Chapter 15, Problem 7PS

Researchers wanted to investigate the relationship between employment and accommodation capacity in the European travel and tourism industry. The file EuroTourism contains a sample of 27 European countries. Variables included are the number of jobs generated in the travel and tourism industry in 2015 and the number of establishments that provide overnight accommodation for tourists.

a. Construct a scatter plot of the number of jobs generated in the travel and tourism industry in 2015 $\left(Y\right)$ and the number of establishments that provide overnight accommodation for tourists $\left(X\right).$

b. Fit a quadratic regression model to predict the number of jobs generated and state the quadratic regression equation.

c. Predict the mean number of jobs generated in the travel and tourism industry for a country with 3,000 establishments that provide overnight accommodation for tourists.

d. Perform a residual analysis on the results and determine whether the regression model is valid.

e. At The 0.05 level of significance, is there a significant quadratic relationship between the number of jobs generated in the travel and tourism industry in 2015 and the number of establishments that provide overnight accommodation for tourists?

f. What is the p-value in (e)? interpret its meaning.

g. At the 0.05 level of significance, determine whether the quadratic model is a better fit than the linear model.

h. Interpret the meaning of the coefficient of multiple determination.

i Compute the adjusted $r^2.$

j. What conclusions can you reach concerning the relationship between the number of jobs generated in the travel and tourism industry in 2015 and the number of establishments that provide overnight accommodation for tourists?