At low speeds fuel consumption may be higher due to increased idle time and frequent acceleration and deceleration. Studies show that fuel consumption tends to be higher at both low and high average urban speeds. The goal is to determine the optimal speed for maximum fuel economy and, as a result, reducing harmful emissions into the atmosphere. Recently there has been a lot of research on the efficient use of road transport in urban areas. So the better-fitting model in this case is the quadratic model. These are significantly lower results that indicate only a moderate correlation which can also be seen from the respective graphs. If we now plug the initial data into our Linear Regression Calculator and Exponential Regression Calculator we well get respectively \(R = 0.623\) and \(R = 0.643\). The value of the correlation coefficient \(R = 0.814\) also indicates that the data points are in strong correlation. $$a\sum _\) and \(R = 0.814.\)Īs you can see from the above graph, the approximating curve is in good agreement with the scatter of points from the data table. These lead to the following set of three linear equations with three variables: The condition for the sum of the squares of the offsets to be a minimum is that the derivatives of this sum with respect to the approximating line parameters are to be zero. Now we can apply the method of least squares which is a mathematical procedure for finding the best-fitting line to a given set of points by minimizing the sum of the squares of the offsets of the points from the approximating line. In particular, we consider the following quadratic model: The quadratic regression is a form of nonlinear regression analysis, in which observational data are modeled by a quadratic function.
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