The data comes from Football-Data.co.uk. It contains individual Premier League match results. We calculate each team’s total points and goal difference from the match results.

## # A tibble: 20 × 5
##    Team              GF    GA Points    GD
##    <chr>          <int> <int>  <dbl> <int>
##  1 Liverpool         86    41     84    45
##  2 Arsenal           69    34     74    35
##  3 Man City          72    44     71    28
##  4 Chelsea           64    43     69    21
##  5 Aston Villa       58    51     66     7
##  6 Newcastle         68    47     66    21
##  7 Nott'm Forest     58    46     65    12
##  8 Brighton          66    59     61     7
##  9 Bournemouth       58    46     56    12
## 10 Brentford         66    57     56     9
## 11 Fulham            54    54     54     0
## 12 Crystal Palace    51    51     53     0
## 13 Everton           42    44     48    -2
## 14 West Ham          46    62     43   -16
## 15 Man United        44    54     42   -10
## 16 Wolves            54    69     42   -15
## 17 Tottenham         64    65     38    -1
## 18 Leicester         33    80     25   -47
## 19 Ipswich           36    82     22   -46
## 20 Southampton       26    86     12   -60

Correlation measures the strength and direction of a linear relationship between two variables, where x represents goal difference and y represents league points.

The sample correlation coefficient is calculated using:

\[ r = \frac{\sum_{i=1}^{n}(x_i-\bar{x})(y_i-\bar{y})} {\sqrt{\sum_{i=1}^{n}(x_i-\bar{x})^2\sum_{i=1}^{n}(y_i-\bar{y})^2}} \]

correlation=cor(teams$GD, teams$Points)
correlation

## [1] 0.9700916

The correlation value of approximately 0.97 indicates a very strong positive relationship between goal difference and league points. This means that teams with higher goal differences generally earn more points, while teams with lower goal differences tend to earn fewer points. This suggests that goal difference is a strong indicator of success in the Premier League.

We use linear regression to investigate how goal difference relates to league points.

The general regression equation is:

\[ \hat{y} = b_0 + b_1x \]

Here, \(\hat{y}\) represents predicted points, \(b_0\) is the intercept, \(b_1\) is the slope, and \(x\) represents goal difference.

Using our regression results, the fitted equation is:

\[ \widehat{\text{Points}} = 52.35 + 0.6664(\text{GD}) \]

The positive slope indicates that teams with higher goal differences tend to earn more points.

model = lm(Points ~ GD, data = teams)
summary(model)

## 
## Call:
## lm(formula = Points ~ GD, data = teams)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -13.6836  -1.8425   0.1476   1.9103   8.9852 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  52.3500     1.0359   50.53  < 2e-16 ***
## GD            0.6664     0.0393   16.95 1.63e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.633 on 18 degrees of freedom
## Multiple R-squared:  0.9411, Adjusted R-squared:  0.9378 
## F-statistic: 287.5 on 1 and 18 DF,  p-value: 1.632e-12

This scatterplot shows the relationship between goal difference and league points.

The scatterplot shows a strong positive relationship between goal difference and league points. Teams with higher goal differences generally earn more points, suggesting that scoring more goals than they concede is associated with greater success in the Premier League.

Comparing league which teams performed best in the season represented by our dataset.

Explore the relationship between goal difference and league points for specific teams.

The Premier League data shows a strong positive relationship between goal difference and total league points. The correlation between these variables is approximately 0.97, and the regression model estimates that each additional goal in goal difference is associated with approximately 0.67 additional league points. The scatterplot supports this finding, showing that teams with higher goal differences generally earned more points. However, goal difference and league points are separate measures, and a team’s success can depend on other factors as well. This analysis shows a strong association between goal difference and league points, but it does not prove that goal difference alone causes a team to earn more points.