20 teams were involved. The points achieved were used as the dependent variable, Y . They were...

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20 teams were involved. The points achieved were used as the dependent variable, Y. They were the league points achieved during the 38-game season, in 2007-2008. The independent variables are as follows: There were 24 “pitch actions”, labelled X1 to X24. But some of these variables provide the same information, such as X1, the number of goals scored, and X2, average goals per game; or X6, percent of goals scored inside the box, and X7, percent of goals scored from outside the box. Therefore, 17 variables were initially retained.

X2, Average goals per game.
X3, Number of shots at goal. 
X4, Percentage shots on target.
X5, Percentage of goals scored to shots at goal.
X7, Percentage of goals scored from outside the box.
X10, Number of total passes.
X11, Ratio of short to long passes of the ball during all games
X12, Overall pass completion percentage. 
X15, Total number of ball crosses. 
X16, Cross completion percentage.
X18, Average number of goals conceded per game.
X19, Number of tackles.
X20, Percentage of tackles won. 
X21, Number of blocks, clearances and interceptions.
X22, Number of fouls.
X23, Number of yellow cards.
X24, Number of red cards.

To avoid problems resulting from highly correlated variables, known as multicollinearity, the analysis should be reduced to the following set of variables.

X5, Percentage of goals scored to shots at goal.
X7, Percentage of goals scored from outside the box.
X11, Ratio of short to long passes of the ball during all games
X15, Total number of ball crosses. 
X18, Average number of goals conceded per game.
X23, Number of yellow cards.

The aim is to study team performance, using this set of play descriptor variables. In this task, you will look at the relationship between the descriptor variables and the team performances.

The data for football team is available at the top of this Case study.

In this task, you will be asked to do some exploratory analysis, including visualisation. This will be followed by multiple linear regression. Finally, ANOVA, the analysis of variance, will be used.

part 1

Q1. Data Preparation and initial investigation.

1.1). Read the file into R (RStudio software). Have the row labels as the team names. For the analyses to follow, select the variables X5, X7, X11, X15, X18, X23.

1.2) Examine all pairwise plots between the variables. Briefly describe this.

1.3) Support this visualisation of the data, by determining the variables’ correlations. Accompany that with a short description.

1.4) Provide three conclusions from this investigation.

part 2

Question 2. Examine the influence of the six play descriptor variables (X5, X7, X11, X15, X18, X23) in relation to performance, as measured by the league points achieved by the team.

2.1) Comment on the effectiveness of multiple linear regression for this objective.

2.2) Support your comment with what the data reveals.

2.3) Describe at least two of the main assumptions for this modelling.

2.4) Write down a null hypothesis for a hypothesis test in regard to each variable's role in the team performance outcome.

2.5) Describe what the regression reveals in regard to each variable's role.

part 3

Q3. The next part of this case study is to examine the following three groups of teams. Firstly, there is the top performing (in terms of their league points) four teams, which will go on the ‘Champions League’ competition. Secondly there is the middle ground of the next twelve teams. Finally, there is the bottom set of four teams, that will be in danger of relegation from the premier league.

3.1) Using ANOVA, determine which variables and how powerfully these variables, influence the top, middle and bottom sets of teams.

3.2) Make a table of your results, so that it can be referred to in your discussion.

3.3) Describe at least two of the main assumptions in regard to this ANOVA assessment.

3.4) Display the data using a boxplot and summarize what this indicates. It is recommended that you do the boxplots for variables, in the case of each of the top, middle and bottom sets of teams.

3.5) Taking account of all your findings, and in particular how much explanatory value the variables provide for the top, middle and bottom performances, give two recommendations, for a team manager, from what emerged from your analysis.