a.) The relationship between the number of tourists and spending is a strongly positive linear relationship. Given the first chart, a scatter plot with a regression line, one can see that the distance of the residuals is nearly identical to the line if not only a minor distance away. It is also clear that as the number of tourists increases so does the spending.
b.) The explanatory variable is the number of tourists and the response variable is the spending.
c.) We would fit a regression line in order to see the strength of the relationship and to see if we can predict the amount of tourist spending in this scenario based on the number of tourists. Predictive power allows for the country to determine how much to spend on things such as advertising, tourism initiatives, and their hospitality industry. Other economic metrics can also be calculated with said predictive data.
d.) The data does not meet the conditions required for fitting a least squares line:
Linearity: The data follows a linear trend according to the regression line scatter plot, however based on the residual plot there is a nonlinear relationship.
Nearly Normal Residuals: Looking at the histogram one can see that the residuals are approximately normal. Even with a very slight skew the sample size allows for leniency and the assumption of an approximately normal distribution still stands.
Constant Variability: The residual plot shows that the variability is constant around the regression line.
Independent Observations: The observations appear to have a hidden pattern as the observations seem to be related and clustered in specific areas.
a.) Given the downward trend of the scatter plot and regression line, the correlation is negative.
urban_correlation = -sqrt(.28)a.) The data does not meet the conditions required for fitting a least squares line:
Linearity: The data follows a linear trend according to the regression line scatter plot and residual plot.
Nearly Normal Residuals: Looking at the residual plot one can see that the residuals are approximately normal. There also appears to be no strong skew based on the plot.
Constant Variability: The residual plot shows that the variability is constant around the regression line.
Independent Observations: The observations appear to have a pattern as the observations diverge at the same point and follow similar trends.