Data Mining and Predictive Analytics, 2nd Edition

Chapter 8Simple Linear Regression

Regression modeling represents a powerful and elegant method for estimating the value of a continuous target variable. In this chapter, we introduce regression modeling through simple linear regression, where a straight line is used to approximate the relationship between a single continuous predictor variable and a single continuous response variable. Later, in Chapter 9, we turn to multiple regression, where several predictor variables are used to estimate a single response.

8.1 An Example of Simple Linear Regression

To develop the simple linear regression model, consider the Cereals data set,¹ an excerpt of which is presented in Table 8.1. The Cereals data set contains nutritional information for 77 breakfast cereals, and includes the following variables:

• Cereal name
• Cereal manufacturer
• Type (hot or cold)
• Calories per serving
• Grams of protein
• Grams of fat
• Milligrams of sodium
• Grams of fiber
• Grams of carbohydrates
• Grams of sugar
• Milligrams of potassium
• Percentage of recommended daily allowance of vitamins (0%, 25%, or 100%)
• Weight of one serving
• Number of cups per serving
• Shelf location (1 = bottom, 2 = middle, 3 = top)
• Nutritional rating, as calculated by Consumer Reports.

Table 8.1 Excerpt from Cereals data set: eight fields, first 16 cereals

Cereal Name	Manufacture	Sugars	Calories	Protein	Fat	Sodium	Rating
100% Bran	N	6	70	4	1	130	68.4030
100% Natural Bran	Q	8	120	3	5	15	33.9837
All-Bran	K	5	70	4	1	260	59.4255
All-Bran ...