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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

Observed Random Process

Let {x_n} be an observed random process which is generated by the following nonlinear recursion x_n = (theta_1)(x_n-1) + (theta_2g)(x_n-2, x_n-3) + w_n where {w_n} is an i.i.d. zero-mean sequence and g(.,.) is a known deterministic function. We are interested in estimating the two parameters theta_1, theta_2. (a) Propose a

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

Stats prob

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

Creating a Least Squares Equation

Listed below is the net sales in $ million for Home Depot, Inc. and its subsidiaries from 1993 to 2002. Year Net Sales 1993 9,239 1994 12,477 1995 15,470 1996 19,535 1997 24,156 1998 30,219 1999 38,434

Least Squares Sale Data

If the least squares equation for sales data going from 1984 to 1990 is Y1 = 10 + 1.3X (in $ millions) found using the coded method, what is the plot on the straight line for 1988? (x and y values)