# Simple Regression Analysis

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Introduction to Regression Analysis

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Regression analysis has been employed as serious evidence by lawyers and other individuals in the legal field. For instance, in the 1964 Civil Rights Act under Title VII, it was used to prove contract actions damages, biasness with regard to race in litigating death penalties and others.
The difference between multiple and simple regression is that for multiple regression, earnings are affected by much more factors in addition to years spent in school while simple regression just assumes that an individual’s earnings are affected solely by the years spent schooling.
Usually omitted variables are likely to result from simple regression because not all variables
One such alternative include minimizing the summation of errors in absolute quantities.
According to Sykes, unbiasedness is when a parameter’s true value equals the mean of probability distribution. He states that consistency is comparison of different estimators that are unbiased and finding the lowest variance. He also defines consistency as generation of accurate estimates by taking advantage of extra data.
The difference in interpretation of coefficient estimates is that multiple regression has the coefficients γX while simple regression does not
Lower variance is an attractive property for an estimator because it lowers the probability of an estimate being far from the true value.
The assumptions about the noise term which makes the estimator obtained by application of the minimum SSE criterion BLUE is that it is taken from a distribution with a mean of zero and also the distributions from which the noise terms are derived have the same variance.
According to Sykes, the logic behind the t-test is that we formulate a hypothesis. We can either accept or reject the hypothesis depending on where the t-statistic falls, that is, in the uppermost of lowermost tail of the
A coefficient is statistically significant if null hypothesis is dismissed after determining that the significance level would not arise more than 1, 5 or 10 percent of the time the null hypothesis holds true.
The critical value of the t-statistic is a section on the t-distribution which is put in comparison with the statistic test to decide whether or not to dismiss the hull hypothesis
P-value is the probability of getting a result either on the extreme or equal to the actual observation when null hypothesis is true
Omitted variable problem is when there is exclusion of variables affecting the dependent variable thereby interfering with the ability of SSE criterion being an estimator that is unbiased.
An example of perfect multicollinearity used in the lecture is the data on the speeches made by Picker and Baird with a correlation of 1. The problem that may arise in imperfect multicollinearity is that it may not be possible to make estimations on the speeches given by each
The problem of measurement error is called observational error. It is the difference a true value and a measured

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