In the United States, baseball has always been a favorite pastime and is rife with statistics and theories. Researchers have shown that major league players who have nicknames live longer than those without them. The following table shows a portion of data on the lifespan (Years) of a player and a Nickname variable (Yes if the player had a nickname, No otherwise). Years Nickname 69 No 62 Yes 64 No 76 No 65 Yes 65 No 75 Yes 64 Yes 67 Yes 79 No 67 Yes 60 No 51 No 75 No 63 No 68 Yes 55 No 66 Yes 64 No 71 Yes 50 Yes 77 No 63 Yes 58 No 60 No 62 Yes 60 No 68 Yes 64 Yes 66 Yes a. Create two subsets, one consisting of players with a nickname and the other one without a nickname. Calculate the average longevity for each subset. (Round your answers to 2 decimal places.) Players with a nickname- (mean years Players without a nickname- (mean years) b-1. Estimate a linear regression model of year on a dummy variables d with value 1 if the player had a nickname, 0 otherwise. Hint: You have to first convert the Nickname categorical variable (Yes/No) into a dummy variable (1/0). (Round coefficient estimates to 4 decimal places) b-2. Compute the predicted longevity of players with and without a nickname. (Round coefficient estimates to at least 4 decimal places and final answers to 2 decimal places.).