Question

•List three variables (X1, X2, X3) you’d include in a Multiple Regression Model in order to better predict an outcome (Y) variable. For example, you might list three variables that could be related to how long a person will live (Y). Or you might list three variables that contribute to a successful restaurant. Your Regression Model should have three variables that will act as “predictors” (X1, X2, X3) of a “criterion” (Y’). Note that the outcome or criterion variable (e.g. how long a person would live, or the success/profit made by a restaurant measured) in must be a “Measurement” variable, that is something that is measured on a scale like inches, pounds, IQ, lifespan, stock value, etc. But that the predictors (X variables) can be either a measurement variable OR a categorical variable such as gender, political party, location, etc.

Answer #1

Consider a regression of y on x1,
x2 and x3. You are told
that x1 and x3 are
positively correlated but x2 is uncorrelated
with the other two variables.
[3] What, if anything, can you say about the relative
magnitudes of the estimated coefficients on each of the three
explanatory variables?
[6] What, if anything, can you say about the precision with
which we can estimate these coefficients?

Consider the multiple regression model E(Y|X1
X2) = β0 + β1X1 +
β2X2 +
β3X1X2
Can we interpret β1 as the change in the conditional
mean response for a unit change in X1 holding all the
other predictors in the model fixed?
Group of answer choices
a. Yes, because that is the traditional way of interpreting a
regression coefficient.
b. Yes, because the response variable is quantitative and thus
the partial slopes are interpreted exactly in that manner.
c. No,...

Shown here are the data for y and three predictors,
x1, x2, and
x3. A stepwise regression procedure has been
done on these data; the results are also given. Comment on the
outcome of the stepwise analysis in light of the data.
y
x1
x2
x3
94
21
1
204
97
25
0
198
93
22
1
184
95
27
0
200
89
31
1
183
91
20
1
159
91
18
1
147
94
25
0
196
98
26...

An analyst is running a regression model using the following
data:
Y
x1
x2
x3
x4
x5
x6
4
1
5
0
-95
17
12
10
5
8
1
-27
7
10
32
1
7
0
-82
0
9
2
2
7
0
17
5
10
9
3
9
1
-46
5
11
Excel performs the regression analysis, but the output looks all
messed up: For example the F statistic cannot be computed, standard
errors are all zero, etc etc....

Say your supervisor performs a regression and later find that
one of your independent variables (X1) is
correlated with another variable that you did not include the
regression (X2), and this other variable
might better explain the variance in the dependent variable
(Y). Explain what is likely to happen if your
supervisor conducts another regression with both of these
independent variables included in the model.

A linear regression of a variable Y against the explanatory
variables X1 and X2 produced the following estimation model:
Y = 1615.495 + 9.957 X1 + 0.081 X2 +
e
(527.96) (6.32) (0.024)
The number in parentheses are the standard errors of each
coefficients
i. State the null and alternative hypothesis for the
coefficients
Select the appropriate test, compute the test statistic based on
the information above, and test the null hypothesis for each
coefficient by using a level of...

X1. X2. X3
Y1. 30. 40 52
(33.46) (41.83)(46.71)
Y2. 18. 20. 15
(14.54)(18.18)(20.29)
The table to the right contains observed values and expected values
in parentheses for two categorical variables, X and Y, where
variable X has three categories and variable Y has two categories.
Use the table to complete parts
(a)Compute the value of the chi-square test statistic. X2/0= (round
three decimal places)
(b)Test the hypothesis that X and Y are independent at the a=0.1
level of significance....

y x1 x2 x3
x4
64 74 22 24
17
43 63 29 15
30
51 78 20 9 25
49 52 17 38
29
39 45 12 19 37
Consider the set of dependent and independent variables given
below. Perform a best subsets regression and choose the most
appropriate model for these data.
Find the most appropriate model for the data. Note that the
coefficient is 0 for any variable that is not included in the
model.
y= _____+...

Use the dependent variable (labeled Y) and the independent
variables (labeled X1, X2, and X3) in the data file. Use Excel to
perform the regression and correlation analysis to answer the
following.
Generate a scatterplot for the specified dependent variable (Y)
and the X1 independent variable, including the graph of the "best
fit" line. Interpret.
Determine the equation of the "best fit" line, which describes
the relationship between the dependent variable and the selected
independent variable.
Determine the coefficient of...

A microcomputer manufacturer has developed a regression model
relating his sales (Y in $10,000s) with three independent
variables. The three independent variables are price per unit
(Price in $100s), advertising (ADV in $1,000s) and the number of
product lines (Lines). Part of the regression results is shown
below.
Coefficient
Standard Error
Intercept
1.0211
22.8752
Price (X1)
-.1523
-.1411
ADV (X2)
.8849
.2886
Lines(X3)
-.1463
1.5340
Source
D.F.
S.S.
Regression
3
2708.651
Error
14
2840.51
Total
17
5549.12
(a) What has...

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