Question

Question: Novelty of a vacation destination. Many tourists choose a vacation destination based on the newness or uniqueness (i.e., the novelty) of the itinerary. The relationship between novelty and vacationing golfers’ demographics was investigated in the Annals of Tourism Research (Vol. 29, 2002). Data were obtained from a mail survey of 393 golf vacationers to a large coastal resort in the south-eastern United States. Several measures of novelty level (on a numerical scale) were obtained for each vacationer, including “change from routine,” “thrill,” “boredom-alleviation,” and “surprise.” The researcher employed four independent variables in a regression model to predict each of the novelty measures. The independent variables were x₁ = number of rounds of golf per year, x₂ = total number of golf vacations taken, x₃ = number of years played golf, and x₄ = average golf score.

1. Give the hypothesized equation of a first-order model for y = change from routine.

1. A test of H₀: β₃ = 0 versus H_a: β₃< 0 yielded a p-value of .005. Interpret this result if α = .01.

1. The estimate of β₃ was found to be negative. Based on this result (and the result of part b), the researcher concluded that “those who have played golf for more years are less apt to seek change from their normal routine in their golf vacations.” Do you agree with this statement? Explain.

1. The regression results for three dependent novelty measures, based on data collected for n = 393 golf vacationers, are summarized in the table below. Give the null hypothesis for testing the overall adequacy of the first-order regression model.

1. Give the rejection region for the test, part d, for α = .01.

1. Use the test statistics reported in the table and the rejection region from part e to conduct the test for each of the dependent measures of novelty.

1. Verify that the p-values reported in the table support your conclusions in part f.

1. Interpret the values of R² reported in the table.

Short answer

(A) First-order model equation for y = change of routine can be written as $y={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+{\beta }_3{x}_3+{\beta }_4{x}_4+\epsilon$.

(B) p-values for testing$H_0:{\beta }_3=0$, and $H_a:{\beta }_3<0$ is 0.005 then for α = 0.01, we reject the H₀ since p-value < α.

(C) ${\beta }_3$ value is negative indicating inverse relationship between dependent and independent variable and the hypothesis testing done in part b indicates is statistically significant. Therefore, the researcher’s conclusion that “those who have played golf for more years are less apt to seek change from their normal routine in their golf vacations” is true.

(D) The null hypothesis for testing the overall adequacy of the first-order regression model can be written as $s{H}_0:{\beta }_1={\beta }_2={\beta }_3={\beta }_4=0$.

(E) The rejection region for the test for overall adequacy is $H_{0}isrejectedifFstatistic>F_{(}\alpha ,n-1,n-k)$

(F) For each one of the dependent measures of novelty, the F-test concluded that there is not sufficient evidence to reject H₀.

(G) For thrill the p-value is less than 0.001, for change from routine the p-value is 0.018 and for surprise, p-value is 0.011. Each of these values are less than α (α = 0.05) meaning that the H₀ will be rejected. This was also the conclusion drawn in part f.

(H) R² values for thrill, change in routine and surprise are 0.055, 0.030, and 0.23 respectively. These values are very low. A model is said to be a good fit for the data if the R²value is higher. Such low value of 5, 3, and 2% indicate that the model fitted is not the ideal and good fit for the data.

Step-by-step solution

Step-by-Step SolutionStep 1: First order model equation

First-order model equation for y = change of routine can be written as$y={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+{\beta }_3{x}_3+{\beta }_4{x}_4+\epsilon$

Hypothesis testing

p-values for testing,and is 0.005 then for α = 0.01, we reject the H₀ since p-value < α.

Step 3: value interpretation

${\beta }_3$value is negative indicating inverse relationship between dependent and independent variable and the hypothesis testing done in part b indicates is statistically significant. Therefore, the researcher’s conclusion that “those who have played golf for more years are less apt to seek change from their normal routine in their golf vacations” is true.

Null hypothesis

The null hypothesis for testing the overall adequacy of the first-order regression model can be written as$H_0:{\beta }_1={\beta }_2={\beta }_3={\beta }_4=0$ .

Rejection region

The rejection region for the test for overall adequacy is$H_{0}isrejectedifFstatistic>F_{(}\alpha ,n-1,n-k)$

Hypothesis testing 

Step 7: Pvalues interpretation

For thrill the p-value is less than 0.001, for change from routine the p-value is 0.018 and for surprise, p-value is 0.011. Each of these values are less than α (α = 0.05) meaning that the H₀ will be rejected.

This was also the conclusion drawn in part f.

R2 interpretation

R² values for thrill, change in routine and surprise are 0.055, 0.030, and 0.23 respectively. These values are very low. A model is said to be a good fit for the data if the R²value is higher. Such low value of 5, 3, and 2% indicate that the model fitted is not the ideal and good fit for the data.