Continuous Energy produced (kW hours) Working hours The large dam is designed by you. The energy produced by two Francis Turbines that can be used in the dam versus their continuous working hours is measured and given in Table 1. 18 513 20 598 22 568 23 513 23 468 25 493 27 568 28 513 29 32 468 413 a) Plot a graph and obtain the linear relationship between energy and working 37 428 hours for the turbine. 41 463 46 b) Estimate the variance, obtain the determination and correlation coefficients 49 383 for the relation that you establish between the energy and working hours. Comment on the accuracy of your model considering these parameters. 53 468 55 423 63 358 c) Estimate the missing values in Table 1 using your linear regression model. 65 423 66 308 d) Estimate the percent error of your model for the working hour of 75 hours. Comment on the accuracy of your model considering the percent error. 67 413 68 308 70 393 e) Comment on the energy production of Francis Turbines depending on their working hours. What changes can you offer? 71 328 72 373 73 288 74 75 463 77 368 79 313 82 368

Continuous Energy produced (kW hours) Working hours The large dam is designed by you. The energy produced by two Francis Turbines that can be used in the dam versus their continuous working hours is measured and given in Table 1. 18 513 20 598 22 568 23 513 23 468 25 493 27 568 28 513 29 32 468 413 a) Plot a graph and obtain the linear relationship between energy and working 37 428 hours for the turbine. 41 463 46 b) Estimate the variance, obtain the determination and correlation coefficients 49 383 for the relation that you establish between the energy and working hours. Comment on the accuracy of your model considering these parameters. 53 468 55 423 63 358 c) Estimate the missing values in Table 1 using your linear regression model. 65 423 66 308 d) Estimate the percent error of your model for the working hour of 75 hours. Comment on the accuracy of your model considering the percent error. 67 413 68 308 70 393 e) Comment on the energy production of Francis Turbines depending on their working hours. What changes can you offer? 71 328 72 373 73 288 74 75 463 77 368 79 313 82 368

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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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

Continuous
Energy
produced
(kW
hours)
Working
The large dam is designed by you. The energy produced by two Francis
hours
Turbines that can be used in the dam versus their continuous working hours is
measured and given in Table 1.
18
513
20
598
22
568
23
513
23
468
25
493
27
568
28
513
29
468
32
413
a) Plot a graph and obtain the linear relationship between energy and working
37
428
hours for the turbine.
41
463
46
b) Estimate the variance, obtain the determination and correlation coefficients
for the relation that you establish between the energy and working hours.
49
383
53
468
Comment on the accuracy of your model considering these parameters.
55
423
63
358
c) Estimate the missing values in Table 1 using your linear regression model.
65
423
66
308
d) Estimate the percent error of your model for the working hour of 75 hours.
Comment on the accuracy of your model considering the percent error.
67
413
68
308
70
393
e) Comment on the energy production of Francis Turbines depending on their
working hours. What changes can you offer?
71
328
72
373
73
288
74
75
463
77
368
79
313
82
368

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