
training=
0
and whose
salary=
0.
As
is often (not always) the case, such data values are outside the range
of
values
used to develop this model,
and
hence we should
not
interpret this Yintercept in
this problem context.
3.
26
Average performance increases 3.26 points for each additional day
of
training,
given that the relationship between salary and performance has already been taken
into account (or, given that salary
is
held constant) .
.
06
92
Average performance increases .0692 points for each additional dollar
of
weekly
salary, given that the relationship between training and performance has already
been
taken
into
account
(or,
given
training
held
constant).
12
How was
it
that
"training" explained 79%
of
the variation
in
performance ratings
"salary" explained 56%
of
the variation in performance ratings
But when the data
for
both predictors was used together, we still were able to explain
only 89%
of
the variation in "performance"?
predictor variables are related to each other, as well as to Y
+
Analysis difficulties created
by
multicollinearity:
•
~~usfy,
l
ll!ilfiMops
:
~
::
WiU~bounce
atound'l

(~ld
even switch
sign
"'
t~ty~~~&inationof
Pl"~ictors
in
_
the
equation
"
13
__
+
Using categorical predictor variables in regression:
How can we incorporate a nominalscaled variable as a regression predictor variable?
Refer again to the data file USTsurvey.mtw
Our "Response variable"
is
"$
spent
on
last date by
you"
The
"Predictor variable" is "Gender"
How different are the average date spending amounts for males vs.females?
Descriptive Statistics: date$you
Variable
gender
N
N*
Mean
SE
Mean
StDev
Minimum
Q1
date$you
0
135
9
7.339
0.795
9.235
0.000000000
0
.0
00000000
1
133
7
28.56
2.05
23.60
0.000000000
15.00
*
7
0
6.29
4.20
11.10
0.000000000
0.000000000
Variable
gender
Median
Q3
Maximum
date$you
0
5.000
12.000
50.000
1
20.00
40.00
120.00
*
0.000000000
10.00
30.00
15
.
~


What
if
we use "Gender" as a predictor
in
a regression equation
How
do
we
know
our interpretation
of
the
"slope" coefficient
needs
to
change?
Regression Analysis: date$you versus gender
s
=
17.87
RSq
=
26
.
2%
RSq(adj)
=
25.9%
Predictor
Coef
SE
coef
T
p
Constant
7.339
1.538
4.77
0.000
gender
21.218
2.183
9.
72
0.000
Regression
equation
date$you
=
7.34
+
21.2
gender
How
do
we
interpret
the
7.34?
How
do
we
interpret
the
21.2?
We
need to "write out the
mod
e
/for
each different value
of
the nominalscale predictor variable;
i.e
..