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Linear Regression Algorithm | Linear Regression in R | Data Science Training | Edureka

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The document provides an overview of data science certification training by Edureka, focusing on linear regression and machine learning. It explains the concepts of regression analysis, types of regression, and practical applications in various fields such as real estate and medicine. Additionally, it includes a detailed example using the Boston housing dataset to demonstrate linear regression analysis and model validation.

Data & Analytics
Related topics:
Big Data Analytics • R Programming Overview • Data Science Insights • Data Visualization Techniques • Data Scientist • Linear Regression • Data Mining Insights • Business Analytics • Data Analytics Insights • Data Analysis Insights
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www.edureka.co/data-scienceEdureka’s Data Science Certification Training Linear Regression
www.edureka.co/data-scienceEdureka’s Data Science Certification Training What Will You Learn Today? What is Regression?Machine Learning Types Of Regression Linear Regression - Example Linear Regression – Use Cases Demo In R: Real Estate Use Case 1 2 3 4 65
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Machine Learning
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Introduction To Machine Learning Machine learning is a type of artificial intelligence (AI) that provides computers with the ability to learn without being explicitly programmed. Training Data Learn Algorithm Build Model Perform Feedback
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Machine Learning - Example  Facebook's News Feed uses machine learning to personalize each member's feed.  When you upload photos to Facebook, the service automatically highlights faces and suggests friends to tag.  Facebook also uses AI(Artificial Intelligence) to personalize • Newsfeeds • Advertisements • Trending news • Friend recommendations
www.edureka.co/data-scienceEdureka’s Data Science Certification Training What Is Regression?
www.edureka.co/data-scienceEdureka’s Data Science Certification Training What Is Regression?  Regression analysis is a predictive modelling technique.  It estimates the relationship between a dependent (target) and an independent variable (predictor). X-axis Y-axis Input value = 7.00 Predicted outcome = 123.9
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Types Of Regression
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Types Of Regression Linear Regression • When there is a linear relationship between independent and dependent variables. • When the dependent variable is binary (0/ 1, True/ False, Yes/ No) in nature. Logistic Regression Polynomial Regression • When the power of independent variable is more than 1. X Y X Y
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Linear Regression
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Linear Regression - Introduction  The linear regression model assumes a linear relationship between the input variables and the outcome variable.  This relationship can be expressed as Where, y = outcome variable x = input variables = random error = slope of the line = intercept y = β0 + β1x + ε β1 β0 ε
www.edureka.co/data-scienceEdureka’s Data Science Certification Training I have a dataset consisting of height and weight of students. Let’s see how would linear regression fit into it.
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Model Description Scatterplot of y vs. x We have a dataset of 10 students. We will use it to draw scatterplot between height and weight: 127 121 142 157 162 156 169 165 181 208 0 50 100 150 200 250 62 64 66 68 70 72 74 76 WEIGHT HEIGHT
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Model Description Scatterplot of height vs. weight Now, the natural question arises — "what is the best fitting line?"  The prediction error (or residual error) is: Where, • yi is the observed value of the unit i (i.e, students). • ŷ is the predicted response (or fitted value) for unit i  The goal is to minimize the sum of the squared prediction errors (Least squared error or LER) ei = yi - ŷ 𝑄 = 𝑖=1 𝑛 (𝑦i − ŷ )2 127 121 142 157 162 156 169 165 181 208 0 50 100 150 200 250 62 64 66 68 70 72 74 76 WEIGHT HEIGHT W2= -331.2 + 7.1h W1= -266.5 + 6.1h
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Model Description  Least squared error (LER) w1 = 597.4  Least squared error (LER) w2 = 766.5 W2 = -331.2 + 7.1h W1 = -266.5 + 6.1h
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Model Description The solid line represented by w = -266.53 +6.1376 will be the best fit line as least squared error is minimum for it. 127 121 142 157 162 156 169 165 181 208 0 50 100 150 200 250 62 64 66 68 70 72 74 76 WEIGHT HEIGHT W1= -266.5 + 6.1h
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Now, lets understand linear regression further with the help of a simple example.
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Linear Regression - Example Here, Dependent variable is Churn_out_rate And Independent variable is Salary_hike Let’s take an example, A company is facing high churnout this year, salary hike being one of the major reason. So let us consider a company’s data where we will find out the relationship between these two variables.
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Linear Regression - Example > plot(Salary_hike, Churn_out_rate) x-axis = Salary_hike y-axis = Churn_out_rate Conclusion: From the graph, we can see that as the Salary hike increases, the Churn out rate decreases. Salary hike
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Linear Regression - Use Cases Real Estate Demand forecasting Real Estate To model residential home prices as a function of the home's living area, bathrooms, number of bedrooms, lot size. Medicine To analyze the effect of a proposed radiation treatment on reducing tumor sizes based on patient attributes such as age or weight. Demand forecasting To predict demand for goods and services. For example, restaurant chains can predict the quantity of food depending on weather. Marketing To predict company’s sales based on previous month’s sales and stock prices of a company. Use-cases Marketing Medicine
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Real Estate Consultation firm has the data comprising price of apartments in Boston. Based on this data, company wants to decide the price of new apartments.
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Data Acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Model Validation Let’s use the inbuilt housing data of Boston for linear regression analysis. To load it we can use following code:  library(MASS)  data(Boston) The Boston Data looks like this: Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo For description of the data we can use > ?Boston It will contain details about the data such as • No. of rows and column • Attributes description Lets move forward to see the description of attributes Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Prediction Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation Description The Boston data frame has 506 rows and 14 columns.
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Optimize Model Model Validation We will divide our entire dataset into two subsets as: • Training dataset -> to train the model • Testing dataset -> to validate and make predictions Here we will divide the data in 7:3 ratio such that 70% will be present as training set and remaining 30% as the testing set.Prediction Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Let’s find the relation among all the variables through scatterplot matrix.  library(lattice)  splom(~Boston[c(1:6,14)], groups=NULL, data=Boston,axis.line.tck = 0,axis.text.alpha = 0)  splom(~Boston[c(1:6,14)], groups=NULL, data=Boston,axis.line.tck = 0,axis.text.alpha = 0) Let’s check the plots Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Data Acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Model Validation  The plot shows positive linear trend between rm (average no. of rooms) and medv (value of home).  No relevant relationship between indus (proportion of non- retail business) and medv Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo  The plot shows negative linear trend between lstat (lower status of population) and medv.  No relevant relationship between tax (property tax rate) and medv Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo When we have various variables, correlation is an important factor to check the dependencies within themselves Correlation analysis gives us an insight, between mutual relationship among variables. To get correlation relationship among different variables for a data set use following code > cr<- cor(Boston) This will give us the correlation values. For visualizing the same we can use corrplot() function > library(corrplot) > corrplot(cr,type = "lower") Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo From the plot we can get visual relationship among different variables: • Dark blue signifies strong positive relationship • Dark red signifies strong negative relationship • Scale varies from red to blue, and size of the circle varies according to correlation factor Example: medv and lstat have large negative relationship medv and rm have large positive relationship Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo  Multicollinearity exists when two or more predictor are highly correlated among themselves.  When correlation among X’s is low, OLS has lots of information to estimate.  When correlation among X’s is high, OLS has very little information to estimate. This makes us relatively uncertain about our estimate. X1 X2 Y X1 X2 Y Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo How can I detect multicollinearity ? You can use VIF (variance inflation factor) for it. Let’s see how Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Optimize Model Variance inflation factor (VIF) measures the increase in the variance (the square of the estimate's standard deviation) of an estimated regression coefficient due to multicollinearity.  A VIF of 1 means that there is no correlation among variables.  Here, rad and tax have higher variance factor values indicating high multicollinearity.  nox, indus and dis are moderately correlated. Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Let’s check the correlation between rad and tax from corrgram.  rad and tax are highly correlated at 0.91  We can remove one of the predictors (rad or tax) to remove multicollinearity Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Let’s find the equation representing this best fit line  summary(model) As per the summary ,the equation representing our regression line is medv= -34.671 + 9.102* rm Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Now let’s build a model with the help of training set using the code below, Here we will be using all variables excluding tax  model<-lm(medv~ crim + zn + indus + chas + nox + rm + age + dis + rad + ptratio + black + lstat,data = training_data) Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Description of the model can be found using Summary() function > summary(model) Some of the important values are: 1. R-squared value 2. P-value Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Here r-squared = 0.726 R-squared value indicates the perfection of the predictive value. If the R-squared value is closer to 1.0, then the Linear Model is best- suited. Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Model Validation  High P values: your data are likely with a true null.  Low P values: your data are unlikely with a true null.  Here, indus and age relatively higher in p- value, so they can be neglected. P values are used to determine statistical significance in a hypothesis test. Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Now let’s build a model with the help of training set using the code below, Here we will be excluding indus and age > model<-lm(medv~ crim + zn + chas + nox + rm + dis + ptratio + black + lstat,data = training_data) Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Model Validation Here, adjusted R-squared value remained same despite of removing indus and age from the model. Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Now we can use our model to predict the output of our testing dataset. We can use the following code for predicting the output > predic<-predict(model,test) Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo For comparing these values we can use plots Here we plot a line graph where green lines represent the actual price and the blue lines represent the predictive model generated for the data.  plot(testing_data$medv,type = "l",lty = 1.8,col = "green")  lines(predic,type = "l",col = "blue") As we can see from the graph most of the predictive values are overlapping the actual values. Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo I have this dataset. What will be the estimated cost of apartment? Here’s the code line and predicted value Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
www.edureka.co/data-scienceEdureka’s Data Science Certification Training Course Details Go to www.edureka.co/data-science Get Edureka Certified in Data Science Today! What our learners have to say about us! Shravan Reddy says- “I would like to recommend any one who wants to be a Data Scientist just one place: Edureka. Explanations are clean, clear, easy to understand. Their support team works very well.. I took the Data Science course and I'm going to take Machine Learning with Mahout and then Big Data and Hadoop”. Gnana Sekhar says - “Edureka Data science course provided me a very good mixture of theoretical and practical training. LMS pre recorded sessions and assignments were very good as there is a lot of information in them that will help me in my job. Edureka is my teaching GURU now...Thanks EDUREKA.” Balu Samaga says - “It was a great experience to undergo and get certified in the Data Science course from Edureka. Quality of the training materials, assignments, project, support and other infrastructures are a top notch.”
www.edureka.co/data-scienceEdureka’s Data Science Certification Training

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Linear Regression Algorithm | Linear Regression in R | Data Science Training | Edureka

  • 1. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Linear Regression
  • 2. www.edureka.co/data-scienceEdureka’s Data Science Certification Training What Will You Learn Today? What is Regression?Machine Learning Types Of Regression Linear Regression - Example Linear Regression – Use Cases Demo In R: Real Estate Use Case 1 2 3 4 65
  • 3. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Machine Learning
  • 4. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Introduction To Machine Learning Machine learning is a type of artificial intelligence (AI) that provides computers with the ability to learn without being explicitly programmed. Training Data Learn Algorithm Build Model Perform Feedback
  • 5. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Machine Learning - Example  Facebook's News Feed uses machine learning to personalize each member's feed.  When you upload photos to Facebook, the service automatically highlights faces and suggests friends to tag.  Facebook also uses AI(Artificial Intelligence) to personalize • Newsfeeds • Advertisements • Trending news • Friend recommendations
  • 6. www.edureka.co/data-scienceEdureka’s Data Science Certification Training What Is Regression?
  • 7. www.edureka.co/data-scienceEdureka’s Data Science Certification Training What Is Regression?  Regression analysis is a predictive modelling technique.  It estimates the relationship between a dependent (target) and an independent variable (predictor). X-axis Y-axis Input value = 7.00 Predicted outcome = 123.9
  • 8. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Types Of Regression
  • 9. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Types Of Regression Linear Regression • When there is a linear relationship between independent and dependent variables. • When the dependent variable is binary (0/ 1, True/ False, Yes/ No) in nature. Logistic Regression Polynomial Regression • When the power of independent variable is more than 1. X Y X Y
  • 10. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Linear Regression
  • 11. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Linear Regression - Introduction  The linear regression model assumes a linear relationship between the input variables and the outcome variable.  This relationship can be expressed as Where, y = outcome variable x = input variables = random error = slope of the line = intercept y = β0 + β1x + ε β1 β0 ε
  • 12. www.edureka.co/data-scienceEdureka’s Data Science Certification Training I have a dataset consisting of height and weight of students. Let’s see how would linear regression fit into it.
  • 13. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Model Description Scatterplot of y vs. x We have a dataset of 10 students. We will use it to draw scatterplot between height and weight: 127 121 142 157 162 156 169 165 181 208 0 50 100 150 200 250 62 64 66 68 70 72 74 76 WEIGHT HEIGHT
  • 14. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Model Description Scatterplot of height vs. weight Now, the natural question arises — "what is the best fitting line?"  The prediction error (or residual error) is: Where, • yi is the observed value of the unit i (i.e, students). • ŷ is the predicted response (or fitted value) for unit i  The goal is to minimize the sum of the squared prediction errors (Least squared error or LER) ei = yi - ŷ 𝑄 = 𝑖=1 𝑛 (𝑦i − ŷ )2 127 121 142 157 162 156 169 165 181 208 0 50 100 150 200 250 62 64 66 68 70 72 74 76 WEIGHT HEIGHT W2= -331.2 + 7.1h W1= -266.5 + 6.1h
  • 15. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Model Description  Least squared error (LER) w1 = 597.4  Least squared error (LER) w2 = 766.5 W2 = -331.2 + 7.1h W1 = -266.5 + 6.1h
  • 16. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Model Description The solid line represented by w = -266.53 +6.1376 will be the best fit line as least squared error is minimum for it. 127 121 142 157 162 156 169 165 181 208 0 50 100 150 200 250 62 64 66 68 70 72 74 76 WEIGHT HEIGHT W1= -266.5 + 6.1h
  • 17. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Now, lets understand linear regression further with the help of a simple example.
  • 18. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Linear Regression - Example Here, Dependent variable is Churn_out_rate And Independent variable is Salary_hike Let’s take an example, A company is facing high churnout this year, salary hike being one of the major reason. So let us consider a company’s data where we will find out the relationship between these two variables.
  • 19. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Linear Regression - Example > plot(Salary_hike, Churn_out_rate) x-axis = Salary_hike y-axis = Churn_out_rate Conclusion: From the graph, we can see that as the Salary hike increases, the Churn out rate decreases. Salary hike
  • 20. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Linear Regression - Use Cases Real Estate Demand forecasting Real Estate To model residential home prices as a function of the home's living area, bathrooms, number of bedrooms, lot size. Medicine To analyze the effect of a proposed radiation treatment on reducing tumor sizes based on patient attributes such as age or weight. Demand forecasting To predict demand for goods and services. For example, restaurant chains can predict the quantity of food depending on weather. Marketing To predict company’s sales based on previous month’s sales and stock prices of a company. Use-cases Marketing Medicine
  • 21. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Real Estate Consultation firm has the data comprising price of apartments in Boston. Based on this data, company wants to decide the price of new apartments.
  • 23. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Data Acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Model Validation Let’s use the inbuilt housing data of Boston for linear regression analysis. To load it we can use following code:  library(MASS)  data(Boston) The Boston Data looks like this: Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
  • 24. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo For description of the data we can use > ?Boston It will contain details about the data such as • No. of rows and column • Attributes description Lets move forward to see the description of attributes Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
  • 25. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Prediction Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation Description The Boston data frame has 506 rows and 14 columns.
  • 26. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Optimize Model Model Validation We will divide our entire dataset into two subsets as: • Training dataset -> to train the model • Testing dataset -> to validate and make predictions Here we will divide the data in 7:3 ratio such that 70% will be present as training set and remaining 30% as the testing set.Prediction Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
  • 27. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Let’s find the relation among all the variables through scatterplot matrix.  library(lattice)  splom(~Boston[c(1:6,14)], groups=NULL, data=Boston,axis.line.tck = 0,axis.text.alpha = 0)  splom(~Boston[c(1:6,14)], groups=NULL, data=Boston,axis.line.tck = 0,axis.text.alpha = 0) Let’s check the plots Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
  • 28. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Data Acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Model Validation  The plot shows positive linear trend between rm (average no. of rooms) and medv (value of home).  No relevant relationship between indus (proportion of non- retail business) and medv Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
  • 29. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo  The plot shows negative linear trend between lstat (lower status of population) and medv.  No relevant relationship between tax (property tax rate) and medv Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
  • 30. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo When we have various variables, correlation is an important factor to check the dependencies within themselves Correlation analysis gives us an insight, between mutual relationship among variables. To get correlation relationship among different variables for a data set use following code > cr<- cor(Boston) This will give us the correlation values. For visualizing the same we can use corrplot() function > library(corrplot) > corrplot(cr,type = "lower") Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
  • 31. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo From the plot we can get visual relationship among different variables: • Dark blue signifies strong positive relationship • Dark red signifies strong negative relationship • Scale varies from red to blue, and size of the circle varies according to correlation factor Example: medv and lstat have large negative relationship medv and rm have large positive relationship Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
  • 32. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo  Multicollinearity exists when two or more predictor are highly correlated among themselves.  When correlation among X’s is low, OLS has lots of information to estimate.  When correlation among X’s is high, OLS has very little information to estimate. This makes us relatively uncertain about our estimate. X1 X2 Y X1 X2 Y Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
  • 33. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo How can I detect multicollinearity ? You can use VIF (variance inflation factor) for it. Let’s see how Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
  • 34. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Optimize Model Variance inflation factor (VIF) measures the increase in the variance (the square of the estimate's standard deviation) of an estimated regression coefficient due to multicollinearity.  A VIF of 1 means that there is no correlation among variables.  Here, rad and tax have higher variance factor values indicating high multicollinearity.  nox, indus and dis are moderately correlated. Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
  • 35. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Let’s check the correlation between rad and tax from corrgram.  rad and tax are highly correlated at 0.91  We can remove one of the predictors (rad or tax) to remove multicollinearity Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
  • 36. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Let’s find the equation representing this best fit line  summary(model) As per the summary ,the equation representing our regression line is medv= -34.671 + 9.102* rm Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
  • 37. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Now let’s build a model with the help of training set using the code below, Here we will be using all variables excluding tax  model<-lm(medv~ crim + zn + indus + chas + nox + rm + age + dis + rad + ptratio + black + lstat,data = training_data) Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
  • 38. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Description of the model can be found using Summary() function > summary(model) Some of the important values are: 1. R-squared value 2. P-value Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
  • 39. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Here r-squared = 0.726 R-squared value indicates the perfection of the predictive value. If the R-squared value is closer to 1.0, then the Linear Model is best- suited. Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
  • 40. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Model Validation  High P values: your data are likely with a true null.  Low P values: your data are unlikely with a true null.  Here, indus and age relatively higher in p- value, so they can be neglected. P values are used to determine statistical significance in a hypothesis test. Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
  • 41. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Now let’s build a model with the help of training set using the code below, Here we will be excluding indus and age > model<-lm(medv~ crim + zn + chas + nox + rm + dis + ptratio + black + lstat,data = training_data) Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
  • 42. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Model Validation Here, adjusted R-squared value remained same despite of removing indus and age from the model. Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
  • 43. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo Now we can use our model to predict the output of our testing dataset. We can use the following code for predicting the output > predic<-predict(model,test) Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
  • 44. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo For comparing these values we can use plots Here we plot a line graph where green lines represent the actual price and the blue lines represent the predictive model generated for the data.  plot(testing_data$medv,type = "l",lty = 1.8,col = "green")  lines(predic,type = "l",col = "blue") As we can see from the graph most of the predictive values are overlapping the actual values. Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
  • 45. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Demo I have this dataset. What will be the estimated cost of apartment? Here’s the code line and predicted value Data acquisition Divide dataset Exploratory Analysis Implement Model Optimize Model Prediction Model Validation
  • 46. www.edureka.co/data-scienceEdureka’s Data Science Certification Training Course Details Go to www.edureka.co/data-science Get Edureka Certified in Data Science Today! What our learners have to say about us! Shravan Reddy says- “I would like to recommend any one who wants to be a Data Scientist just one place: Edureka. Explanations are clean, clear, easy to understand. Their support team works very well.. I took the Data Science course and I'm going to take Machine Learning with Mahout and then Big Data and Hadoop”. Gnana Sekhar says - “Edureka Data science course provided me a very good mixture of theoretical and practical training. LMS pre recorded sessions and assignments were very good as there is a lot of information in them that will help me in my job. Edureka is my teaching GURU now...Thanks EDUREKA.” Balu Samaga says - “It was a great experience to undergo and get certified in the Data Science course from Edureka. Quality of the training materials, assignments, project, support and other infrastructures are a top notch.”

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