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Ordinary Least Squares

Ordinary least squares is a method for estimating the unknown parameters in a linear regression model. This method minimizes the sum of squared vertical distances between the observed responses in the dataset and the responses predicted by the linear approximation. The resulting estimator can be expressed by a simple formula, especially in the case of a single regressor on the right hand side. The ordinary least square estimator is consistent when the regressors are exogenous and there is no perfect multicollinearity, and optimal in the class of linear unbiased estimators when the errors are homoscedastic and serially uncorrelated. Ordinary least square is the maximum likelihood estimator.

There are many frameworks in which the linear regression model can be cast in order to make the ordinary least square technique applicable. Each of these settings produces the same formulas and same results; the only difference is the interpretation and the assumptions which have to be imposed in order for the method to give meaningful results. One of the lines of difference in interpretation is whether to treat the regressors as random variables, or as predefined constants.

Ordinary least squares analysis often includes the use of diagnostic plots designed to detect departures of the data from the assumed form of the model. Residuals against the explanatory variable, residuals against explanatory variables, residuals against the fitted values and residuals against the preceding residuals are common diagnostic plots. 

Linear regression equation between torque and diameter

4. The torque, T Nm, required to rotate shafts of different diameters, D mm, on a machine has been tested and recorded below. D(mm) 6 10 14 18 21 25 T(Nm) 5.5 7.0 9.5 12.5 13.5 16.5 (a) Plot a scatter diagram of the results with diameter of the machine as the independent variable. (b) Use the me

Statistics: The Least Squares Equation

Listed in the attached file is the net sales in $ million for Home Depot, Inc. and its subsidiaries from 1993 to 2002. Task: Determine the least squares equation. On the basis of this information, what are the estimated sales for 2005?

Least Squares Line and Predicting Sales Performance

For the past 12 months, your real estate company has been requiring applicants for employment as sales agents to take an aptitude test, which it is hoped will predict the person's ability to sell. The results of the aptitude test have not been made available to the people who make the hiring decisions. The applicants who have

Least Squares Trend in Annual Glass Production

The following table lists the annual amounts of glass cullet produced by Kimble Glass Works, Inc. Year Code Scrap (tons) 1999 1 2.0 2000 2 4.0 2001 3 3.0 2002 4 5.0 2003 5 6.0 Determine the least squares trend equation. Est