{"id":477,"date":"2020-02-23T19:39:52","date_gmt":"2020-02-23T19:39:52","guid":{"rendered":"https:\/\/fcpython.com\/?p=477"},"modified":"2020-12-18T20:08:55","modified_gmt":"2020-12-18T20:08:55","slug":"introduction-to-simple-linear-regression-in-python","status":"publish","type":"post","link":"https:\/\/fcpython.com\/machine-learning\/introduction-to-simple-linear-regression-in-python","title":{"rendered":"Introduction to Simple Linear Regression in Python"},"content":{"rendered":"

Linear regression allows us to model the relationship between variables. This might allow us to predict a future outcome if we already know some information, or give us an insight into what is needed to reach a goal.<\/span><\/p>\n

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To fit a linear regression model, we need one dependent variable, which we will study the changes of as one or more independent variables are changed. As an example, we could model how many goals are scored (dependent variable), as more shots are taken (independent variable). As we have just one independent variable, this is a simple linear regression – models that take in multiple independent variables are are known as multiple linear regressions.<\/p>\n

This article is going to apply a simple linear regression model to squad value data against performance in the Premier League. This might help us to see how much a squad might need to invest to avoid relegation, make European spots or to create a data-driven target for our team.<\/p>\n

The steps that we are going to take include a quick look & explore of our dataset, creating the model & then making some assessments on the back of it. Then, we’ll calculate a better metric to improve our model. We will use the sklearn module to make this much less intimidating than it might seem right now! Let’s get the modules in place and read in a local dataset called positionsvsValue – which you can download here<\/a>.<\/p>\n

Initial set-up & exploration<\/h3>\n<\/div>\n<\/div>\n<\/div>\n
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import<\/span> pandas<\/span> as<\/span> pd<\/span>\nimport<\/span> numpy<\/span> as<\/span> np<\/span>\n\nimport<\/span> matplotlib.pyplot<\/span> as<\/span> plt<\/span>\nimport<\/span> seaborn<\/span> as<\/span> sns<\/span>\n%<\/span>matplotlib<\/span> inline\n\nfrom<\/span> sklearn.model_selection<\/span> import<\/span> train_test_split<\/span>\nfrom<\/span> sklearn.linear_model<\/span> import<\/span> LinearRegression<\/span>\nfrom<\/span> sklearn<\/span> import<\/span> metrics<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[2]:<\/div>\n
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#load data<\/span>\ndata<\/span> =<\/span> pd<\/span>.<\/span>read_csv<\/span>(<\/span>\"positionsvsValue.csv\"<\/span>)<\/span>\ndata<\/span>.<\/span>head<\/span>()<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[2]:<\/div>\n
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<\/th>\nLeague<\/th>\nSeason<\/th>\nTeam<\/th>\nSquad<\/th>\nAverage Age<\/th>\nNon-Homegrown<\/th>\nSquad Value<\/th>\nAvg Player Value<\/th>\nGD<\/th>\nPoints<\/th>\nPosition<\/th>\n<\/tr>\n<\/thead>\n
0<\/th>\nEPL<\/td>\n2008<\/td>\nChelsea FC<\/td>\n28<\/td>\n25.6<\/td>\n21<\/td>\n406.70<\/td>\n14.53<\/td>\n44<\/td>\n83<\/td>\n3<\/td>\n<\/tr>\n
1<\/th>\nEPL<\/td>\n2008<\/td>\nManchester United<\/td>\n31<\/td>\n24.3<\/td>\n20<\/td>\n356.10<\/td>\n11.49<\/td>\n44<\/td>\n90<\/td>\n1<\/td>\n<\/tr>\n
2<\/th>\nEPL<\/td>\n2008<\/td>\nLiverpool FC<\/td>\n28<\/td>\n23.9<\/td>\n24<\/td>\n257.23<\/td>\n9.19<\/td>\n50<\/td>\n86<\/td>\n2<\/td>\n<\/tr>\n
3<\/th>\nEPL<\/td>\n2008<\/td>\nArsenal FC<\/td>\n38<\/td>\n21.3<\/td>\n30<\/td>\n250.85<\/td>\n6.6<\/td>\n31<\/td>\n72<\/td>\n4<\/td>\n<\/tr>\n
4<\/th>\nEPL<\/td>\n2008<\/td>\nTottenham Hotspur<\/td>\n35<\/td>\n22.5<\/td>\n18<\/td>\n212.60<\/td>\n6.07<\/td>\n0<\/td>\n51<\/td>\n8<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[3]:<\/div>\n
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data<\/span>.<\/span>describe<\/span>()<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[3]:<\/div>\n
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<\/th>\nSeason<\/th>\nSquad<\/th>\nAverage Age<\/th>\nNon-Homegrown<\/th>\nSquad Value<\/th>\nGD<\/th>\nPoints<\/th>\nPosition<\/th>\n<\/tr>\n<\/thead>\n
count<\/th>\n220.000000<\/td>\n220.000000<\/td>\n220.000000<\/td>\n220.000000<\/td>\n220.000000<\/td>\n220.000000<\/td>\n220.000000<\/td>\n220.000000<\/td>\n<\/tr>\n
mean<\/th>\n2013.000000<\/td>\n36.304545<\/td>\n24.793636<\/td>\n22.886364<\/td>\n225.792909<\/td>\n0.000000<\/td>\n52.245455<\/td>\n10.500000<\/td>\n<\/tr>\n
std<\/th>\n3.169489<\/td>\n5.410372<\/td>\n1.136427<\/td>\n5.377171<\/td>\n183.079602<\/td>\n27.061405<\/td>\n17.569788<\/td>\n5.779431<\/td>\n<\/tr>\n
min<\/th>\n2008.000000<\/td>\n21.000000<\/td>\n21.300000<\/td>\n8.000000<\/td>\n22.500000<\/td>\n-54.000000<\/td>\n16.000000<\/td>\n1.000000<\/td>\n<\/tr>\n
25%<\/th>\n2010.000000<\/td>\n33.000000<\/td>\n23.975000<\/td>\n19.000000<\/td>\n99.662500<\/td>\n-20.000000<\/td>\n40.000000<\/td>\n5.750000<\/td>\n<\/tr>\n
50%<\/th>\n2013.000000<\/td>\n36.000000<\/td>\n24.800000<\/td>\n22.000000<\/td>\n158.275000<\/td>\n-7.000000<\/td>\n47.000000<\/td>\n10.500000<\/td>\n<\/tr>\n
75%<\/th>\n2016.000000<\/td>\n40.000000<\/td>\n25.500000<\/td>\n26.000000<\/td>\n299.782500<\/td>\n20.250000<\/td>\n64.250000<\/td>\n15.250000<\/td>\n<\/tr>\n
max<\/th>\n2018.000000<\/td>\n54.000000<\/td>\n28.100000<\/td>\n41.000000<\/td>\n1000.100000<\/td>\n79.000000<\/td>\n100.000000<\/td>\n20.000000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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So we have a 220-row dataset, with each row being a team in each Premier League season since 2008\/09. For each of the teams, we get squad sizes, ages, squad value (in Euros) as well as performance data with goal difference, points & position. The values are taken from Transfermarkt (once again, you can find the data here)<\/a>.<\/p>\n
Our aim is to get a model together that would help us to predict a team’s points based on their squad value. Before we do that, we should check to see what the relationships are among some of the key variables. Let’s do that visually with a pair plot.<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[4]:<\/div>\n
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sns<\/span>.<\/span>pairplot<\/span>(<\/span>data<\/span>[[<\/span>'Season'<\/span>,<\/span>'GD'<\/span>,<\/span> 'Squad Value'<\/span>,<\/span> 'Points'<\/span>,<\/span> 'Position'<\/span>]])<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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<seaborn.axisgrid.PairGrid at 0x1a261dbb50><\/pre>\n<\/div>\n<\/div>\n
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\"Python<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Some interesting points to keep in mind:<\/p>\n