Regression Project: Price

Regression Project: Price

Estimation of the regression model, there is a need to analyze the data provided. The model will be dependent on the value x, which is the demand for widgets. Additionally, a constant value, b, will also play a role in determining the price at any given demand. The explanation herein shows that a linear equation with price as the dependent variable and demand as the independent variable is required. Using the tabulated data, then the steps are as follows. First, take two arbitrary values of demand and the corresponding price values. Using these two random values assume that the function expects the general form of p (x) = m x + b, where m is the slope of the regression function plot, and b is a constant.

Using the two arbitrary pairs, estimate the value of the slope. It will be given by the difference between the values of price divided by the difference between the corresponding values of demand. Based on the values (20,133) and (100,53), the result is, the difference for the price is 80 while the difference for demand is also 80. Therefore, the slope of the line is -1. To proceed with the derivation, substitute the value obtained with m. The function becomes p (x) = -x + b. The value (20,133) can be substituted into the function to help find the value of b, which is a constant. The function becomes 133 = -20 + b. By simplifying this, it can be found that b is 153. This may not be the exact value as only one value of the function has been used, thus affecting the accuracy detrimentally. Finally, it is possible to derive that the function is p (x) = -x + 153.

From the data provided, a scatter plot for the data can easily be obtained. To confirm whether the function obtained from the previous step is a fitful model of the data, the scatter plot, and a plot of the function are included in the same axis below.

Price of Widgets

Figure 1: A graph of the price of widgets against the annual widget demand.

From the plot above, it is rather clear that the function may not be the line of best fit, but is a proper model for the data. Most of the data points lie above the line of the function. However, several points lie on the line, and the rest lie close enough to it. It leads to the deduction that the regression function is a fitful representation of the relationship between price and demand.

The regression function can be used in finding the values of the price at different points, including those that are not provided as data points. For instance, the feature can be used in finding the price at the demand being 0. This is done by substituting x with 0 in the function. Thus, we obtain a cost of $153. The rationale behind this value is that at $153, there would be no demand for the product.

On the other hand, when the demand is 35, we have the function as p (x) = -35 + 153; this yields price to be $118. Finally, at the demand of 105 units, we find the amount using the function p (x) = -105 + 153. The result becomes; cost is $48. Conversely, the rationale behind this is that for $48, the demand would exceed the production.

Obtaining the demand for the price p(x)=0 requires one to substitute 0 in the function. Here we have 0 = -x + 153. Therefore, the value of x at this point would be 153. It means that if the widgets were given out for free, only 153 purchases would be made annually. This is dependent on the units for demand.