The following questions refer to data on the Zillow Home Value Index of homes in the United States, the dataset is provided on Blackboard in csv format (HomeValues.csv). The data is sourced from Zillow.com (https://www.zillow.com/research/data/). 1. For each of the following 4 variables: Zillow Home Value Index (Zhvi), Peak Zillow Home Value Index (PeakZHVI), Month-on-Month Growth (MoM) and Year-on-Year Growth (YoY): - construct a histogram - calculate descriptive statistics (use the describe command from the psych package) - construct a boxplot - calculate the five number summary (min, 1st quartile, median, 3rd quartile, max) Write a sentence or two about each of the 4 variables, for each variable discuss its distribution including: shape, measures of spread, measures of center and outliers or unusual values. 2. Next you will explore the relationships between the 4 variables you looked at in Question 1: - Zhvi and Peak ZHVI - Zhvi and MoM - MoM and YoY For each of the 3 pairs of variables listed above: - construct a scatterplot - calculate the correlation coefficient r Write a sentence or two about each of the 3 pairs of variables, for each pair discuss the relationship including: form, direction and strength. Also discuss any outliers or unusual values. 3. Use least squares regression to fit a linear model that has YoY as the Response Variable and MoM as the Explanatory Variable. For your linear model: - report the slope and the y-intercept - report the coefficient of determination r^2 and describe what it tells you - construct a scatterplot that includes the regression line Then repeat what you did above but this time fit a linear model that has PeakZHVI as the Response Variable and Zhvi as the Explanatory Variable. BUS309 Statistics for Business and Economics I Fall 2018 Dr. James P. Minas 4. To explore the distribution of the residuals for your linear model of YoY vs MoM: - construct a residual plot - construct a Normal quantile plot for residuals Discuss whether you believe a linear (straight line) model is a good fit for this data, if not what form of model might fit better? In answering this refer to the two plots above and the scatterplot with the regression line from Question 3. Then repeat what you did above for your linear model of PeakZHVI vs Zhvi. 5. Use your first linear model to predict the YoY for a vehicle that has: MoM = 0.004 MoM = 0.015 Use your second linear model to predict the PeakZHVI for a vehicle that has: Zhvi = 300000 (this is the same as 3e+05) Zhvi = 900000 (this is the same as 9e+05) As well as reporting your four predictions, discuss how confident you are in each prediction and why, in answering this refer to the: scatterplot with the regression line, residual plot and Normal quantile plot for residuals.