A researcher is interested in finding out the factors which determined the yearly spending on family outings last year (Y, measured in dollars). She compiles data on the number of members in a family (X₁), the annual income of the family (X₂), and the number of times the family went out on an outing in the last year (X3). She collects data from 196 families and estimates the following regression: =120.45 +1.54X₁ +2.12X₂ +2.12X3. Suppose B₁, B₂, B3, denote the population slope coefficients of X₁, X₂, and X3, respectively. The researcher wants to check if neither X₁ nor X₂ have a significant effect on Y or at least one of them has a significant effect, keeping X3 constant. She calculates the value of the F-statistic for the test with the two restrictions (Ho: B₁ = 0₁ B₂ = 0 vs. H₁: B₁ #0 and/or B₂ ‡0) to be 3.00. The p-value for the test will be (Round your answer to two decimal places.)
A researcher is interested in finding out the factors which determined the yearly spending on family outings last year (Y, measured in dollars). She compiles data on the number of members in a family (X₁), the annual income of the family (X₂), and the number of times the family went out on an outing in the last year (X3). She collects data from 196 families and estimates the following regression: =120.45 +1.54X₁ +2.12X₂ +2.12X3. Suppose B₁, B₂, B3, denote the population slope coefficients of X₁, X₂, and X3, respectively. The researcher wants to check if neither X₁ nor X₂ have a significant effect on Y or at least one of them has a significant effect, keeping X3 constant. She calculates the value of the F-statistic for the test with the two restrictions (Ho: B₁ = 0₁ B₂ = 0 vs. H₁: B₁ #0 and/or B₂ ‡0) to be 3.00. The p-value for the test will be (Round your answer to two decimal places.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
A researcher is interested in finding out the factors which determined the yearly spending on family outings last year
(Y,
measured in dollars). She compiles data on the number of members in a family
(X1),
the annual income of the family
(X2),
and the number of times the family went out on an outing in the last year
(X3).
She collects data from
196
families and estimates the following regression:Y=120.45+1.54X1+2.12X2+2.12X3.
Suppose
β1,
β2,
β3,
denote the population slope coefficients of
X1,
X2,
and
X3,
respectively.The researcher wants to check if neither
X1
nor
X2
have a significant effect on Y or at least one of them has a significant effect, keeping
X3
constant. She calculates the value of the
F-statistic
for the test with the two restrictions
(H0: β1=0, β2=0 vs. H1: β1≠0 and/or β2≠0)
to be
3.00.
The
p-value
for the test will be
enter your response here?
Transcribed Image Text:A researcher is interested in finding out the factors which determined the yearly spending on
family outings last year (Y, measured in dollars). She compiles data on the number of members
in a family (X₁), the annual income of the family (X₂), and the number of times the family went
out on an outing in the last year (X3). She collects data from 196 families and estimates the
following regression:
Y=120.45 +1.54X₁ +2.12X₂ +2.12X3.
Suppose B₁, B₂, B3, denote the population slope coefficients of X₁, X₂, and X3, respectively.
The researcher wants to check if neither X₁ nor X₂ have a significant effect on Y or at least one
of them has a significant effect, keeping X3 constant. She calculates the value of the F-statistic
for the test with the two restrictions (H: B₁ = 0, B₂ = 0 vs. H₁: B₁ ‡0 and/or ₂ #0) to be 3.00.
The p-value for the test will be
(Round your answer to two decimal places.)
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