Linear equation

4 The Simplex Method As we have seen, a linear programming problem forms a convex polygon in the best possible scenario. It is imperative to obtain a process that would assist in determining the optimal solution without the need to examine the graphical representation. The need for an algorithm that would perform such process was essential in the early days of the formulations of linear programming problems. Although challenging, the task was accomplished by a mathematician of the twentieth…

expansion in general. After that, I will introduce Jade Mirror of the Four Unknowns written by Zhu Shijie around 14th century AD. My focus will be his idea of using the “four unknowns” to convert a problem into a mathematical system of polynomial equations. Later on, I will also…

Chemical kinetics are governed by the mathematics of systems of differential equations (Thermodynamics and Kinetics). This means that the rate of any chemical reaction is determined by the type, and amount, of reactants present. Note the rate of a reaction is how fast it occurs. Furthermore, such rate equations can either be distinctively linear or non-linear when graphed. Non-linear equations are supposedly more complex as they generally react to small changes within its parameters…

determined when the linear regression analysis was used, showing the acceleration, acceleration standard error, intercepts, and Intercept Standard Errors of the truck shown below. Acceleration, a (m/s) Acceleration Standard Error [±m/s^2] Intercept [m/s] Intercept Standard Error [±m/s] 0.4750 0.01182 0.06267 0.2200 The residual mean and the residual standard error have also been calculated. This has been displayed in Table 5. Table 5 –The results that were determined when the linear…

Linear programming which is also known as “Linear Optimization” is a way to achieve best outcomes in a Mathematical Model using different linear solutions .Linear Programming is a special case of Mathematical Optimization .Linear programming can be applied to a wide variety of fields of study, and has proved useful in planning, routing, scheduling, assignment, and design, such as in transportation or manufacturing industries. The method of Linear Programming was originally developed by American…

of three months. Notably, forecasting entails application of simple linear regression in order to understand the underlying relationship between sales volumes and number of hits on the company’s website. In this case, an Excel worksheet is used to analyze the data, and to forecast the sales based on the data collected on the number of hits. Chase (2013) explains that forecasting in business scenarios entails…

an increase from the projected sales by $8000 dollars. This increase would equate to a 2.7% change from the forecast and within the 3.6% standard error percentage. The data in this forecast model is built the correlation between the seasonal and linear yearly growth of sales for C’mon Back Restaurant. This model assumes no other independent variable which could impact sales. As Puerto Rico is a Caribbean nation, it is subject to severe weather patterns, hurricanes. The impact of a hurricane…

Contrary to sigmoidal response hypothesized previously for ramped stimulus, we observed opposite pattern i.e. inverse sigmoid pattern in BOLD response. A new biophysical model was proposed to account for this non-linearity. We found that the non-linear model showed improved r2 which is an indicator of good ness of fit for a model. This would suggest that the new proposed model better describes the BOLD response. We then investigated the age long variation in the fitted parameters in BOLD…

Linear Regression By p Nitin Feb 16, 2013 Linear Regression Definition states that it can be measured by using lines of regression. Regression measures the amount of average relationship or mathematical relationship between two variables in terms of original units of data. Whereas, correlation measures the nature of relationship between two variables. i.e.., positive or negative or uncorrelated. Regression is used for estimating the value of one variable if you know the value of other variable.…

Scatter Diagram In Figure 1, the straight line fits through the data plotted below showing that a positive linear relationship exists. The small scatter around the line shows the strong linear correlation as well as positive slope. Figure 1: Scatter diagram showing strong positive linear relationship 3. The estimated linear equation is Yi = b0 + b1X1 + e1, where Y is the estimated dependent value for the observation, X is the estimated independent variable for the observation…