Simple linear regression tutorial

Learn how to fit a simple regression model, check the assumptions of the ordinary least squares linear regression method, and make predictions using the fitted model.

On March 1, 1984 the Wall Street Journal published data on the advertising spend and yield for a number of commercial TV adverts. The advertisements were selected by an annual survey conducted by Video Board Tests, Inc., a New York ad-testing company, based on interviews with 20,000 adults who were asked to name the most outstanding TV commercial they had seen, noticed, and liked. The retained impressions were based on a survey of 4,000 adults, in which regular product users were asked to cite a commercial they had seen for that product category in the past week. Of interest is fitting a model to describe the relationship, and making predictions using the model. For more information see DASL Story: TV Advertising Yields.

In this tutorial you will perform the following tasks:

1. Plotting bivariate data
   Create a scatter plot of the relationship between the variables.
2. Fitting a simple regression model
   Fit a polynomial regression model to describe the relationship.
3. Checking the assumptions of the regression model
   Check the assumptions and robustness of the model.
4. Changing the regression fit
   Change the model to a logarithmic regression to better describe the relationship.
5. Making predictions
   Estimate the average retained impressions given a $100 million spend.