In this tutorial, we discuss how to do a regression analysis in Excel. I will teach you how to activate the regression analysis feature, what are the functions and methods we can use to do a regression analysis in Excel and most importantly, how to interpret the regression analysis results. Source: https://tinytutes.com/tutorials/regression-analysis-in-excel/
Matrix theory" redirects here. For the physics topic, see Matrix string theory.
An m × n matrix: the m rows are horizontal and the n columns are vertical. Each element of a matrix is often denoted by a variable with two subscripts. For example, a2,1 represents the element at the second row and first column of the matrix.
In mathematics, a matrix (plural matrices) is a rectangular array[1] (see irregular matrix) of numbers, symbols, or expressions, arranged in rows and columns.[2][3] For example, the dimension of the matrix below is 2 × 3 (read "two by three"), because there are two rows and three columns:
{\displaystyle {\begin{bmatrix}1&9&-13\\20&5&-6\end{bmatrix}}.}{\displaystyle {\begin{bmatrix}1&9&-13\\20&5&-6\end{bmatrix}}.}
Provided that they have the same size (each matrix has the same number of rows and the same number of columns as the other), two matrices can be added or subtracted element by element (see conformable matrix). The rule for matrix multiplication, however, is that two matrices can be multiplied only when the number of columns in the first equals the number of rows in the second (i.e., the inner dimensions are the same, n for an (m×n)-matrix times an (n×p)-matrix, resulting in an (m×p)-matrix). There is no product the other way round, a first hint that matrix multiplication is not commutative. Any matrix can be multiplied element-wise by a scalar from its associated field.
In this tutorial, we discuss how to do a regression analysis in Excel. I will teach you how to activate the regression analysis feature, what are the functions and methods we can use to do a regression analysis in Excel and most importantly, how to interpret the regression analysis results. Source: https://tinytutes.com/tutorials/regression-analysis-in-excel/
Matrix theory" redirects here. For the physics topic, see Matrix string theory.
An m × n matrix: the m rows are horizontal and the n columns are vertical. Each element of a matrix is often denoted by a variable with two subscripts. For example, a2,1 represents the element at the second row and first column of the matrix.
In mathematics, a matrix (plural matrices) is a rectangular array[1] (see irregular matrix) of numbers, symbols, or expressions, arranged in rows and columns.[2][3] For example, the dimension of the matrix below is 2 × 3 (read "two by three"), because there are two rows and three columns:
{\displaystyle {\begin{bmatrix}1&9&-13\\20&5&-6\end{bmatrix}}.}{\displaystyle {\begin{bmatrix}1&9&-13\\20&5&-6\end{bmatrix}}.}
Provided that they have the same size (each matrix has the same number of rows and the same number of columns as the other), two matrices can be added or subtracted element by element (see conformable matrix). The rule for matrix multiplication, however, is that two matrices can be multiplied only when the number of columns in the first equals the number of rows in the second (i.e., the inner dimensions are the same, n for an (m×n)-matrix times an (n×p)-matrix, resulting in an (m×p)-matrix). There is no product the other way round, a first hint that matrix multiplication is not commutative. Any matrix can be multiplied element-wise by a scalar from its associated field.
Correspondence analysis (CA) or reciprocal averaging is a multivariate statistical technique proposed by Hirschfeld and later developed by Jean-Paul Benzécri. It is conceptually similar to principal component analysis, but applies to categorical rather than continuous data. In a similar manner to principal component analysis, it provides a means of displaying or summarising a set of data in two-dimensional graphical form.
Correspondence analysis (CA) or reciprocal averaging is a multivariate statistical technique proposed by Hirschfeld and later developed by Jean-Paul Benzécri. It is conceptually similar to principal component analysis, but applies to categorical rather than continuous data. In a similar manner to principal component analysis, it provides a means of displaying or summarising a set of data in two-dimensional graphical form.
Applied Numerical Methods Curve Fitting: Least Squares Regression, InterpolationBrian Erandio
Correction with the misspelled langrange.
and credits to the owners of the pictures (Fantasmagoria01, eugene-kukulka, vooga, and etc.) . I do not own all of the pictures used as background sorry to those who aren't tagged.
The presentation contains topics from Applied Numerical Methods with MATHLAB for Engineers and Scientist 6th and International Edition.
FSE 200AdkinsPage 1 of 10Simple Linear Regression Corr.docxbudbarber38650
FSE 200
Adkins Page 1 of 10
Simple Linear Regression
Correlation only measures the strength and direction of the linear relationship between two quantitative variables. If the relationship is linear, then we would like to try to model that relationship with the equation of a line. We will use a regression line to describe the relationship between an explanatory variable and a response variable.
A regression line is a straight line that describes how a response variable y changes as an explanatory variable x changes. We often use a regression line to predict the value of y for a given value of x.
Ex. It has been suggested that there is a relationship between sleep deprivation of employees and the ability to complete simple tasks. To evaluate this hypothesis, 12 people were asked to solve simple tasks after having been without sleep for 15, 18, 21, and 24 hours. The sample data are shown below.
Subject
Hours without sleep, x
Tasks completed, y
1
15
13
2
15
9
3
15
15
4
18
8
5
18
12
6
18
10
7
21
5
8
21
8
9
21
7
10
24
3
11
24
5
12
24
4
Draw a scatterplot and describe the relationship. Lay a straight-edge on top of the plot and move it around until you find what you think might be a “line of best fit.” Then try to predict the number of tasks completed for someone having been without sleep 16 hours.
Was your line the same as that of the classmate sitting next to you? Probably not. We need a method that we can use to find the “best” regression line to use for prediction. The method we will use is called least-squares. No line will pass exactly through all the points in the scatterplot. When we use the line to predict a y for a given x value, if there is a data point with that same x value, we can compute the error (residual):
Our goal is going to be to make the vertical distances from the line as small as possible. The most commonly used method for doing this is the least-squares method.
The least-squares regression line of y on x is the line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible.
Equation of the Least-Squares Regression Line
· Least-Squares Regression Line:
· Slope of the Regression Line:
· Intercept of the Regression Line:
Generally, regression is performed using statistical software. Clearly, given the appropriate information, the above formulas are simple to use.
Once we have the regression line, how do we interpret it, and what can we do with it?
The slope of a regression line is the rate of change, that amount of change in when x increases by 1.
The intercept of the regression line is the value of when x = 0. It is statistically meaningful only when x can take on values that are close to zero.
To make a prediction, just substitute an x-value into the equation and find .
To plot the line on a scatterplot, just find a couple of points on the regression line, one near each end of the range of x in the data. Plot the points and connect them with a line. .
is used. Mathematics is applied in day to day life, so we can now review the concepts of Algebra and its uses in daily life. Here in our work we have made a small split up of items in a bag while shopping. Basic Algebra is where we finally put the algebra in pre-algebra. The concepts taught here will be used in every math class you take from here on. Well introduce you to some exciting stuff like drawing graphs and solving complicated equations. Since we are learning Algebra, Geometry in the school days. But the is a real life application of Algebra which is used in Geometry. Now a days the social media has improved a lot. We cant able to solve those figured puzzles, hence we can solve them by using algebraic equations. S. Ambika | R. Mythrae | S. Saranya | K. Selvanayaki "Algebra in Real Life" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-2 , February 2019, URL: https://www.ijtsrd.com/papers/ijtsrd21517.pdf
Paper URL: https://www.ijtsrd.com/mathemetics/algebra/21517/algebra-in-real-life/s-ambika
BUS 308 Week 4 Lecture 3 Developing Relationships in Exc.docxShiraPrater50
BUS 308 Week 4 Lecture 3
Developing Relationships in Excel
Expected Outcomes
After reading this lecture, the student should be able to:
1. Calculate the t-value for a correlation coefficient
2. Calculate the minimum statistically significant correlation coefficient value.
3. Set-up and interpret a Linear Regression in Excel
4. Set-up and interpret a Multiple Regression in Excel
Overview
Setting up correlations and regressions in Excel is fairly straightforward and follows the
approaches we have seen with our previous tools. This involves setting up the data input table,
selecting the tools, and inputting information into the appropriate parts of the input window.
Correlations
Question 1
Data set-up for a correlation is perhaps the simplest of any we have seen. It involves
simply copying and pasting the variables from the Data tab to the Week 4 worksheet. Again,
paste them to the right of the question area. The screenshot below has the data for both the
question 1 correlation and the question 2 multiple regression pasted them starting at column V.
You can paste all the data at once or add the multiple regression variables later (as long as you
do not sort the original data).
Specifically, for Question 1, copy the salary data to column V (for example). Then copy
the Midpoint thru Service columns and paste them next to salary. Finally copy the Raise column
and paste it next to the service column. Notice that our data input range for this question now
includes Salary in Column V and the other interval level variables found in Columns W thru AA.
Question 1 asks for the correlation among the interval/ratio level variables with salary
and says to exclude compa-ratio. For our example, we will correlation compa-ratio with the
other interval/ratio level variables with the exclusion of salary. Since compa-ratio equals the
salary divided by the midpoint, it does not seem reasonable to use salary in predicting compa-
ratio or compa-ratio in predicting salary.
Pearson correlations can be performed in two ways within Excel. If we have a single pair
of variables we are interested in, for example compa-ratio and performance rating, we could use
the fx (or Formulas) function CORREL(array1, array2) (note array means the same as range) to
give us the correlation.
However, if we have several variables we want to correlate at the same time, it is more
effective to use the Correlation function found in the Analysis ToolPak in the Data Analysis tab.
Set up of the input data for Correlation is simple. Just ensure that all of the variables to be
correlated are listed together, and only include interval or ratio level data. For our data set, this
would mean we cannot include gender or degree; even though they look like numerical data the 0
and 1 are merely labels as far as correlation is concerned.
In the Correlation data input box shown below, list the entire data range, indicate if your
dat ...
Introduction to linear regression and the maths behind it like line of best fit, regression matrics. Other concepts include cost function, gradient descent, overfitting and underfitting, r squared.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
3. DEPENDENT & INDEPENDENT VARIABLES
Cause and effects
Variables as Independent (cause) & other as Dependent (Effect)
For example: Assume an engineer is studying an automobile (the system) and
is interested in the factors that affect its speed.
The dependent variable -> speed
Some independent variables -> Rate of fuel entering the engine f, tire
pressure p, air temperature T, air pressure P, road grade r, car mass m etc
S = s (f,p,T,P,r,m)
4. TABLES
It is the best way to present technical data
It is a convenient way to list dependent & independent variables
The independent -> left most side
Dependent -> right most side
Table example 8.1
Significant figure should be in mind
Units should be properly reported
5. GRAPHS
To represent tabulated data, graph is best suited way.
To represent data in graphs is an art, those who are good at it are often able
to see things in data that are missed by others.
A well-constructed graph is self contained just like a well constructed table;
also it must communicate information accurately & rapidly
Title should be descriptive like effect of fuel rate and road grade on car speed
not like car speed v fuel consumption
Dependent -> ordinate (y-axis)
Independent -> abscissa (x-axis)
The units are enclosed in parenthesis or separated by the label by a comma
Each axis is graduated with tick marks
6. Properly spaced
We can use SI unit multiplier in case the number is too long
& if the gaps between the numbers is too big then we use logarithmic scale
Data points & complex numbers are represented by as in book
Lines representation as in book
Symbols are generally represented in three ways in graph
Figure title
Legends
Adjacent to the lines
Data may be categorized into
Observed: Data are often simply presented without an attempt to smooth them or correlate
them with a mathematical model
Empirical: Data are presented with a smooth line, which may be determined by a
mathematical model or perhaps it is just the author’s best judgment of where the data points
would have fallen had there been no error in the experiment
Theoretical: Data are generated by mathematical model
7. LINEAR EQUATIONS
(x1,y1) and (x2,y2) establish a straight line
(x,y) is an arbitrary point on the line
Slope = m = y2-y1/x2-x1 if x2 not equals to x1
Equation for slope = m =y –y1/ x -x1
y = mx + b
b=y – intercept i.e here x=0
a=x – intercept i.e here y=0
8. POWER EQUATIONS
rectilinear graph, log-log graph
y = k x ^m -> this eq show parabola if m is +ive
Otherwise we take log and get a straight line
The slope of log-log graph is not meaningful
For slope we use rectilinear graph
If m is –ive in above case then y = k x ^m shows a hyperbola
9. EXPONENTIAL EQUATIONS
y= K B^ mx where B is desired base i.e 2, e or 10
Here we used B =10
& find out the calculations on semi log graph
Semi log graph has an advantage that we doesn’t need to calculate log y
because the graph does itself
11. INTERPOLATION & EXTRAPOLATION
Interpolation
We could use our function to predict the value of the dependent variable for an
independent variable that is in the midst of our data. In this case we are preforming
interpolation.
Suppose that data with x between 0 and 10 is used to produce a regression line y =
2x + 5. We can use this line of best fit to estimate the y value corresponding to x = 6.
Simply plug this value into our equation and we see that y = 2(6) + 5 =17. Because
our x value is among the range of values used to make the line of best fit, this is an
example of interpolation.
Extrapolation
We could use our function to predict the value of the dependent variable for an
independent variable that is outside the range of our data. In this case we are
preforming extrapolation.
Suppose as before that data with x between 0 and 10 is used to produce a regression
line y = 2x + 5. We can use this line of best fit to estimate the y value corresponding
to x = 20. Simply plug this value into our equation and we see that y = 2(20) + 5 =45.
Because our x value is not among the range of values used to make the line of best fit,
this is an example of extrapolation.
12. LINEAR REGRESSION
Normally we have given a formula from which we can calculate the number. If
we reverse this, determine the formula from the numbers then this process is
called regression. If the equation given is a straight line then the process is
called Linear Regression.
Selected points: By plotting the data and then manually drawing a line that
best describes these data as judged by the person analyzing the data
PROBLEM: It relies on the person judging the data e.g. if 100 peoples were to analyze the
data, there likely would be 100 different slopes and 100 different y-intercepts
Least squares: uses a rigorous mathematical procedure to find a line that is
close to all data points. The difference between the actual data points yi and
the point predicted by the straight line ys is the residual di:
Best line: y = mx +b
Best line through the origin: y = mx