Brandon works as a statistician for the Toronto Blue Jays, and wants to analyze the relationship between a pitcher's age and how many strikeouts they accumulate in a season. He takes a sample of 7 Blue Jays pitchers with ages between 25 and 34 and finds there is a linear relationship between their ages and the number of strikeouts they had in the 2015 season. Here are the numerical summaries for age and the number of strikeouts:
$r = 0.62$, $\bar{age} = 28.8$, $s_{age} = 3.96$, $\bar{strikeout} = 102.7$, $s_{strikeout} = 7.1$
(a) What is the value of $b_1$, the estimated slope? (Round your answer to 3 decimal places, if needed.)
Answer:
(b) What is the value of $b_0$, the estimated intercept? (Round your answer to 3 decimal places, if needed.)
Answer:
(c) What is the percent of variation in the number of strikeouts that is explained by age, using linear regression? (Round your answer to 2 decimal places, if needed.)
Answer:
(d) Can we use this linear regression to predict the number of strikeouts for a player age at 39?
$\circ$ Yes, because it is a linear relationship.
$\circ$ No, because we cannot extrapolate.
$\circ$ No, because we are uncertain about the range of the number of strikeouts.
$\circ$ No, because the correlation coefficient is not 1.
$\circ$ Yes, because we know the slope and intercept values.
