Generate and explain the derivation of insights using regression analysis and its associated visualization.CO 5: Differentiate between the signals identified by business analytics and the noise that is inherent in the system.X: C18 (total employees hours worked per week) versus Y: C19 (clinic patients seen per week)C1882235405773788798C196.169.8814.3524.0630.3432.1742.1843.2348.76

Answered: Generate and explain the derivation of…

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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Generate and explain the derivation of insights using regression analysis and its associated visualization.
CO 5: Differentiate between the signals identified by business analytics and the noise that is inherent in the system.

X: C18 (total employees hours worked per week) versus Y: C19 (clinic patients seen per week)

C18
8
22
35
40
57
73
78
87
98

C19
6.16
9.88
14.35
24.06
30.34
32.17
42.18
43.23
48.76

Expert Solution

Step 1

Since, patients seen are dependent on the total employees hours worked per week, therefore, the regression model is Y=a+bX

To find the regression equation:

$\begin{array}{rcl} x & = & \frac{\sum_{i = 1}^{n} x_{i}}{n} \\ = & 55.333 \end{array}$

$\begin{array}{rcl} y & = & \frac{\sum_{i = 1}^{n} y_{i}}{n} \\ = & 27.903 \end{array}$

Then,

$\begin{array}{rcl} r_{x y} & = & \frac{\sum_{i = 1}^{n} (x_{i} - x) (y_{i} - y)}{\sqrt{[\sum_{i = 1}^{n} {(x_{i} - x)}^{2}] [\sum_{i = 1}^{n} {(y_{i} - y)}^{2}]}} \\ = & 0.98315 \end{array}$

and

$\begin{array}{rcl} s_{x} & = & \sqrt{\frac{\sum_{i = 1}^{n} {(x_{i} - x)}^{2}}{n - 1}} \\ = & 30.927 \end{array}$

$\begin{array}{rcl} s_{y} & = & \sqrt{\frac{\sum_{i = 1}^{n} {(y_{i} - y)}^{2}}{n - 1}} \\ = & 15.386 \end{array}$

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