Lecture "Applied data science: Linear regression (review)" includes content: the regression model formulation, understanding the regression results, potential problems in regression model, . We invite you to consult! | Linear regression review Overview 1. Introduction 8. Validation 2. Application 9. Regularisation 3. EDA 10. Clustering 4. Learning Process 11. Evaluation 5. Bias-Variance Tradeoff 12. Deployment 6. Regression review 13. Ethics 7. Classification Lecture outline - The regression model formulation - Understanding the regression results - Potential problems in regression model and its training data The linear regression formulation Approximated by By minimising An example The Advertising dataset - Sales in 200 different markets together with budget spent on marketing on 3 media types TV Radio and Newspaper. - Unit of Sales is in thousand units - Unit of market budget is in thousand dollars We have been given a regression model of Sales on TV Radio and Newspaper Some of the results from the model Interpreting the regression results Some of the questions we can and should ask - Which media contribute to sales - How strong is the relationship - How accurate is the effect of each medium on sales - How accurately can we predict future sales - Is the relationship strictly linear Which media contributes to sales Sample regression model vs population regression model Which media contributes to sales In other words how confident are we that each beta is non-zero If t-statistic of each beta is very large or its p-value is very small then we are confident that beta is non-zero. But What if we have a large beta but p-value is also large What if we have a very small beta but p-value is small How strong is the relationship R-squared the proportion of variance in the response explained by the model. Residual standard error RSE the standard deviation of the response from the population regression. How accurate is the effect of each medium on sales The 95 confidence interval of each beta is following the empirical rule Notes. Factor 2 is an approximate can be replaced by the quantile of a Student distribution with a degree of freedom of n-2 n is the number of data points . How .
