Question

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

b₀ = -10      b₁ = 4.5     b₂ = -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 + 6X₁ -- 3 X₂

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 X₂ increases by 1 unit, Y increases by 3 units.

b.    Y is more strongly correlated with X₂ than with X₁ because the coefficient of X₂   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, X₁ be the age of the car in years; and X₂ 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 = b₀ + b₁ L + b₂ 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

            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 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 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. (6 pts)

b.    Is there evidence of a linear relationship between X₂   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!