Questions: Figure 1 shows a typical composition of neurons in a net. This discussion questions aimed at learning how natural composition of neural nets can be mimicked to derive algorithms that can provide prediction at higher levels of complexity. Consider a multiple regression model of your choice containing two predictors. Calculate the values of the regression equation with a range chosen by you for the values of the predictors. Provide the graph of the regression equation which is a plane. Augment your regression model by a sigmoid posterior filter. Calculate the values of the regression equation within the range chosen in part 1. Provide the graph of the regression equation, which will be a sigmoidal surface. Show that this graph cannot have a local extremum. Now, add another regression model with sigmoid posterior containing the same two predictors in the previous part. Repeat parts 1 and 2 for this new regression model.  Now consider a model of a neural net, which has two parallel hidden layers, which are the two regression models considered above. The output of the net is simply the superposition of the two regression models. Show that by proper choice of the parameters you can have an output, which has a local extremum within the choice for the range of the values of the predictor. Provide the graph of the regression equation.  How does this observation indicate an application of neural networks modeling in practice?     Figure 1 Typical Composition of Neurons in a Net Bowerman, B., Drougas, A. M., Duckworth, A. G., Hummel, R. M. Moniger, K. B., & Schur, P. J. (2019). Business statistics and analytics in practice (9th ed.). McGraw-Hill ISBN 9781260187496

Overview Recall that samples are used to generate a statistic, which businesses use to estimate the population parameter. You have learned how to take samples from populations and use them to produce statistics. For two quantitative variables, businesses can use scatterplots and the correlation coefficient to explore a potential linear relationship. Furthermore, they can quantify the relationship in a regression equation. Prompt This assignment picks up where the Module Two assignment left off and will use components of that assignment as a foundation. You have submitted your initial analysis to the sales team at D.M. Pan Real Estate Company. You will continue your analysis of the provided Real Estate Data spreadsheet using your selected region to complete your analysis. You may refer back to the initial report you developed in the Module Two Assignment Template to continue the work. This document and the National Statistics and Graphs spreadsheet will support your work on the assignment. Note: In the report you prepare for the sales team, the dependent, or response, variable (y) should be the listing price and the independent, or predictor, variable (x) should be the square feet. Using the Module Three Assignment Template, specifically address the following: Regression Equation: Provide the regression equation for the line of best fit using the scatterplot from the Module Two assignment. Determine r: Determine r and what it means. (What is the relationship between the variables?) Determine the strength of the correlation (weak, moderate, or strong). Discuss how you determine the direction of the association between the two variables. Is there a positive or negative association? What do you see as the direction of the correlation? Examine the Slope and Intercepts: Examine the slopeb1{"version":"1.1","math":"b1"} and intercept b0{"version":"1.1","math":"b0"}. Draw conclusions from the slope and intercept in the context of this problem. Does the intercept make sense based on your observation of the line of best fit? Determine the value of the land only. Note: You can assume, when the square footage of the house is zero, that the price is the value of just the land. This happens when x=0, which is the y-intercept. Does this value make sense in context? Determine the R-squared Coefficient: Determine the R-squared value. Discuss what R-squared means in the context of this analysis. Conclusions: Reflect on the Relationship: Reflect on the relationship between square feet and sales price by answering the following questions: Is the square footage for homes in your selected region different than for homes overall in the United States? For every 100 square feet, how much does the price go up (i.e., can you use slope to help identify price changes)? What square footage range would the graph be best used for?