10. Predicting Continuous Target Variables with Regression Analysis

Question 1

What is the goal of simple (univariate) linear regression?

Answer 1

to model the relationship between a single feature (explanatory variable x) and a continuous valued response (target variable y). The equation of a linear model with one explanatory variable is defined as follows:

y = w0 + w1 * x

Question 2

Exploratory Data Analysis (EDA) is

Answer 2

An important and recommended first step prior to the training of a machine learning model.

1) First, we will create a scatterplot matrix that allows us to visualize the pair-wise correlations between the different features in this dataset in one place.
2) To quantify the linear relationship between the features, we will now create a correlation matrix.

Question 3

Describe the correlation matrix

Answer 3

The correlation matrix is a square matrix that contains the Pearson product-moment correlation coefficients (often abbreviated as Pearson’s r), which measure the linear dependence between pairs of features. The correlation coefficients are bounded to the range -1 and 1. Two features have a perfect positive correlation if r = 1, no correlation if r = 0, and a perfect negative correlation if r = -1respectively. As mentioned previously, Pearson’s correlation coefficient can simply be calculated as the covariance between two features x and y (numerator) divided by the product of their standard deviation (denominator).