08 - Linear Regression - Suggested Exercises MBAA-515, Fall 2020 Jesus A. Sierra J. Questions The following table, Table 1, includes the daily returns of Royal Bank of Canada (RY), Shopify (SHOP) and the Toronto Stock Exchange (TSX). Refer to this table to answer the questions below. # # date ry shop tsx ## 1 2020-10-19 -0. 0123 -0.0072 -0.0100 ## 2 2020-10-20 -0. 0025 -0. 0064 0. 0000 # # 3 2020-10-21 0. 0086 -0. 0340 -0. 0026 ## 4 2020-10-22 0. 0064 -0. 0144 0. 0030 # # 5 2020-10-23 0.0002 0. 0200 0. 0015 ## 6 2020-10-26 -0. 0186 0. 0156 -0.0138 # # 7 2020-10-27 -0. 0168 0. 0371 -0.0037 # # 8 2020-10-28 -0.0185 -0. 0396 -0. 0271 ## 9 2020-10-29 0. 0186 -0. 0498 0. 0054 ## 10 2020-10-30 0. 0029 -0. 0526 -0. 0057 1. Estimate the covariance and correlation coefficient between the returns of Royal Bank of Canada (RY) and the Toronto Stock Exchange (TSX). 2. The table below shows the mean annual percentage return on capital (profitability) and the mean annual percentage sales growth for eight aerospace and defense companies. Calculate the intercept and slope coefficients in a linear regression of profitability on growth. Can we conclude that the relationship between profitability and growth is non-zero? company profitability growth Alliant Techsystems 23.10 8.00 Boeing 13.20 15.60 General Dynamics 24.20 31.20 Honeywell 11.10 2.50 L-3 Communications 10.10 35.40 Northrop Grunmman 10.80 6.00 Rockwell Collins 27.30 8.70 United Technologies 20.10 3.20## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## 3. A dog trainer is studying the relationship between kilometers traveled (km) and daily food consumption (measured in cups). Below is the result of a sample of 18 observations. Estimate a linear regression of km on cups. How much does each additional cup change the estimated distance traveled of the dog? km cups 1 41 3 2 148 8 3 79 5 4 41 4 5 85 5 6 111 6 7 37 3 8 111 6 9 41 3 10 91 5 11 109 6 12 207 10 13 49 3 14 113 6 15 84 5 16 95 5 17 57 4 18 168 9 4. Estimate a market model using linear regression with the data in Table 1 on the returns of Royal Bank of Canada (RY) and the Toronto Stock Exchange (TSX) as the \"market portfolio\". Can we conclude that BBC has a beta coefcient on the market equal to 1? Also, what percentage of the variation in RY is explained by TSX? 5. Using the returns of Shopify (SHOP) and the Toronto Stock Exchange (TSX)7 estimate a market model and predict the return on SHOP when the return of the market is 5%