(a) From the scatter plot and a correlation coefficient of 0.9939 we can conclude that there’s a strong, positive, linear relationship between the two variables.
plot(df1$tourist_spending~df1$visitor_count_tho, xlab= "Number of tourists (inthousands", ylab = "Spending (in millions USD)")
cor(df1$tourist_spending,df1$visitor_count_tho)
[1] 0.9939657
(b)
Explanatory: Number of tourists (in thousands).
Response: Total tourism spending (in millions USD).
(c)
Unlike the correlation coefficient, a regression allows us to predict how much revenue will be generated based on the amount visitors. From this, we could also analyze how much each visitor spends on average. This information would be useful to keep track of the growth of that industry and create strategies to attract more tourists.
(d)
The residual plot shows indication of a a non-linear relationship so a simple linear regression is not adequate to model this data. Part of the problem with this data is that each case is measured sequentially over a very long time span (1963 to 2009). So it’s very possible that the data generating process has changed over time, something that isn’t accounted for in this simple model.
plot(lm1$residuals~df1$tourist_spending,ylab="Residuals", xlab="Number of Tourists (in Thousands)")
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
