1. Consider the mutual fund "AMRMX" and 4 exchange traded funds (ETFs) with the symbols "IWD", "IWF", "IWO", and "VONG". Use the R package "quantmod" (using Yahoo! Finance as the source) to obtain price series from January 3, 2011 to December 29, 2016. (a) (2 pts) Compute the daily log returns of the 5 symbols. Produce a scatter plot and a correlation plot. Interpret the plots. (b) (2 pts) Fit a regression model with AMRMX log returns as the response and the ETFs' log re- turns as predictors. State the value of the coefficients of the regression. Are the coefficients significant under 5% significance level? What is the sample correlation between fitted and ob- served values of AMRMX log returns? (c) (2 pts) Obtain the ANOVA table for the model in part (b), and interpret it. What is the total sum of squares of the model? (d) (2 pts) Do a F-test to see if the coefficients of "IWO" and "VONG" and the intercept are simul- taneously zero. That is, the null hypothesis is Ho : BIwo = PYONG = Bo = 0. (e) (2 pts) If you can only choose one ETF (and the intercept) as the predictor, which one would you choose? What if you can choose 2 predictors? What is the best model with three predictors? You must support your answers using appropriate R outputs