1. Compute the coefficient of determination r2. Comment on the goodness of fit.2. Compute the correlation coefficient.3. Use the t test to test the following hypothesis β1 = 0 at α = .05. **Predictive Analysis of Photocopy Paper Usage**Peter Thompson, responsible for office supplies at Top Hill Estates, aims to predict the quantity of paper used in office photocopying machines each month. He hypothesizes that the number of clients seen monthly influences the volume of photocopying performed. Below is the recent monthly data he has compiled. This analysis requires the use of Excel.| Number of Clients in a Month | Sheets of Photocopy Paper Used (in thousands) ||------------------------------|----------------------------------------------|| 40 | 24 || 26 | 12 || 50 | 25 || 54 | 26 || 40 | 22 || 23 | 15 || 34 | 22 || 52 | 26 |**Data Explanation:**- **Column 1**: Represents the number of clients seen in a month, showing a range from 23 to 54 clients.- **Column 2**: Indicates the corresponding sheets of photocopy paper used in thousands. For instance, with 40 clients, 24,000 sheets are used, while with 26 clients, 12,000 sheets are necessary.This data can be used to establish a correlation between the number of clients and the paper usage, which can then be applied to predict future trends. Excel tools such as scatter plots, trend lines, and regression analysis may be useful for this purpose.

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Answered: 1. Compute the coefficient of…

1. Compute the coefficient of determination r2. Comment on the goodness of fit. 2. Compute the correlation coefficient. 3. Use the t test to test the following hypothesis β1 = 0 at α = .05.

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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Assume that we estimated the following model by OLS: y =β₁ + β₂x + u.The sample size of the data is n=62. We calculated that the standard errors for β₁ and β₂ are se(β₁)=1 and se(β₂)=2. Also, the estimates for β₁ and β₂ are β₁=3 and β₂=5. We want to test: H₀ : β₂=0 H₁ : β₂≠0.for α=0.05 significance level. What is the t statistic? [We denote the estimates by bold font]
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