This assessment has 6 multi-part questions that will all use the setup below. Game attendance in baseball varies partly as a function of how well a team is playing.
Load the Lahman library. The Teams data frame contains an attendance column. This is the total attendance for the season. To calculate average attendance, divide by the number of games played, as follows:
library(tidyverse)
library(broom)
library(Lahman)
Teams_small <- Teams %>%
filter(yearID %in% 1961:2001) %>%
mutate(avg_attendance = attendance/G)
Use linear models to answer the following 3-part question about Teams_small.
Question 1a
0.0/2.0 points (graded)
Use runs (R) per game to predict average attendance.
For every 1 run scored per game, average attendance increases by how much? incorrect
Use home runs (HR) per game to predict average attendance.
For every 1 home run hit per game, average attendance increases by how much? incorrect
Question 1b
Use number of wins to predict average attendance; do not normalize for number of games.
For every game won in a season, how much does average attendance increase? unanswered
Suppose a team won zero games in a season.
Predict the average attendance.
Question 1c
0.0/1.0 point (graded)
Use year to predict average attendance.
How much does average attendance increase each year? unanswered
Question 2
0.0/2.0 points (graded)
Game wins, runs per game and home runs per game are positively correlated with attendance. We saw in the course material that runs per game and home runs per game are correlated with each other. Are wins and runs per game or wins and home runs per game correlated?
What is the correlation coefficient for wins and runs per game? unanswered
What is the correlation coefficient for wins and home runs per game? unanswered
Stratify Teams_small by wins: divide number of wins by 10 and then round to the nearest integer. Keep only strata 5 through 10, which have 20 or more data points.
Use the stratified dataset to answer this three-part question.
Question 3a
0.0/1.0 point (graded)
How many observations are in the 8 win strata?
(Note that due to division and rounding, these teams have 75-85 wins.)
unanswered
Question 3b
0.0/2.0 points (graded)
Calculate the slope of the regression line predicting average attendance given runs per game for each of the win strata.
Which win stratum has the largest regression line slope?
5
6
7
8
9
10
Calculate the slope of the regression line predicting average attendance given HR per game for each of the win strata.
Which win stratum has the largest regression line slope?
5
6
7
8
9
10
incorrect
Question 3c
0.0/1.0 point (graded)
Which of the followng are true about the effect of win strata on average attendance?
Select ALL that apply.
Across all win strata, runs per game are positively correlated with average attendance.
Runs per game have the strongest effect on attendance when a team wins many games.
After controlling for number of wins, home runs per game are not correlated with attendance.
Home runs per game have the strongest effect on attendance when a team does not win many games.
Among teams with similar numbers of wins, teams with more home runs per game have larger average attendance.
Question 4
0.0/3.0 points (graded)
Fit a multivariate regression determining the effects of runs per game, home runs per game, wins, and year on average attendance. Use the original Teams_small wins column, not the win strata from question 3.
What is the estimate of the effect of runs per game on average attendance? unanswered
What is the estimate of the effect of home runs per game on average attendance? unanswered
What is the estimate of the effect of number of wins in a season on average attendance? unanswered
Question 5
0.0/2.0 points (graded)
Use the multivariate regression model from Question 4. Suppose a team averaged 5 runs per game, 1.2 home runs per game, and won 80 games in a season.
What would this team's average attendance be in 2002? unanswered
What would this team's average attendance be in 1960? unanswered
Question 6
0.0/1.0 point (graded)
Use your model from Question 4 to predict average attendance for teams in 2002 in the original Teams data frame.
What is the correlation between the predicted attendance and actual attendance?