8.21 Tourism spending.

The Association of Turkish Travel Agencies reports the number of foreign tourists visiting Turkey and tourist spending by year.14 Three plots are provided: scatterplot showing the relationship between these two variables along with the least squares fit, residuals plot, and histogram of residuals.

8.21 graphic

8.21 graphic

(a) Describe the relationship between number of tourists and spending.

There is a strong, positive, and linear relationship between number of tourists and spending.

(b) What are the explanatory and response variables?

The explanatory variable is the number of tourists and the response variable is the spending.

(c) Why might we want to fit a regression line to these data?

We would fit a regression line ot this data in order to predict the amount of spending a certain number of tourists would predict.This will impact a country planning for things such as sales tax revenue that can be estimated if you know roughly how many tourists you will be having.

(d) Do the data meet the conditions required for fitting a least squares line? In addition to the scatterplot, use the residual plot and histogram to answer this question.

The conditions for the least squares line are: Linearity, nearly normal residuals, constant variability, and Independent observations

The data does not meet the conditions redquired for fitting a least squares line. We can see based on the residual plot that they are not linear along the dotted line. You can also see based on both graphs that the variability is not constant. In the histogram you can see that the residuals do not have even variablity. In the plot the variablity increases as the explanatory variable increases, which is the most common pattern observed when the condition fails. Finally, the observations are taken year after year. Time-series data such as this often have an underlying structure that should be considered when modeled.