Regression Modeling in Practice: WEEK 2

Basics of Linear Regression

Assignment: Test a Basic Linear Regression Model 

Source: Data from OECD (“The Organisation for Economic Co-operation and Development”)

Variables Used: 

*Employment Rate -  It is the number of employed persons aged 15 to 64 over the population of the same age. (source: OECD)

*Life Satisfaction - This indicator considers people's evaluation of their life as a whole (source: OECD)

Introduction:

Introduction:

This week I decided to test the association between Employment Rate (explanatory variable) and Life Satisfaction (response variable) using basic linear regression model.

First, I centered the quantitative explanatory variable "Work" (Employment Rate) by substracting the mean and created a new variable "Work_c" (Centered Employment Rate). I checked the centering by using the means procedure for the new variable and it appeared that the value of the mean was exactly zero (0).

Next, I ran linear regression procedure with the new explanatory variable (“Work_c" - Centered Employment Rate)  and Life Satisfaction (response variable).

Program:

Output:

Summary:

After centering the explanatory quantitative variable (Employment Rate) I obtained a new variable (centered Employment Rate), with the mean equal to zero (0), and I used it in the Linear regression model.

The results of the linear regression model indicate that Life Satisfaction (F =28.49, p<.0001) is significantly and positively associated with the centered Employment Rate.

The parameter estimates show a coefficient value of 0.074943946 and an intercept value of 6.588235294. Therefore, the best fit line equation for the linear regression is:

Life Satisfaction = 0.074943946*Employment Rate (centered) + 6.588235294

The p-values for both the intercept and coefficient values are very small (both p < 0.0001). This indicates there is indeed a straight-line relationship between Life Satisfaction and Employment Rate.

The R-square value of 0.47 indicates that the proportion of variance in the response variable that can be attributed to the explanatory variable is 47%.