Question

Use a written essay format to answer the following questions

1. When performing Linear Regression to estimate the Law of Demand in a market, please accurately explain the following procedures:
   1. What is the role of the Ordinary Least Squares (OLS) procedure, and why is it considered to be a reasonable method of estimation?
   2. When using sample data to estimate a population-level relationship, why is it necessary to engage in hypothesis testing?
   3. What are Type I and Type II errors, and why should researchers estimating demand relationships be concerned about these errors?

Answer 1

Linear Regression attempts to model the relationship between two variables by fitting a linear equation to observed data. One variable is considered to be an explanatory variable, and the other is considered to be a dependent variable.

(a) Ordinary Least Squares (OLS) is one of the simplest methods of linear regression. The goal of OLS is to closely "fit" a function with the data. It does so by minimizing the sum of squared errors between the observed data and the predicted one. It is basically used to predict the behavior of dependable variables. This estimator is consistent when the regressors are exogenous and optimal in the class of linear unbiased estimators when the errors are homoscedastic and serially uncorrelated. Also, under these conditions the method of OLS provides minimum variance mean unbiased estimation when the errors have finite variances.

(b) The hypotheses is based on available information and the investigator's belief about the population parameters.The process of hypotheses testing involves setting up two competing hypothesis, the null hypothesis and the alternate hypothesis.

It is necessary to engage in hypothesis testing, as it is a means to decide if something really happened or if certain treatments have positive effects or if groups differ from each other or if one variable predicts another. In essence then, a hypothesis test is a test of significance.

(c) In all types of hypothesis there are two types of errors that can be committed. The first is called the Type I error and refers to the situation where we incorrectly reject H₀ when in fact it is true. This is called a false positive result ( as we incorrectly conclude that the research hypothesis is true when in fact it isn't). A Type I error() is the probability of rejecting a true null hypothesis.

When we run a test of hypothesis and decide not to reject H₀ then either we make a correct decision because the null hypothesis is true or we commit a Type II error. Type II error () is the probability of failing to reject a false null hypothesis.