Derive the ordinary least squares estimator in case of multiple regression analysis

Expert Solution

The ordinary least squares (OLS) estimator for the simple linear regression case, only one independent variable (only one x), was derived. The procedure relied on combining calculus and algebra to minimize of the sum of squared deviations.

The simple linear case although useful in illustrating the OLS procedure is not very realistic. Rarely, are you interested in only one independent variable’s potential affect on the dependent variable, y.

For example, if interested forecasting sales for your would you find only own price in the econometric forecasting equation(s). Other factors such as competitors’ price and the general state of the economy will affect your sales.

This more realistic case, more than one independent variable, is the subject of this reading assignment. The OLS estimator is derived for the multiple regression case. Multiple regression simply refers to the inclusion of more than one independent variable.

orchestra answered 2 years ago

what is the regression technique of ordinary least squares?

Describe the two assumptions used in class to derive the ordinary least squares estimates of the...

Describe the two assumptions used in class to derive the ordinary least squares estimates of the intercept and slope. Why are these assumptions important and what do they mean? Which assumption is needed to estimate each parameter?

. Under the Gauss-Markov assumptions, we know that the Ordinary Least Squares (OLS) estimator βˆ is...

. Under the Gauss-Markov assumptions, we know that the Ordinary Least Squares (OLS) estimator βˆ is unbiased, efficient, and consistent. However, if the assumption that E[ϵ 2 i |X] = σ 2 i = σ 2 is violated while the assumption of E[ϵi , ϵj ] = 0 , ∀i ̸= j holds, that the least squares estimator is unbiased but is no longer efficient. The Generalized Least Squares (GLS) estimator, in this case, may be unbiased, consistent, and efficient...

State the ordinary least squares (OLS) estimation criterion. State the OLS normal equations. Derive the...

State the ordinary least squares (OLS) estimation criterion. State the OLS normal equations. Derive the OLS normal equations from the OLS estimation criterion. Perform a test of the null hypothesis H0:β2 = 0 against the alternative hypothesis H1:β2 ≠ 0 at the 1% significance level ( i.e. for significance level α = 0.01 ). Show how you calculated the test statistic. State the decision rule you use, and the inference you would draw from the test. Briefly explain what...

Why would researchers believe that an ordinary least squares regression is superior to a partial correlation...

Why would researchers believe that an ordinary least squares regression is superior to a partial correlation coefficient?

Whywould researchers believe that an ordinary least squares regression is superior to a partial correlation coefficient?

3) Derive the matrix equation used to solve for the coefficients for least-squares polynomial regression for...

3) Derive the matrix equation used to solve for the coefficients for least-squares polynomial regression for a quadratic model. 4) Derive the matrix equation used to solve for the coefficients for least-squares multiple linear regression for a function of 2 variables.

In simple linear regression analysis, the least squares regression line minimizes the sum of the squared...

In simple linear regression analysis, the least squares regression line minimizes the sum of the squared differences between actual and predicted y values. True False

What are Least Squares Assumptions for simple linear regression? For each least squares assumption, provide an...

What are Least Squares Assumptions for simple linear regression? For each least squares assumption, provide an example in which the assumption is valid, then provide an example in which the assumption fails.

According to Pollock and Edwards, a multiple regression analysis contains at least __ independent variables a....

According to Pollock and Edwards, a multiple regression analysis contains at least __ independent variables a. 0 b. 1 c. 2 d. none of the above According to Pollock and Edwards, the .05 threshold suggests that researchers wish to commit _____ less than five times out of 100 tests. a. individual fallacy b. Type I error c. Type II error d. ecological fallacy According to Pollock and Edwards, a p-value determines the exact probability of obtaining the observed sample difference...

Question