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 313 families and estimates the following regression: Ŷ= 120.45+1.12X₁ +1.05X2 +1.05X3. 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 = 0, B₂ = 0 vs. H₁: B₁ #0 and/or ß2 0) to be 4.61. The p-value for the test will be (Round your answer to two decimal places.) At the 5% significance level, we will the null hypothesis.
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 313 families and estimates the following regression: Ŷ= 120.45+1.12X₁ +1.05X2 +1.05X3. 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 = 0, B₂ = 0 vs. H₁: B₁ #0 and/or ß2 0) to be 4.61. The p-value for the test will be (Round your answer to two decimal places.) At the 5% significance level, we will the null hypothesis.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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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 313 families and estimates the following
regression:
Ŷ=
120.45+1.12X₁ +1.05X2 +1.05X3.
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 = 0, B₂ = 0 vs. H₁: B₁ #0 and/or ß2 0) to be 4.61.
The p-value for the test will be
(Round your answer to two decimal places.)
At the 5% significance level, we will
the null hypothesis.
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