Unweighted Linear Regression with Errors in

The most commonly used form of linear regression is based on three assumptions (1) that any difference between the experimental data and the calculated regression line is due to indeterminate errors affecting the values of y, (2) that these indeterminate errors are normally distributed, and (3) that the indeterminate errors in y do not depend on the value of x. Because we assume that indeterminate errors are the same for all standards, each standard contributes equally in estimating the slope and y-intercept. For this reason the result is considered an unweighted linear regression. 

Finding the Estimated Slope andy-Intercept The derivation of equations for calculating the estimated slope and y-intercept can be found in standard statistical texts and is not developed here. The resulting equation for the slope is given as 

Residual error in linear regression, where the filled circle shows the experimental value/, and the open circle shows the predicted value/,. 

Although equations 5.13 and 5.14 appear formidable, it is only necessary to evaluate four summation terms. In addition, many calculators, spreadsheets, and other computer software packages are capable of performing a linear regression analysis based on this model. To save time and to avoid tedious calculations, learn how to use one of these tools. For illustrative purposes, the necessary calculations are shown in detail in the following example. 

Using the data from Table 5.1, determine the relationship between by an unweighted linear regression. 

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