Final Project Week 4

Regression Model : Diagnostic of the Assumptions

The linear regression model heavily relies on the fulfillment of specific and strong assumptions. If those assumptions are not met, then simply the linear regression model may yield unreliable results. There are different ways of expressing such assumptions, but ultimately they can be summarized as follows:

1. There is a linear relationship between the dependent variable Y and the predictors \({{X}_{1}}\),…, \({{X}_{n}}\), stated by the following model:
   \[{{Y}_{i}}={{\beta }_{0}}+{{\beta }_{1}}{{X}_{1i}}+{{\beta }_{2}}{{X}_{2i}}+...+{{\beta }_{n}}{{X}_{ni}}+{{\varepsilon }_{i}}\]
   where \({{\varepsilon }_{i}}\) is the (random) error term of the model.
2. The error terms are independent from each other respond to the following distribution \({{\varepsilon }_{i}}\tilde{\ }N\left( 0,{{\sigma }^{2}} \right)\), which means that the error term has a mean of 0 and variance of \({{\sigma }^{2}}\), which is independent of the level of the predictors.

Strictly speaking, there is not a completely certain way of establishing the fulfillment of the assumptions, but there a series of procedures to assess whether or not a significant departure from the assumptions is observed. More specifically, we need to test for the normality and homoskedasticity of residuals.

Regression Diagnostics

First, the following regression results are obtained:

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Solution: The downloadable solution consists of 4 pages, 296 words and 2 charts.
Deliverable: Word Document