Identify any errors within the above testing approach and write out the hypothesis test correcting these errors so that the test appropriately tests the hypothesis. You should explain each of the errors you have corrected in a separate sentence.
Identify any errors within the above testing approach and write out the hypothesis test correcting these errors so that the test appropriately tests the hypothesis. You should explain each of the errors you have corrected in a separate sentence.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Identify any errors within the above testing approach and write out the hypothesis
test correcting these errors so that the test appropriately tests the hypothesis. You
should explain each of the errors you have corrected in a separate sentence.
Transcribed Image Text:1. (a) Consider the following output from a regression in R
Call:
1m (formula = Y X + Z + W)
Residuals:
Min
10 Median
3Q
-1.84572 -0.47207 -0.01262 0.54948 2.62708
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.32540 2.63484 1.262 0.219
0.52183 8.554 9.45e-09 ***
4.46385
-2.45113
0.05868 -41.771
<2e-16 ***
10.97813
0.02063 532.116
<2e-16 ***
X
Z
W
Signif. codes: 0 *** 0.001 ** 0.01 0.05. 0.11
Residual standard error: 1.031 on 24 degrees of freedom
Multiple R-squared: 0.9999, Adjusted R-squared: 0.9999
F-statistic: 9.441e+04 on 3 and 24 DF, p-value: < 2.2e-16
In the notes below somebody has attempted to test, at a 5% significance level, the
hypothesis that the parameter on the variable Z, in the above regression, is equal
to -2. (Note 8z is the parameter on Z in this model.)
Hypothesis Test Notes
Max
Hence we use a t statistic where
t=
Ho: 8z = -2
3z - 2
s.e.(3z)
t=
~t
At the 5% significance level and n = 28, the critical value is 1.701 and hence we
reject the null if t > 1.701. Hence we use a t statistic where, under Ho.
-2.45-2
0.522
As -8.531.701 then we can conclude the null hypothesis is true.
=-8.53
01
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