Design and Analysis of Urban Land Lease Price Predicting Model Using Batch Gradient Descent Algorithm

Abstract

Standard and econometric models are appropriate for causal relationships and interpretations among facets of the economy. But with prediction, they tend to over-fit samples and simplify poorly to new, undetected data. This paper presents a batch gradient algorithm for predicting the rice of land with large datasets. This paper uses a batch gradient descent algorithm to minimize the cost function,  iteratively with possible combinations of the number of iterations i=1500 and learning rates, of 0.01, 0.02, 0.03 for the linear regression case and i = 100, 0.3, 0.2, and 0.1 for the multiple regression case. The paper uses Octave-4.0.3(GUI) for implementing 129 samples of the lease bid price of Mekelle City as training sets and feature inputs of two and three for linear regression and multiple regressions. Using  = 0.01, the best fitting parameters found by training the dataset are with a cost of J=67.82. The model predicts with an accuracy of 92.6% using LR and 91.15% using MLR for a 315 m² land size. As the learning rate increases, the fitting parameters increase and decrease respectively with an equal cost but the model’s prediction error increments slowly. With multiple regression, as the learning rate lowers, the model under fits prediction drastically (with an accuracy of 60%) with gradient descent and predicts with an accuracy of 91.5% with ordinary equations. So, prediction with ordinary equations provides the best fit for multiple regressions.