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The following table shows observed electrical power consumption at several different levels of a...

Question:

The following table shows observed electrical power consumption at several different levels of a factory's operation.

Level 2 3 5 7
Power 1 3 3 5

Engineers want to fit the estimating relationship

power ={eq}\beta_0 + \beta_1 {/eq} level

to these data in a way that minimizes the sum of the absolute deviations between predicted and observed power requirements. Both parameters {eq}\beta _0 {/eq} and {eq}\beta _1 {/eq} should be nonnegative.

(a). Formulate an LP to choose optimal parameter values.

Mean Absolute Deviation

Mean absolute deviation is a measure of variability between the observed value and the predicted value .The aim is to minimize the sum of squares of error but here the total variation is more as the difference are taken in absolute terms.

Answer and Explanation: 1

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Given Information:

Here the number of observations is 4.

Let the predicted value be denoted by {eq}{\hat \beta _0} \ and \ {\hat \beta _1}. {/eq}

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Absolute & Relative Error: Definition & Formula

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Chapter 6 / Lesson 7
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Did you know that measuring tools are not 100% accurate? Read this lesson to learn more about the accuracy of measuring tools and how this influences the absolute and relative error of measurements.


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