A Statistical Study on the Slope of a Line for Data Related to Height-Weight and COVID Infections-Recoveries

Abstract

The slope of the line reveals changes in y-coordinate with respect to x-coordinate, represented by the equation “y=mx+c”, known as the equation of a line. The slope m is of significance in several areas including artificial intelligence and regression analysis where it helps in predicting the response by using one known value of the predictor. Our aim here is to predict the average value of y for a given value of x. A related analysis has been discussed in. To begin the analysis, we take data of two dependent sets. The data analysed relate to height-weight and COVID infections recoveries. We first initialize the value of k which is the range for our discrete uniform probability distribution U[1,2,3…k] as discussed in the paper. The probability variate is used to generate 30 random numbers using the formula u = 1+integral part of (r*k) where r is a continuous U[0,1] variate. This formula gives 30 independent U[1, 2…k] variates; k is then incremented by 30 after each run. We run the loop for 6 times and for every k we have the values of m (slope of the line) and c (constant) which are calculated by the Least Squares Method discussed in. Using the values of m, c and x we estimate the value of y which is referred to as the y-estimate. Every regression equation gives some error; in order to find the error, we subtract the estimated y from the observed y. To see the change, we use the method of plotting. The graphs of k versus m and k versus c are plotted. The experimental results show that 
• In case of height and weight data. the values of m and c do not depend on the discrete uniform variate’s range k.
 • In case of COVID infections and recoveries data, the regression equation depicts a quadratic pattern for both m and c which depend on k.