**Educational Content on iPod Touch Pricing and Demand**The iPod Touch has been on the market for several years, and significant data has been collected regarding its pricing and demand. Below is a table illustrating the relationship between the *Price of an iPod Touch* and its *Weekly Demand*:| Price $P$ ($) | Weekly Demand $S$ (1,000s) ||-----------------|-----------------------------|| 150 | 212 || 170 | 207 || 190 | 193 || 210 | 186 || 230 | 176 || 250 | 174 |**Instructions:****A.** Use regression analysis to determine the linear model that best fits this data. Round the slope value to the nearest 0.01 and the constant parameter to the nearest 1.\[ T(p) = \underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \]**B.** Based on your model, predict the weekly demand if the price of an iPod Touch is $231.*Round your answer to the nearest 100.***C.** According to the model, determine the price necessary to achieve a weekly demand of 180,100 iPod Touches.*Round your answer to the nearest $1.*

Let us define the independent (x) and dependent (y) first. Let , P be the independent (predictor) variable . That is , P = Price of an IPOD touch. And S be the dependent (response) variable. That is , S = Weekly Demand. It is asked to find The regression equation. Find weekly demand if the price of an IPOD touch is $231. Find price if weekly demand of 180,100 IPOD touches.It is asked to find the regression equation for the given data. That is , the equation of the least squares line is required. It can be easily drawn by using MS-Excel. Please refer the following steps to draw regression equation in excel. Enter P and S data set in excel. Select "Data" from the toolbar. The "Data" menu displays. Select "Data Analysis". The Data Analysis - Analysis Tools dialog box displays. From the menu, select "Regression" and click "OK". In the Regression dialog box, click the "Input Y Range" box and select the weekly demand. Click the "Input X Range" box and select the independent variable as price. Click "OK" to run the results. The regression output will be immediately inserted in your worksheet and it will looks like, From this output , Intercept = 274.1905 rounded this figure up to nearest one decimal places it would be 274.2. X Variable 1 = -0.41429 rounded this figure to nearest 0.01 it would be -0.41. Thus , the Regression equation is , S = T(P) = Intercept + Slope* P S =T(p) = 274.2 - 0.41 P. It is asked to find the model predict will be the weekly demand if the price of an IPOD touch is $231. That is , P = $231 and asked to find S. Here we know the regression equation so plug the value of P and solve for S. Therefore , S = 274.2 - 0.41*P =274.2 *0.41($231)=179.49 Thus , the predicted value is equal to $179.49. It is asked to find the price to be set in order to have a weekly demand of 180,100 IPOD touches. That is, S = 180,100 and asked to find P. Here we know the regression equation so plug the value of weekly demand and solve for P Therefore , 180,100 = 274.2 - 0.41*P180,100 - 274.2 = -0.41P179825.8 = -0.41PP = $-438600. Thus , the price to be set in order to have a weekly demand of 180,100 IPOD touches is $-438599.5.

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Statistics

A. Find the linear model that best fits this data using regression and enter the model below (for entry round the slope value to nearest 0.01 and constant parameter to nearest 1) T(p) = Now answer these two questions: B. What does the model predict will be the weekly demand if the price of an ipod touch is $231 ? (nearest 100) C. According to the model at what should the price be set in order to have a weekly demand of 180,100 ipod Touches? $ (nearest $1)

A. Find the linear model that best fits this data using regression and enter the model below (for entry round the slope value to nearest 0.01 and constant parameter to nearest 1) T(p) = Now answer these two questions: B. What does the model predict will be the weekly demand if the price of an ipod touch is $231 ? (nearest 100) C. According to the model at what should the price be set in order to have a weekly demand of 180,100 ipod Touches? $ (nearest $1)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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