Question

1. In a multiple regression model, the following coefficients were obtained:

b_{0} = -10 b_{1}
= 4.5 b_{2} = -6.0

a. Write the equation of the estimated multiple regression model. (3 pts)

b Suppose a sample of 25 observations produces this result, SSE = 480. What is the estimated standard error of the estimate? (5 pts)

2. Consider the following estimated sample regression equation:

Y = 12 + 6X_{1} -- 3 X_{2}

Determine which of the following statements are true, which are false, and which are indeterminate. Use one sentence to explain your choice. (4 pts)

a. When
X_{2} increases by 1 unit, Y increases by 3 units.

b. Y is more
strongly correlated with X_{2} than with X_{1}
because the coefficient of X_{2} is larger.

c. It is possible that the coefficient 6 might not be significantly different from 0 and that the coefficient minus 3 could be significantly different from 0 if we tested each coefficient using alpha = .05.

3. Suppose we want
to develop a model to predict the resale value of an automobile and
we believe the resale value depends upon the age of the automobile
and whether or not the automobile has a well-documented service
record. Let Y be the resale value of the car in dollars,
X_{1} be the age of the car in years; and X_{2} be
1 if the car has a well-documented service record and 0 if not.
Below is the data set.

Car Price Age ServiceRecord

1 14000 1 0

2 13050 2 0

3 14350 1 1

4 13900 1 0

5 11950 3 0

6 13000 2 0

7 11400 4 1

8 14500 1 1

9 12950 2 0

10 10900 4 0

11 13600 2 1

12 14100 1 0

13 12100 3 0

14 11000 4 0

15 12400 3 1

16 14000 1 0

17 14400 1 1

18 12900 2 0

19 14450 1 1

20 12050 3 0

For the data set supplied, use Excel to run the appropriate multiple regression model for the situation described above. This is a Computer Deliverable and will have points allocated to the regression printout.

a. What is the equation used to predict resale car prices? (3 pts)

b. Is there evidence that a car’s resale value decreases as the car gets older? Use alpha = .01. (15 pts)

c. How much does a well-documented service record change the resale value of an automobile? (3 pts)

d. Develop the appropriate ANOVA table for the information provided. (10 pts)

4. An economist wants to estimate the following production function relating output for a given firm during period t:

Q = b_{0} + b_{1} L + b_{2} K + e

where L = dollars of labor employed

K = dollars of capital expenditure

The firm’s budget is such that the firm always spends $80,000 per year for capital and labor.

Is there a multicollinearity problem? Please explain your answer. (6 pts)

5. Using a series of 40 annual observations, a student estimated a model that included the following variables:

Y = yearly Dow Jones Industrial Average

X_{1} = ratio of annual corporate profit to annual
corporate sales

X_{2} = index of industrial production

X_{3} = corporate bond yield

X_{4} = disposable income per capita

X_{5} = consumer price index.

The results included the following:
R^{2} = .885 dw =
1.046

a. Is there evidence of a linear relationship between the Dow Jones and any of the independent variables? Use alpha =.05. (15 pts)

b. Should we conclude that 1st order autocorrelation is a problem? Use alpha = .05. (15 pts)

6. Consider the following sample regression results:

Y hat = 15.4 + 2.20 X_{1} +
48.14 X_{2}
R^{2} = .355

(6.14) (.42) (5.21) n = 27

The numbers in the parentheses are the estimated standard errors of the sample regression coefficients.

6. (continued)

a. Construct a 95%
confidence interval for b_{1}. (6 pts)

b. Is there evidence
of a linear relationship between X_{2} and Y at
the 5% level of significance? (15 pts)

c. If you were to use a global test to determine if this model had explanatory power, what would your CRITICAL value be if alpha = .01? (4 pts)

PLEASE ANDWER THEM ALL!!!! THANK YOU

Answer #1

**1.)**

**a.)** Multiple regression equation is given
as:

**Y = -10 + 4.5 X1 - 6X2**

**b.)** The Standard error of estimate is:

For us SSE =
(Y-)^{2}
= 480

So,
_{est} =

_{est}
= 4.3817

2.) GIven equation

Y = 12 + 6X1 - 3 X2

a.) When X2 increases by 1 unit, Y increases by 3 units.

**This is False, since if X2 increase by 2 unit Y
decreases by 3 units**

**b.)** Y is more strongly correlated with X2 than
with X1 because the coefficient of X2 is larger.

This is false statement.

It is a common error to confuse correlation and causation. All that correlation shows is that the two variables are associated. There may be a third variable, a confounding variable that is related to both of them. For example, monthly deaths by drowning and monthly sales of ice-cream are positively correlated, but no-one would say the relationship was causal!

6. Consider the following sample regression
results:
Y hat = 15.4 + 2.20 X1 +
48.14
X2
R2 = .355
(6.14)
(.42)
(5.21)
n = 27
The numbers in the parentheses are the estimated standard errors
of the sample regression coefficients.
6. (continued)
a. Construct a 95% confidence interval for
b1.
b. Is there evidence of a linear relationship
between X2 and Y at the 5% level of
significance?
c. If you were to use a global test...

In the simple linear regression model estimate Y =
b0 + b1X
A. Y - estimated average predicted value, X –
predictor, Y-intercept (b1), slope
(b0)
B. Y - estimated average predicted value, X –
predictor, Y-intercept (b0), slope
(b1)
C. X - estimated average predicted value, Y –
predictor, Y-intercept (b1), slope
(b0)
D. X - estimated average predicted value, Y –
predictor, Y-intercept (b0), slope
(b1)
The slope (b1)
represents
A. the estimated average change in Y per...

The estimated regression equation for a model involving two
independent variables and 10 observations follows.
y=27.1671 + 0.7533x1 + 0.7419x2
b1=
b2=
estimate y when x1=180 and x2= 310

Using a series of 40 annual
observations, a student estimated a model that included the
following variables:
Y = yearly Dow Jones Industrial Average
X1 = ratio of annual corporate profit to annual
corporate sales
X2 = index of industrial production
X3 = corporate bond yield
X4 = disposable income per capita
X5 = consumer price index.
The results included the following:
R2 = .885 dw =
1.046
a. Is there evidence...

You want to construct a multiple linear regression model. The
dependent variable is Y and independent variables are x1 and x2.
The samples and STATA outputs are provided:
How would you make an ANOVA from the following information?
Y
X1
X2
3
2
1
4
1
2
6
3
3
6
3
4
7
4
5
STATA
Y
Coef.
Std. Err.
t
P> abs. value (t)
95% confidence interval
X1
0.25
0.4677072
0.53
0.646
-1.762382 , 2.262382
X2
0.85
0.3372684...

You want to construct a multiple linear regression model. The
dependent variable is Y and independent variables are x1 and x2.
The samples and STATA outputs are provided:
Y
X1
X2
3
2
1
4
1
2
6
3
3
6
3
4
7
4
5
STATA
Y
Coef.
Std. Err.
t
P> abs. value (t)
95% confidence interval
X1
0.25
0.4677072
0.53
0.646
-1.762382 , 2.262382
X2
0.85
0.3372684
2.52
0.128
-.601149 , 2.301149
_cons
2
0.7245688
2.76
0.110...

You want to construct a multiple linear regression model. The
dependent variable is Y and independent variables are x1 and x2.
The samples and STATA outputs are provided:
Y
X1
X2
3
2
1
4
1
2
6
3
3
6
3
4
7
4
5
STATA
Y
Coef.
Std. Err.
t
P> abs. value (t)
95% confidence interval
X1
0.25
0.4677072
0.53
0.646
-1.762382 , 2.262382
X2
0.85
0.3372684
2.52
0.128
-.601149 , 2.301149
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2
0.7245688
2.76
0.110...

15-12: Consider the following regression model:
y=β0+β1x1+β2x2+ε
where:
x1=A quantitative variable
x2=1 if x1<20
0 if x1>20
The following estimate regression equation was obtained from a
sample of 30 observations:
y^=24.1+5.8x1+7.9x2
Provide the estimate regression equation for instances in which
x1<20.
Determine the value of y^ when x1=10.
Provide the estimate regression equation for instances in which
x1>20.
Determine the value of y^ when x1=30.
please not handwritten so I can read it

6. The following estimated regression model was developed
relating yearly income (Y in $1,000s) of 30 individuals with their
age (X1) and their gender (X2) (0 if male and 1 if female).
ˆ Y =20+0.7X1 +2X2 SST = 1,000 and SSE = 256
b) Is there a significant relationship between the yearly income
and the set of predictors (i.e., age and gender)? Use α=0.05 and
make sure to show all your steps.

1.
Suppose the variable x2 has been omitted from
the following regression equation, y = β0 +
β1x1 +β2x2 + u.
b1 is the estimator obtained when x2 is
omitted from the equation. The bias in b1 is positive
if
A.
β2<0 and x1 and x2 are
positive correlated
B.
β2=0 and x1 and x2 are negative
correlated
C.
β2>0 and x1 and x2 are
negative correlated
D.
β2>0 and x1 and x2 are
positive correlated
2.
Suppose the true...

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