Brandon works as a statistician for the Toronto Blue Jays, and wants to analyze the relationship between a player’s age and how many strikeouts they accumulate in a season.

Question

He takes a sample of 7 Blue Jays players with age 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 = 0.67, average age=29.9, S_age= 3.97, average strikeout= 100.4, S_strikeout= 7.21

a) What is the value of b₁, i.e. the fitted slope?(Round to 3 decimal places)

b) What is the value of b₀, i.e. the fitted intercept?(Round to 3 decimal places)

c) What is the percent of variation of the number of strikeouts that is explained by age using a linear regression?(Round to 2 decimal places)

d) Can we use this linear regression to predict the number of strikeouts for a player age 22? Why/Why not?

Answer 1

a) b₁ = r * (s_y / s_x)

= .67 * (7.21 / 3.97)

= 1.217

b) b₀ = average_y - b₁ * average_x

= 100.4 - 1.217 * 29.9

= 64.012

c) r^2 = 0.67^2

= 0.4489

= 44.89%

d) No, this would be extrapolation. We don't have any data for anyone younger than 25. We don't know whether the same relationship we observed here holds for anyone outside of the age range for which we have data.