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Suppose pitcher A and pitcher D had major problems this offseason and your GM says they are definitely off the table (i.e., they will not be acquired under any circumstances).  Which of the following is definitely true? You may select more than one. Hint: I do NOT want you to solve this new linear program.  Just state what happens by adding these new constraints.

According to Draftkings Sportsbook odds, Kyle McCord is +1500 to win the Heisman next year.  What is the implied probability he wins?   Report your answer as a decimal to 4 places.

Run the following linear regression was run to predict Wins in the MLB from 2015-2022 (minus 2020) based on the following statistics: OPS: On-base percentage + Slugging percentage WHIP: Walks + hits given up per inning pitched (You can copy this code directly into your R session–and should have done so prior to the quiz) teams15_22 %filter(yearID >= 2015, yearID !=2020) %>%mutate(OBP = (H + BB + HBP)/(AB + BB + HBP + SF), SLG = (H + X2B + 2 * X3B + 3 * HR)/AB,OPS = OBP + SLG,WHIP = (BBA + HA)/(IPouts/3)) The standard deviations of OPS and WHIP are 0.037 and 0.096 respectively. If I could take an average team in OPS and WHIP to the 84th percentile (one standard deviation above or below average—since low WHIP is better) in one (and only one) of the two statistics, which would I prefer? (i.e., would I get more wins by increasing OPS by one standard deviation or decreasing WHIP by one standard deviation?)—Check Mathletics Ch. 18 (This isn’t as hard as you may think!) First, how many additional wins would I expect to get if I increased my team OPS by 1 standard deviation? Report your answer to 2 decimal places.

Using the output, give the PROBABILITY (not the logit probability) that Joe Burrow makes the Pro Bowl if he starts for 2 more years (5 total years starting) and continues his current stats of 1.95 Pass TD/game, 0.74 Int/game, 0.24 Rush TD/game, Comp%=0.682. Recall he was the 1st overall pick and was 24 years old at the draft. Use all variables regardless of their significance in question 7.  Enter your answer as a decimal to 2 places.  i.e., 26% = .26

How would you write constraint 4?

The traditional Pythagorean developed by Bill James used an exponent of 2 for baseball and we’ll use this exponent. In the 2023 season, the Reds scored 783 runs and allowed 821 runs.  Let’s assume the lineup as constructed would repeat this output next year. Suppose the Reds had their choice of 2 players: 1) Cody Bellinger: accounted for 15 more runs than an average player due to his batting and baserunning and PREVENTED opponents from scoring 7 more run than an average fielder would have (i.e., he increases runs scored by 15 and DECREASES runs allowed by 7) 2) Blake Snell: allowed 20 fewer runs than an average pitcher and has no effect on the batting as the pitcher spot doesn’t hit.   What would the Pythagorean predict as the win% for the Reds if they replace an average player with Snell? Report your answer as a decimal to 4 places: i.e., 20.34% should be entered as .2034

Run the following linear regression was run to predict Wins in the MLB from 2015-2022 (minus 2020) based on the following statistics: OPS: On-base percentage + Slugging percentage WHIP: Walks + hits given up per inning pitched (You can copy this code directly into your R session–and should have done so prior to the quiz) teams15_22 %filter(yearID >= 2015, yearID !=2020) %>%mutate(OBP = (H + BB + HBP)/(AB + BB + HBP + SF), SLG = (H + X2B + 2 * X3B + 3 * HR)/AB,OPS = OBP + SLG,WHIP = (BBA + HA)/(IPouts/3)) The standard deviations of OPS and WHIP are 0.037 and 0.096 respectively. If I could take an average team in OPS and WHIP to the 84th percentile (one standard deviation above or below average—since low WHIP is better) in one (and only one) of the two statistics, which would I prefer? (i.e., would I get more wins by increasing OPS by one standard deviation or decreasing WHIP by one standard deviation?)—Check Mathletics Ch. 18 (This isn’t as hard as you may think!) Next, how many additional wins would I expect to get if I decreased my team WHIP by 1 standard deviation? Report your answer to 2 decimal places.  

In the metric system, which of the following units is the base unit for distance?

MRI gives much greater detail on a hemorrhagic stroke than CT. 

The first-generation CT scanners took only a few minutes to complete a scan.