1. Suppose you wanted to understand the relationship between a customer’s yearly income (X) and the number of movies (Y) the customer watched in a year. You then gather data on incomes and the number of movies watched in a year. The range of incomes in your data set is $5K to $150K. After fitting a simple linear model and performing all the appropriate diagnostics, the model showed that, on average, for every $10K in income, the customer watched 1.5 movies in the year. So, for example, if a customer earned 60K in a year, he or she would be expected to watch nine movies during the year. Now you want to apply this model to your very wealthy friend who will earn $1 million in the next year. Is this an appropriate application of your model? Why or why not? Provide specific examples to justify your opinion.
2. If you regress daily high temperature (Y) on the amount of ice cream sales (X), you will notice that there is a strong positive correlation between the two. In other words, as daily ice cream sales increase, the daily high temperature increases. This implies that if we knew the amount of ice cream sales in a particular day, we could estimate, with a high level of accuracy, the high temperature in that day. Does this mean that if we wanted to increase the daily temperature, we need to sell more ice cream? Explain why or why not?