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?

2. Consider the data set has four variables which are Y, X1, X2
and X3. Construct a multiple regression
model using Y as response variable and other X variables as
explanatory variables.
(a) Write mathematics formulas (including the assumptions) and give
R commands to obtain linear
regression models for Y Xi, i =1, 2 and 3.
(b) Write several lines of R commands to obtain correlations
between Xi and Xj , i 6= j and i, j =
1, 2,...

Let X1, X2 , X3 be independent
random variables that represent lifetimes (in hours) of three key
components of a device. Say their respective distributions are
exponential with means 1000, 1500, and 1800. Let Y be the minimum
of X1, X2, X3 and compute P(Y >
1000).

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,...

You have a data set with three predictors: X1 = GPA, X2 = IQ,
and X3 = Gender (1 for female, 0 for male). The response is
starting salary after graduation (in $ thousands). We use least
squares to fit the model, and we get b0 = 50, b1 = 20, b2 = 0.07,
and b3 = 35.
a. Predict the salary of a woman with an IQ of 110 and a GPA of
4.0 (for calculation please use Excel.)...

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.

Consider an estimated multiple regression model as given
below.
log(y)ˆ=3.45+0.12log(x1)−0.42x2+0.36x3
Which of the following statements is correct in relation to the
above estimated model?
1. If x3 increases by 1 unit,
y declines by 0.36
2. If x2 falls by 2 per cent,
log(y) decreases by 42percent
3. When the values of x1,
x2 and
x3 are three, the predicted value of
y is 5.2
4. f x1 increases by 1 percent,
y rises by 0.12 percent

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...

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