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In a study of the determinants of household expenditures on vacation travel, data were obtained from a sample of 2226 households. The model estimated is shown below, with R² = 0.187. The numbers in parentheses under the coefficients are the estimated coefficient standard errors. Complete parts a through d. log y = - 4.061 +1.1532 log x₁ -0.4416 log x₂ y = expenditure on vacation travel x₁ = total annual consumption expenditure X₂ = number of members in household (0.0527) (0.0453) Click the icon to view a table of critical values for the Student's t-distribution. increase in the log of total consumption expenditures and log of the number of members in the household. B. The coefficient of determination, 0.187, is the percentage in vacation travel expenditures that can be explained by the variations in the log of total consumption expenditures and log of the number of members in the household. C. The coefficient of determination, 0.187, is the percentage in vacation travel expenditures that cannot be explained by the variations in the log of total consumption expenditures and log of the number of members in

In a study of the determinants of household expenditures on vacation travel, data were obtained from a sample of 2226 households. The model estimated is shown below, with R² = 0.187. The numbers in parentheses under the coefficients are the estimated coefficient standard errors. Complete parts a through d. log y = - 4.061 +1.1532 log x₁ -0.4416 log x₂ y = expenditure on vacation travel x₁ = total annual consumption expenditure X₂ = number of members in household (0.0527) (0.0453) Click the icon to view a table of critical values for the Student's t-distribution. increase in the log of total consumption expenditures and log of the number of members in the household. B. The coefficient of determination, 0.187, is the percentage in vacation travel expenditures that can be explained by the variations in the log of total consumption expenditures and log of the number of members in the household. C. The coefficient of determination, 0.187, is the percentage in vacation travel expenditures that cannot be explained by the variations in the log of total consumption expenditures and log of the number of members in

MATLAB: An Introduction with Applications
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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ANSWER C IN THE PICTURE AND D FROM THE PASTED TEXT. THE BELOW TEXT IS AN EXAMPLE QUESTION JUST ANSWER THE QUESTION BUT USE INFORMATION FROM THE PICTURE PROVIDED
d. Assuming that the model is correctly​ specified, test, at the​ 1% significance​ level, the null hypothesis​ that, all else being​ equal, the number of members in a household does not affect expenditures on vacation travel against the alternative that the greater the number of household​ members, the lower the vacation travel expenditures.
 
This is a hypothesis test for the regression coefficients.
Part 13
The null and alternative hypotheses are shown below.
 
H0​:
β2=0
H1​:
β2<0
Part 14
Find
tn−K−1,α=t2195,0.01​,
the critical value with an area of 0.01 in the​ upper-tail of the t distribution with
2195
degrees of freedom. Use​ technology, rounding to two decimal places.
 
t2195,0.01=−2.33
Part 15
The test statistic shown below approximately follows a t distribution with
n−K−1
degrees of​ freedom, where n is the number of data points and K is the number of independent variables used in the regression​ analysis,
bj
is the​ least-squares estimate of the coefficient
βj​,
β*
is the hypothesized value of the​ coefficient, and
sbj
is the standard error of the estimate
bj.
 
t=bj−β*sbj
Part 16
Substitute the values
b2=−0.4367
and
sb2=0.0499
calculate the value of​ t, rounding to two decimal places.
 
−0.43670.0499=−8.75
Part 17
Since the alternative hypothesis is
β2<0​,
the decision rule is to reject
H0
if the value of the test​ statistic, t, is less than the critical value
−tν,α.
​Otherwise, there is insufficient evidence to reject the null hypothesis.
In a study of the determinants of household expenditures on vacation travel, data were obtained from a sample of 2226 households. The model estimated is shown below, with R² = 0.187. The numbers in parentheses under the coefficients are the estimated coefficient standard errors. Complete parts a through d. log y = - 4.061 + 1.1532 log x₁ -0.4416 log x₂ y = expenditure on vacation travel x₁ = total annual consumption expenditure X₂ = number of members in household (0.0527) (0.0453) Click the icon to view a table of critical values for the Student's t-distribution. increase in the log of total consumption expenditures and log of the number of members in the household. B. The coefficient of determination, 0.187, is the percentage in vacation travel expenditures that can be explained by the variations in the log of total consumption expenditures and log of the number of members in the household. C. The coefficient of determination, 0.187, is the percentage in vacation travel expenditures that cannot be explained by the variations in the log of total consumption expenditures and log of the number of members in the household. c. All else being equal, find a 95% confidence interval for the percentage increase in expenditures on vacation travel resulting from a 1% increase in total annual consumption expenditures. (Round to three decimal places as needed.)
Transcribed Image Text:In a study of the determinants of household expenditures on vacation travel, data were obtained from a sample of 2226 households. The model estimated is shown below, with R² = 0.187. The numbers in parentheses under the coefficients are the estimated coefficient standard errors. Complete parts a through d. log y = - 4.061 + 1.1532 log x₁ -0.4416 log x₂ y = expenditure on vacation travel x₁ = total annual consumption expenditure X₂ = number of members in household (0.0527) (0.0453) Click the icon to view a table of critical values for the Student's t-distribution. increase in the log of total consumption expenditures and log of the number of members in the household. B. The coefficient of determination, 0.187, is the percentage in vacation travel expenditures that can be explained by the variations in the log of total consumption expenditures and log of the number of members in the household. C. The coefficient of determination, 0.187, is the percentage in vacation travel expenditures that cannot be explained by the variations in the log of total consumption expenditures and log of the number of members in the household. c. All else being equal, find a 95% confidence interval for the percentage increase in expenditures on vacation travel resulting from a 1% increase in total annual consumption expenditures. (Round to three decimal places as needed.)
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