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 (X,), the annual income of the family (X,), and the number of times the family went out on an outing in the last year (X). She collects data from 152 families and estimates the following regression: Y = 120.45 + 1.12X, + 1.98X2 + 1.98X3. Suppose B1, B2. B3, denote the population slope coefficients of X,, X2, and X3, respectively. The researcher wants to check if neither X, nor X, have a significant effect on Y or at least one of them has a significant effect, keeping X, constant. She calculates the value of the F-statistic for the test with the two restrictions (Ho: B, =0, B, = 0 vs. H,: B, #0 and/ or B, #0) to be 2.30. The p-value for the test will be . (Round your answer to two decimal places.) At the 1% significance level, we will V 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 (X,), the annual income of the family (X,), and the number of times the family went out on an outing in the last year (X). She collects data from 152 families and estimates the following regression: Y = 120.45 + 1.12X, + 1.98X2 + 1.98X3. Suppose B1, B2. B3, denote the population slope coefficients of X,, X2, and X3, respectively. The researcher wants to check if neither X, nor X, have a significant effect on Y or at least one of them has a significant effect, keeping X, constant. She calculates the value of the F-statistic for the test with the two restrictions (Ho: B, =0, B, = 0 vs. H,: B, #0 and/ or B, #0) to be 2.30. The p-value for the test will be . (Round your answer to two decimal places.) At the 1% significance level, we will V the null hypothesis.
Chapter4: Linear Functions
Section4.3: Fitting Linear Models To Data
Problem 34SE: For the following exercises, consider this scenario: The profit of a company decreased steadily...
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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 (X, ), the annual income of the family (X,), and the number of times the family went out on an outing in the last year (Xa). She collects
data from 152 families and estimates the following regression:
Y= 120.45+ 1.12X, + 1.98X2 + 1.98X3.
Suppose B1, B2, B3, denote the population slope coefficients of X1, X2, and X3, respectively.
The researcher wants to check if neither X, nor X, have a significant effect on Y or at least one of them has a significant effect, keeping X, constant. She calculates
the value of the F-statistic for the test with the two restrictions (Ho: B, =0, B, = 0 vs. H, : B, #0 and/or B, #0) to be 2.30.
The p-value for the test will be.
(Round your answer to two decimal places.)
At the 1% significance level, we will
V the null hypothesis.
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