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!

Multiple choice!
Consider the model Yi = B0 + B1X1i + B2X2i + B3X3i + B4X4i + Ui.
To test the null hypothseis of B2 = B3 = 0, the restricted
regression is:
A. Yi = B0 + B1X1i + B2X2i + B3X3i + B4X4i + Ui
B. Yi = B0 + Ui
C. Yi = B0 + B1X1i + B4X4i + Ui
D. Yi = B0 + B2X2i + B3X3i + Ui
Consider the model Yi = B0 +...

Given the following regression model: Y = B0 + B1X1 + B2X2 +
B3X3 + u
If we want to test the null hypothesis H0: B0 + B1 = 5, which of
the following is correct?
1) Estimate Y = gamma0 + gamma1(X1 - 1) + gamma2X2 + gamma3X3 +
u and test the hypothesis gamma0 = 5
2) Estimate Y = gamma0 + gamma1(X1 + 1) + gamma2X2 + gamma3X3 +
u and test the hypothesis gamma1 = 5...

The estimated regression equation for a model involving two
independent variables and 10 observations follows.
Y= 30.7752 + 0.6659x1+ 0.3724x2
a. Interpret b1 and b2 in this estimated
regression equation.
b1= -------
Select your answer:
-y changes by 0.6659 when x1 increases by 1 unit and x2
stays the same
-y changes by 0.6659 when x2 increases by 1 unit and x1
stays the same
- y changes by 0.3724 when x1 increases by 1 unit and x2
stays the...

The estimated regression equation for a model involving two
independent variables and observations follows. y = 29.1379 + .7302
x1 + .5196 x2
A. Interpret and in this estimated regression equation.
b1 =
b2 =
B. Estimate when y x1=180 and x2=310 (to 3 decimals).

The estimated regression equation for a model involving two
independent variables and 10 observations follows.
^
y = 25.0793 + 0.6944x1 + 0.8028x2
a. Interpret and in this estimated regression equation.
b1 = ____
Select your answer: y changes by 0.6944 when x1 increases by 1 unit
and x2 stays the same
y changes by 0.6944 when x2
increases by 1 unit and x1 stays the same
y changes by 0.8028 when x1
increases by 1...

In a multiple regression, the following sample regression
equation is obtained:
yˆ = 161 + 12.4x1 + 2.6x2.
a. Predict y if x1 equals 20 and x2 equals 42. (Round your answer
to 1 decimal place.)
yˆ = _________
b. Interpret the slope coefficient of x1.
As x1 increases by one unit, y is predicted to decrease by 2.6
units, holding x2 constant.
As x1 increases by one unit, y is predicted to decrease by 12.4
units, holding x2 constant....

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

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 a regression analysis involving 30 observations, the
following estimated regression equation was obtained.
ŷ = 18.9 + 3.2x1 − 2.2x2 +
7.8x3 + 2.9x4
(a)
Interpret
b1
in this estimated regression equation.
b1 = 7.8 is an estimate of the change in
y corresponding to a 1 unit change in
x3 when x1,
x2, and x4 are held
constant.b1 = 3.2 is an estimate of the change
in y corresponding to a 1 unit change in
x1 when x2,...

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...

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