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Simple Linear Regression Model. These videos will help you understand all basic proofs and theorems related to it.  We discuss following issues in these videos

Normal equations simple linear regression model

We start by deriving normal equations in a simple linear regression model and get the OLS estimates of constant and slope parameter

Beta two hat simplification

In the earlier video, we derived some messy estimate of slope parameter. Here, we try to derive its simpler version.

Regression line will pass through sample means

In this video, we explain how regression line will pass through sample means. For Yt = β1 + β2Xt + ut , β1^ and β2^ will pass through mean of x and mean of y.

Mean value of est Y is equal to mean value of actual Y

Here, we prove how estimated value of Y is equal to mean value of Y.

Mean value of residuals is equal to zero

On an average, residuals are zero. Here, we make use of first normal equation to prove this.

Sample regression function in deviation form

Most of the proofs become simpler, when tackled in deviation, instead of, actual form. Deviation form means, all variables will be deviation from their respective means.

Residuals are uncorrelated with predicted y

In order to prove this, we make use of deviation form.

Unbiasedness of slope estimator

This is one of the most important concept. Here, we prove that OLS estimate of slope parameter on an average, will be equal to true parameter value.

Variance of slope parameter

In the last recording we have found expectation of slope parameter, here we try to find, variance of slope parameter. This will be used in efficiency property of OLS estimates

Gauss Markov Theorem

Under the class of linear, unbiased, efficient estimators, OLS estimators have minimum variance. This is the classic Gauss Markov theorem, which we present here

Computation of R2

Here, we discuss what is R2? How do you compute it? Is R2 in a simple linear regression model equal to r2 of correlation?

 

Normal equations simple linear regression model

Beta two hat simplification

Regression line will pass through sample means

Mean value of est Y is equal to mean value of actual Y

Mean value of residuals is equal to zero

Sample regression function in deviation form

Residuals are uncorrelated with predicted y

Unbiasedness of slope estimator

Variance of beta two hat

Gauss markov theorem part 1

Gauss markov theorem part 2

Computation of R2 Part 1

Computation of R2 Part 2