Virtual Reality #2

1)

Arizona Lumber Company uses the number of construction permits issued to help forecast its sales. 
The firm collected the data in the following diagram (which is presented as a SORITEC screen dump) 
on annual sales (in millions of dollars) and the number of construction permits issued in its 
market area (in thousands)


1981 . 5.15000 3.25000
1982 . 5.05000 3.10000
1983 . 5.25000 3.30000
1984 . 5.40000 3.65000
1985 . 5.60000 3.90000
1986 . 5.70000 4.10000
1987 . 5.65000 4.15000

REGRESS : dependent variable is SALES

Using 1981 - 1987

Variable | Coefficient | Std Err | T-stat | Signf

 --------|------------|----------|----------|------ 

   ^CONST | -5.20679 | .616404 | -8.44704 | .000 

    PERMITS | 1.63750 | .114037 | 14.3594 | .000

No. of Observations = 7 R2= .9763 (adj)= .9716
Sum of Sq. Resid. = .260089E-01 Std. Error of Reg.= .721234E-01
Log(likelihood) = 9.65072 Durbin-Watson = 2.00127
Schwarz Criterion = 7.70481 F ( 1, 5) = 206.191
Akaike Criterion = 7.65072 Significance = .000030

What is the equation of the estimated least squares regression?

Sales = .616404 + .114037 (Permits)
Permits = -5.20679 + 1.63750 (Sales)
Sales = -5.20679 + 1.63750 (Permits)
Permits = .616404 + .114037 (Sales)


2)

Test the hypothesis that there is no relationship between the dependent and independent variable (at the 95 percent confidence level) in the Arizona Lumber Company Regression. Your results indicate that

you would accept the null hypothesis and conclude that the two variables are related
you would reject the null hypothesis and conclude that the two variables are related
you would accept the null hypothesis and conclude that the two variables are not related
you would reject the null hypothesis and conclude that the two variables are not related


3)

The coefficient of determination for this Arizona Lumber Company regression indicates that

97.63 percent of the variation in sales is explained by variation in permits
t97.63 percent of the variation in permits is explained by variation in sales
.114037 of the error is due to variation in permits
the dependent variable is significant


4)

Suppose that 6,300 construction permits are expected to be issued in 19x8. What would be the point estimate of Arizona Lumber Company's sales for 19x8?

$ 4.62 million
$ 4.95 million
$ 4.99 million
$ 5.11 million

5)

What would be the 95 percent confidence interval for the Arizona Lumber Company estimate in the previous question?

t$ 4.97 to $ 5.25 million
$ 3.68 to $ 6.49 million
$ 4.67 to $ 5.45 million
$ 2.77 to $ 6.19 million

6)

An equation is estimated as:

Q = 400 - 2.0P + .015I -.17Px

.
(250) (1.0) (.010) (.10)

(standard errors are in parentheses)

The most statistically significant coefficient is the constant term.
The most significant coefficient is of P.
The most significant coefficient is of I.
The most significant coefficient is of Px.

7)

The statistic used to test whether the independent variables taken as group statistically explain variation in the dependent variable is the

R-squared statistic.
t-statistic.
Durbin-Watson statistic.
F-test statistic.

8)

Serial correlation occurs when

independent variables are correlated across observations.
dependent variables are correlated across observations.
error terms are correlated across observations.
R-squared is near one and the t-statistics are near zero.

9)

The statistic that tests an individual coefficient for statistical significance is the

R-squared statistic.
t-statistic.
Durbin-Watson statistic.
F-test statistic.

10)

Multiple regression differs from simple regression in that

there can be multiple dependent variables.
the time periods over which observations are taken are multiplied to increase explanatory power.
a simple regression is done multiple times to increase explanatory power.
there are multiple independent variables.

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