Using the gapminder data, looking at only data from the Americas, fit a linear regression to predict population as a function of year and country. Calculate predicted values for years ranging from 1950 to 2025, in intervals of five years. Include a 95% prediction interval. Plot your predictions for two countries of your choosing. In addition, create a plot of the residuals versus the fitted values. What does this plot tell you about the reasonableness of using a linear model here?