Degree of Freedom

Degree of freedom It is the number of independent observations used to obtain a

sum of squares. For example, 3yi

2 has n-1 degrees of freedom because we must

first calculateY6 . A sum of squares divided by the number of degrees of freedom

gives the variance. The t tests and the F tests are done taking account of the

degrees of freedom..

b) Normal distribution. It is the probability distribution whose density function has

the shape of a bell. Many statistical phenomena can be represented by a normal

distribution (because of the central limit theorem). In the regression model, one of

the assumptions is that ui follows a normal distribution with mean 0 and variance

F2. The assumption of the normal distribution is necessary to do the hypothesis

testing in the regression model.

c) t-distribution. It is a probability distribution that is related to the normal

distribution. The t distribution has the shape of a bell curve like the normal

distribution, but its tails are thicker. When the sample is small and the variance of

the parameter must be estimated, we use the t distribution to do the hypothesis

tests on the parameter. When the number of degrees of freedom is large, the t

distribution tends towards the normal distribution.

d) Unbiased estimator. It is an estimator whose mean (or expectation) is equal to the

true value of the parameter. If we took a large number of samples from the

population and if we estimated the parameters each time, we would get on

average the true value. Unbiasedness is a desirable property for an estimator. In

the linear regression model, it can be shown, if we make the proper assumptions,

that b$0 and b$1 are unbiased.

e) Analyse ofvariance. Statistical method that consists in comparing two variances

by taking their ratio. The result follows an F distribution with degrees of freedom

in the numberator and the denominator corresponding to those two variances.. In

the regression model, the method of analysis of variance is used to test the overal