Use the data set hseinv on canvas to estimate a dynamic regression model where Housing Price Index (price) is a function of up to three lags each of US Population in 1000s (pop) and Annual Real Housing Investments in millions of $ (inv). (a) Convert your data from a data.frame into a ts. (b) Are your time series variance stable? How do vou know? If not. what can you do to make it variance stable? (c) Are your time series stationary? How do you know? If not, how can you make it stationary? (d) What is the optimal number of lags of pop and inv to be used in your regression model? How do you know? (e) Once you've determined the optimal number of lags, estimate an initial ARIMA error for your regression. Are any nearby models a better fit for the data than the initial model? How do you know? (P) Are the residuals of your best model white noise? How do you know? (Note it is possible that you don't find a model that has white noise residuals. If that's the case move forward forecasting your best fitting model.) (g) Forecast your best model 1 year ahead. Use auto.arima() to create forecasts of your predictors first.