Consider lnY = B₁ + B₂X₂ + B₃X₃ + B₄*X₄ + u . The result of this regression is

B: (beta)

ln^Y = 3 + 5.3X₂ - 2X₃ + 5X₄

s.e (0.2) (0.02) (0.74) (2)

a) Suppose the null hypothesis is H₀ : B₄ = 1 . Which test do you use? Calculate the statistic value for the test by using numbers.
b) Suppose you want to do the overall significance test. What is the null hypothesis? Which test do you use in this case?

c) What is the general formula for (b) (specifically for the overall significant test)?

d) Show the formula obtained in (c) in terms of R^₂.

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Beverley SmithLv2

16 Feb 2019

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Problem 1.

You are conducting a study on the price of houses in Los Angeles county, and studied data from n= 25 houses. Let the following variables denote your observations:

y^ = price of a house in thousands of dollars

x1= square footage

x2= distance in miles to nearest grocery store

x3 = a dummy variable that equals 1 if the house is in the top 50 state-

ranked school district and 0 otherwise.

x4= a dummy variable that equals 1 if the house is in Beverly Hills or Malibu

and 0 otherwise.

A) What do you predict would be the sign of each coefficient (bi) in the regression line? Briefly explain each.

B) Suppose b1=. 17 interpret the coefficient.

C) Suppose b4= 244.32. Interpret the coefficient

D) Suppose you run a restricted regression using x1, x2, and x4 yields R2 =

857. Furthermore, suppose the complete regression using x1, x2, x3 and x4 yields R2 = .772.

Which model do you think is better to use? Why?

E) Interpret R2 and R2 of the complete regression?

F) Why might the interaction term x1*x4 be useful to include in your

regression?

Thanks for your time

TABLE 22


Year	PIX	HDI	Gas
1	53.8	1,638.3	98185
2	56.9	1,825.3	124228
3	60.6	2,030.9	151907
4	65.2	2,294.7	176002
5	72.6	2,563.3	212007
6	82.4	2,789.5	249750
7	90.9	3,128.4	265067
8	96.5	3,255.0	247642
9	99.6	3,536.7	268901
10	103.9	3,933.2	332418
11	107.6	4,220.3	338088
12	109.6	4,462.8	368425
13	113.6	4,739.5	409765
14	118.3	5,103.8	447189
15	124.0	5,484.4	477665
16	130.7	5,803.1	498438
17	136.2	5,995.9	491020
18	140.3	6,337.7	536528
19	144.5	6,657.4	589394
20	148.2	7,072.2	668690
21	152.4	7,397.7	749374
22	156.9	7,816.9	803113
23	160.5	8,304.3	876470
24	163.0	8,747.0	917103
25	166.6	9,268.4	1029980
26	172.2	9,817.0	1224408
27	177.1	10,128.0	1145900
28	179.9	10,469.6	1164720
29	184.0	10,960.8	1260717
30	188.9	11,712.5	1472926
31	195.3	12,455.8	1677371

Refer to table 22 which gives data on Gas, HDI, and PIX for Iraq. Consider the following log-log model:

lnImports = B1 + B2 lnGDP + B3 lnCPI + u

***********************please use "SAS format" ************************* (where/if possible)

1) Estimate the parameters using the data given in the table 22.

2) Do you suspect that there is multicollinearity in the data? Why or why not?

3) Regress:

(a) ln GAS = A1 + A2 ln(HDI)

(b) ln GAS = B1 + B2 ln(PIX)

On the basis of these regressions, what could you say about the nature of multicollinearity in the data?

4) Suppose there is multicollinearity in the data but B2 and B3 are individually significant at the 5% level and the overall F test is also significant. In this case should we worry about the collinearity problem?