University of Waterloo
Math-Business Program
STAT 371: Statistics for Business 1
Assignment #2
Winter 2013 Dr. H. Fahmy
The Assignment is due on (or before) Friday 15th of February, 2013 in my mailbox or in the
bin
...
University of Waterloo
Math-Business Program
STAT 371: Statistics for Business 1
Assignment #2
Winter 2013 Dr. H. Fahmy
The Assignment is due on (or before) Friday 15th of February, 2013 in my mailbox or in the
bin (labeled STAT 371) next to o¢ ce 2001, M3 building, at 4:00 PM sharp.
Instructions:
Late assignments are not acceptable.
All your answers should be justi…ed. Final answers without any justi…cations are worth zero points.
1. [12] LS Under Restriction. A regression equation is speci…ed as follows
Yt = 1 + 2X2t + 3X3t + ut; t = 1; 2; :::; 30:
Suppose that the following data, measured as deviations from sample means, are available:
X x2 2 = 50; X x2 3 = 10; X y2 = 104
X x2x3 = 20; X yx2 = 40; X yx3 = 10:
(a) [4.5] Estimate 2, 3, their standard errors, and R2: Are 2 and 3 statistically signi…cant?
(b) [1.5] Test the hypothesis that 2 = 3:
(c) [2] Re-estimate the coe¢ cients imposing the restriction that 2 = 3:
(d) [2] Construct con…dence intervals for the restricted coe¢ cients.
(e) [2] Test for the validity of the restriction.
2. [6] Consider the regression model
Yt = 0 + 1X1t + 2X2t + 3X3t + ut; t = 1; 2; :::; n:
Suppose that you have the following sums of squares and products of deviations from means for the
n = 24 observations:
X y2 = 60; X x2 1 = 10; X x2 2 = 30; X x2 3 = 20
X yx1 = 7; X yx2 = 7; X yx3 = 26
X x1x2 = 10; X x1x3 = 5; X x2x3 = 15:
(a) [3] Test each of the following hypotheses
1 = 1; 2 = 1; 3 = 2;
(b) [3] Test the hypothesis that 1 + 2 + 3 = 0: Explain how does this di¤er from the hypothesis
that 1 2 3 = 1 1 2 ? Test the latter hypothesis.
3. [10] Consider the following regression model in deviation form
yt = 1x1t + 2x2t + ut
with sample data
n = 10; X y2 = 493 3 ; X x2 1 = 30; X x2 2 = 3;
X x1y = 30; X x2y = 20; X x1x2 = 0:
[Show More]
