Linear Regression

• A simple yet useful supervised learning approac for predicting quantitative (numeric) response
• Makes prediction by simply computing a weighted sum of input feature, plus a contst called as bias term.
• Finding Parameters
  • Choose parameters in a way so that prediction is close to actual values for the training samples
  • Define a cost function to find the parameters that minimize the cost function => MSE (Mean squared Error)
• Some methods: Least Squares Method, Gradient Descent
• Main Steps:
  • Use least-squares to fit a line to the data
  • Calculate R-Squared
  • Calculate p-value
• Terminology:
  • R-Squared: a goodness of fit measure for linear regression modesl
  • Null Hypothesis: An initial statement claiming that there is no relationship between two measured events
  • P-Value: Tests the null hypothesis
  • Low p-value (< 0.05): Null hypothesis can be rejected
    • Predictor likelya meaningful addition to your model
    • Changes in the predictor’s values are related to changes in the response variable
  • Large p-value: Suggest that predictor not associated with changes in response

Tidymodels steps

• Split data ({rsample})
• prepare recipe ({recipes})
• Specify model ({parsnip})
• Tune hyperparameters ({tune})
• Fit model ({parsnip})
• Analyze model ({broom})
• Predict ({parsnip})
• Interpret the results ({yardstick})

Linear Regression with known dataset diamonds

• Lets build the price predictor
  
  
  
  
• Now lets find all the columns which have high correlation with price
  
• Now lets split the training and testing data from this data
  
• Now lets use lm to create the model for the training data
  
• broom package has a method to summarize models in a way they are easy to read broom::tidy(model)
  
• According to work which we have done so far carat, x, y, z can be used to predict the price of diamond, Lets use all the variables and see the results, y and z will be insignificant if we consider all variables