Economics 2P91 Fall 2022: Practice problems Question 1 Suppose that you have just started your first job as a junior data analyst for the Toronto Maple Leafs hockey club in the National Hockey League (NHL) and your general manager has asked you to describe the relationship between team success and team defensive ability. You have the data on the number of wins and the corresponding number of average shots against for the following five teams in the most recent season: Table 1: Average shots against and wins in 2021-2022 NHL season (a) Use the OLS formulas provided in class to regress the number of wins (Yi) on the correpponding average shots against (Xi). That is, estimate the following regression model: Yi=0+1Xi+ui Report your estimates ^0 and ^1. Show your work. (b) Use the formula provided in class to estimate the sampling variance of the regression coefficient for 1. That is, find 12. (c) Use your estimates to test the following hypothesis: H0:1=0H1:1=0 Based on your result, which conclusions you can (or cannot) draw about the relationship between team wins and defensive ability? (Hint: Compare the absolute value of your calculated t-statistic to the t-critical value of 1.96 (which corresponds to the 5% significance level), can you reject the null hypothesis? What does that tell you?) Economics 2P91 Fall 2022: Practice problems Question 1 Suppose that you have just started your first job as a junior data analyst for the Toronto Maple Leafs hockey club in the National Hockey League (NHL) and your general manager has asked you to describe the relationship between team success and team defensive ability. You have the data on the number of wins and the corresponding number of average shots against for the following five teams in the most recent season: Table 1: Average shots against and wins in 2021-2022 NHL season (a) Use the OLS formulas provided in class to regress the number of wins (Yi) on the correpponding average shots against (Xi). That is, estimate the following regression model: Yi=0+1Xi+ui Report your estimates ^0 and ^1. Show your work. (b) Use the formula provided in class to estimate the sampling variance of the regression coefficient for 1. That is, find 12. (c) Use your estimates to test the following hypothesis: H0:1=0H1:1=0 Based on your result, which conclusions you can (or cannot) draw about the relationship between team wins and defensive ability? (Hint: Compare the absolute value of your calculated t-statistic to the t-critical value of 1.96 (which corresponds to the 5% significance level), can you reject the null hypothesis? What does that tell you?)