Isotonic Regression is a statistical technique of fitting a free-form line to a sequence of observations such that the fitted line is non-decreasing (or non-increasing) everywhere, and lies as close to the observations as possible. Isotonic Regression is limited to predicting numeric output so the dependent variable must be numeric in nature…
What is bayesian statistics and how is it different?Wayne Lee
Gentle intro to Bayesian Statistics and how it's different from classical frequentist statistics. Assumes you have basic statistical knowledge.
Why "Am I pregnant?" is a question more suitable for Bayesian techniques and not actually suitable at all for Frequentist techniques!
What is bayesian statistics and how is it different?Wayne Lee
Gentle intro to Bayesian Statistics and how it's different from classical frequentist statistics. Assumes you have basic statistical knowledge.
Why "Am I pregnant?" is a question more suitable for Bayesian techniques and not actually suitable at all for Frequentist techniques!
Mathematical Optimisation - Fundamentals and ApplicationsGokul Alex
My Session on Mathematical Optimisation Fundamentals and Industry applications for the Academic Knowledge Refresher Program organised by Kerala Technology University and College of Engineering Trivandrum, Department of Interdisciplinary Studies.
How do you use the Weibull Distribution? It’s just one of many useful statistical distribution we have to master as reliability engineers. Let’s explore an array of distribution and the problems they can help solve in our day to day work.
Detailed Information: When confronted with a set of time to failure data, what is your goto analysis approach. For me it’s a Weibull plot. It’s quick, often provides some insight to ask better questions, and easy to explain to others. A histogram is another great starting point. If we know a little about the source of the data, we may favor the normal or lognormal distributions. If discreet data, then binomial is the first choice, yet Poisson or hypergeometric have uses, too. A basic understanding of statistical distributions provides you a way to summarize data providing insights to identify or solve problems. In this webinar we’ll explore a few distributions useful for reliability engineering work and talk about how to select a distribution, basics on interpreting distributions and just touch on judging if you have selected the right distribution.
This Accendo Reliability webinar originally broadcast on 14 April 2015.
Abstract: This PDSG workshop introduces basic concepts of multiple linear regression in machine learning. Concepts covered are Feature Elimination and Backward Elimination, with examples in Python.
Level: Fundamental
Requirements: Should have some experience with Python programming.
2016. 7. 27 Presentation (Co-presenter: Jia Li)
Research Method for Political Science III (Instructor: Yuki Yanai)
Graduate School of Law, Kobe University, Japan
Some characters in this slide are invisible. High-resolution slide is available on my homepage (http://www.jaysong.net).
Multiple Linear Regression is a statistical technique that is designed to explore the relationship between two or more. It is useful in identifying important factors that will affect a dependent variable, and the nature of the relationship between each of the factors and the dependent variable. It can help an enterprise consider the impact of multiple independent predictors and variables on a dependent variable, and is beneficial for forecasting and predicting results.
Multiple Linear Regression is a statistical technique that is designed to explore the relationship between two or more. It is useful in identifying important factors that will affect a dependent variable, and the nature of the relationship between each of the factors and the dependent variable. It can help an enterprise consider the impact of multiple independent predictors and variables on a dependent variable, and is beneficial for forecasting and predicting results.
Mathematical Optimisation - Fundamentals and ApplicationsGokul Alex
My Session on Mathematical Optimisation Fundamentals and Industry applications for the Academic Knowledge Refresher Program organised by Kerala Technology University and College of Engineering Trivandrum, Department of Interdisciplinary Studies.
How do you use the Weibull Distribution? It’s just one of many useful statistical distribution we have to master as reliability engineers. Let’s explore an array of distribution and the problems they can help solve in our day to day work.
Detailed Information: When confronted with a set of time to failure data, what is your goto analysis approach. For me it’s a Weibull plot. It’s quick, often provides some insight to ask better questions, and easy to explain to others. A histogram is another great starting point. If we know a little about the source of the data, we may favor the normal or lognormal distributions. If discreet data, then binomial is the first choice, yet Poisson or hypergeometric have uses, too. A basic understanding of statistical distributions provides you a way to summarize data providing insights to identify or solve problems. In this webinar we’ll explore a few distributions useful for reliability engineering work and talk about how to select a distribution, basics on interpreting distributions and just touch on judging if you have selected the right distribution.
This Accendo Reliability webinar originally broadcast on 14 April 2015.
Abstract: This PDSG workshop introduces basic concepts of multiple linear regression in machine learning. Concepts covered are Feature Elimination and Backward Elimination, with examples in Python.
Level: Fundamental
Requirements: Should have some experience with Python programming.
2016. 7. 27 Presentation (Co-presenter: Jia Li)
Research Method for Political Science III (Instructor: Yuki Yanai)
Graduate School of Law, Kobe University, Japan
Some characters in this slide are invisible. High-resolution slide is available on my homepage (http://www.jaysong.net).
Multiple Linear Regression is a statistical technique that is designed to explore the relationship between two or more. It is useful in identifying important factors that will affect a dependent variable, and the nature of the relationship between each of the factors and the dependent variable. It can help an enterprise consider the impact of multiple independent predictors and variables on a dependent variable, and is beneficial for forecasting and predicting results.
Multiple Linear Regression is a statistical technique that is designed to explore the relationship between two or more. It is useful in identifying important factors that will affect a dependent variable, and the nature of the relationship between each of the factors and the dependent variable. It can help an enterprise consider the impact of multiple independent predictors and variables on a dependent variable, and is beneficial for forecasting and predicting results.
Generalized Linear Regression with Gaussian Distribution is a statistical technique which is a flexible generalization of ordinary linear regression that allows for response variables that have error distribution models other than a normal distribution. The Generalized Linear Model (GLM) generalizes linear regression by allowing the linear model to be related to the response variable via a link function (in this case link function being Gaussian Distribution) and by allowing the magnitude of the variance of each measurement to be a function of its predicted value.
Simple Linear Regression is a statistical technique that attempts to explore the relationship between one independent variable (X) and one dependent variable (Y). The Simple Linear Regression technique is not suitable for datasets where more than one variable/predictor exists.
Simple Linear Regression is a statistical technique that attempts to explore the relationship between one independent variable (X) and one dependent variable (Y). The Simple Linear Regression technique is not suitable for datasets where more than one variable/predictor exists.
Distribution of EstimatesLinear Regression ModelAssume (yt,.docxmadlynplamondon
Distribution of Estimates
Linear Regression Model
Assume (yt, xt) are independent and identically distributed and E(xtet) = 0
Estimation Consistency
The estimates approach the true values as the sample size increases.
Estimation variance decreases as the sample size increases.
Illustration of Consistency
Take a random sample of U.S. men
Estimate a linear regression of log(wages) on education
Total sample = 9089
Start with 100 observations, and sequentially increase sample size until in the final regression use the whole 9089.
Sequence of Slope Coefficients
Asymptotic Normality
4
Illustration of Asymptotic Normality
Time Series
Do these results apply to time-series data?
Consistency
Asymptotic Normality
Variance Formula
Time-series models
AR models, i.e., xt = yt-1
Trend and seasonal models
One-step and multi-step forecasting
Derivation of Variance Formula
For simplicity
Assume the variables have zero mean
The regression has no intercept
Model with no intercept:
Model with no intercept
OLS minimizes the sum of squares
The first-order condition is
Solution
Now substitute
We have
The denominator is the sample variance (when x has mean zero), so
10
Then
Where
Since
Then
From the covariance formula
When the observations are independent, the covariances are zero.
And since
We obtain
We have found
As stated at the beginning.
Extension to Time-Series
The only place in this argument where we used the assumption of the independence of observations was to show that vt = xtet has zero covariance with vj = xjej.
This is saying that vt is not autocorrelated.
Unforecastable one-step errors
In one-step-ahead forecasting, if the regression error is unforecastable, then vt is not autocorrelated.
In this case, the variance formula for the least-squares estimate is
Why is this true?
The error is unforecastable if
For simplicity, suppose that xt = 1.
Then for
Summary
In one-step-ahead time-series models, if the error is unforecastable, then least-squares estimates satisfy the asymptotic (approximate) distribution
As the sample size T is in the denominator, the variance decreases as the sample size increases.
This means that least-squares is consistent.
Variance Formula
The variance formula for the least-squares estimate takes the form
This formula is valid in time-series regression when the error is unforecastable.
Classical Variance Formula
If we make the simplifying assumption
Then
Homoskedasticity
The variance simplification is valid under “conditional homoskedasticity”
This is a simplifying assumption made to make calculations easier, and is a conventional assumption in introductory econometrics courses.
It is not used in serious econometrics.
Variance Formula: AR(1) Model
Take the AR(1) model with unforecastable homoscedastic errors
Then the variance of the OLS estimate is
Since in this model
AR(1) Asymptotic Variance
We know that
So
The asymp ...
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.
Regression Analysis is simplified in this presentation. Starting with simple linear to multiple regression analysis, it covers all the statistics and interpretation of various diagnostic plots. Besides, how to verify regression assumptions and some advance concepts of choosing best models makes the slides more useful SAS program codes of two examples are also included.
Data Science - Part IV - Regression Analysis & ANOVADerek Kane
This lecture provides an overview of linear regression analysis, interaction terms, ANOVA, optimization, log-level, and log-log transformations. The first practical example centers around the Boston housing market where the second example dives into business applications of regression analysis in a supermarket retailer.
This overview discusses the predictive analytical technique known as Gradient Boosting Regression, an analytical technique that explore the relationship between two or more variables (X, and Y). Its analytical output identifies important factors ( Xi ) impacting the dependent variable (y) and the nature of the relationship between each of these factors and the dependent variable. Gradient Boosting Regression is limited to predicting numeric output so the dependent variable has to be numeric in nature. The minimum sample size is 20 cases per independent variable. The Gradient Boosting Regression technique is useful in many applications, e.g., targeted sales strategies by using appropriate predictors to ensure accuracy of marketing campaigns and clarify relationships among factors such as seasonality, product pricing and product promotions, or for an agriculture business attempting to ascertain the effects of temperature, rainfall and humidity on crop production. Gradient Boosting Regression is just one of the numerous predictive analytical techniques and algorithms included in the Assisted Predictive Modeling module of the Smarten augmented analytics solution. This solution is designed to serve business users with sophisticated tools that are easy to use and require no data science or technical skills. Smarten is a representative vendor in multiple Gartner reports including the Gartner Modern BI and Analytics Platform report and the Gartner Magic Quadrant for Business Intelligence and Analytics Platforms Report.
Prediction of house price using multiple regressionvinovk
- Constructed a mathematical model using Multiple Regression to estimate the Selling price of the house based on a set of predictor variables.
- SAS was used for Variable profiling, data transformations, data preparation, regression modeling, fitting data, model diagnostics, and outlier detection.
Similar to What is Isotonic Regression and How Can a Business Utilize it to Analyze Data? (20)
Prediction of Crime Type plays a vital role in preventing crime in the society as well as assisting law agencies to design optimal strategies to ward off crime happenings in turn increasing public safety and decreasing economical loss.
"Multilayer perceptron (MLP) is a technique of feed
forward artificial neural network using back
propagation learning method to classify the target
variable used for supervised learning. It consists of multiple layers and non-linear activation allowing it to distinguish data that is not linearly separable."
Random Forest Classification is a machine learning technique utilizing aggregated outcome of many decision tree classifiers in order to improve precision of the outcome. It measures the relationship between the categorical target variable and one or more independent variables.
Predictive analytics of students' academic performance can help decision makers take appropriate actions at the right moment and plan appropriate training in order to improve the student’s success rate.
This overview discusses the predictive analytical technique known as Random Forest Regression, a method of analysis that creates a set of Decision Trees from a randomly selected subset of the training set, and aggregates by averaging values from different decision trees to decide the final target value. This technique is useful to determine which predictors have a significant impact on the target values, e.g., the impact of average rainfall, city location, parking availability, distance from hospital, and distance from shopping on the price of a house, or the impact of years of experience, position and productive hours on employee salary. Random Forest Regression is limited to predicting numeric output so the dependent variable has to be numeric in nature. The minimum sample size is 20 cases per independent variable. Random Forest Regression is just one of the numerous predictive analytical techniques and algorithms included in the Assisted Predictive Modeling module of the Smarten augmented analytics solution. This solution is designed to serve business users with sophisticated tools that are easy to use and require no data science or technical skills. Smarten is a representative vendor in multiple Gartner reports including the Gartner Modern BI and Analytics Platform report and the Gartner Magic Quadrant for Business Intelligence and Analytics Platforms Report.
sing advanced analytics to identify quality issues will improve production processes, protect the business against liability claims and allow the organization to focus on quality issues and change product design and/or processes.
Predictive analytics for maintenance management can take the guesswork out of equipment maintenance, which parts to order and when equipment should be replaced.
Predictive analytics targets data to predict if ATL advertising is more effective than BTL advertising and to target customer segments and characteristics.
Predictive analytics for human resource attrition identifies areas of dissatisfaction, analyzes processes, benefits, training and environs to improve retention.
Predictive Analytics for customer targeting identifies buying frequency, what causes customers to buy, factors informing purchases and messaging by segment.
Naive Bayes is a classification algorithm that is suitable for binary and multiclass classification. It is suitable for binary and multiclass classification. Naïve Bayes performs well in cases of categorical input variables compared to numerical variables. It is useful for making predictions and forecasting data based on historical results.
The KNN (K Nearest Neighbors) algorithm analyzes all available data points and classifies this data, then classifies new cases based on these established categories. It is useful for recognizing patterns and for estimating. The KNN Classification algorithm is useful in determining probable outcome and results, and in forecasting and predicting results, given the existence of multiple variables.
The independent sample t-test is a statistical method of hypothesis testing that determines whether there is a statistically significant difference between the means of two independent samples. It is helpful when an organization wants to determine whether there is a statistical difference between two categories or groups or items and, furthermore, if there is a statistical difference, whether that difference is significant.
Sampling is the technique of selecting a representative part of a population for the purpose of determining the characteristics of the whole population. There are two types of sampling analysis: Simple Random Sampling and Stratified Random Sampling. Sampling is useful in assigning values and predicting outcomes for an entire population, based on a smaller subset or sample of the population.
Binary Logistic Regression Classification makes use of one or more predictor variables that may be either continuous or categorical to predict target variable classes. This technique identifies important factors impacting the target variable and also the nature of the relationship between each of these factors and the dependent variable. It is useful in the analysis of multiple factors influencing an outcome, or other classification where there two possible outcomes.
The Paired Sample T Test is used to determine whether the mean of a dependent variable. For example, weight, anxiety level, salary, or reaction time is the same in two related groups. It is particularly useful in measuring results before and after a particular event, action, process change, etc.
An ARIMAX model can be viewed as a multiple regression model with one or more autoregressive (AR) terms and/or one or more moving average (MA) terms. It is suitable for forecasting when data is stationary/non stationary, and multivariate with any type of data pattern, i.e., level/trend /seasonality/cyclicity. ARIMAX provides forecasted values of the target variables for user-specified time periods to illustrate results for planning, production, sales and other factors.
The Karl Pearson's correlation measures the degree of linear relationship between two variables. This method can be used to identify negative, positive and neutral correlations between two data points, e.g., the relationship between the age of a consumer and the color of shirt they might purchase or the level of education of a consumer and the delivery mechanism they choose for news and information.
Explore our comprehensive data analysis project presentation on predicting product ad campaign performance. Learn how data-driven insights can optimize your marketing strategies and enhance campaign effectiveness. Perfect for professionals and students looking to understand the power of data analysis in advertising. for more details visit: https://bostoninstituteofanalytics.org/data-science-and-artificial-intelligence/
Adjusting primitives for graph : SHORT REPORT / NOTESSubhajit Sahu
Graph algorithms, like PageRank Compressed Sparse Row (CSR) is an adjacency-list based graph representation that is
Multiply with different modes (map)
1. Performance of sequential execution based vs OpenMP based vector multiply.
2. Comparing various launch configs for CUDA based vector multiply.
Sum with different storage types (reduce)
1. Performance of vector element sum using float vs bfloat16 as the storage type.
Sum with different modes (reduce)
1. Performance of sequential execution based vs OpenMP based vector element sum.
2. Performance of memcpy vs in-place based CUDA based vector element sum.
3. Comparing various launch configs for CUDA based vector element sum (memcpy).
4. Comparing various launch configs for CUDA based vector element sum (in-place).
Sum with in-place strategies of CUDA mode (reduce)
1. Comparing various launch configs for CUDA based vector element sum (in-place).
Techniques to optimize the pagerank algorithm usually fall in two categories. One is to try reducing the work per iteration, and the other is to try reducing the number of iterations. These goals are often at odds with one another. Skipping computation on vertices which have already converged has the potential to save iteration time. Skipping in-identical vertices, with the same in-links, helps reduce duplicate computations and thus could help reduce iteration time. Road networks often have chains which can be short-circuited before pagerank computation to improve performance. Final ranks of chain nodes can be easily calculated. This could reduce both the iteration time, and the number of iterations. If a graph has no dangling nodes, pagerank of each strongly connected component can be computed in topological order. This could help reduce the iteration time, no. of iterations, and also enable multi-iteration concurrency in pagerank computation. The combination of all of the above methods is the STICD algorithm. [sticd] For dynamic graphs, unchanged components whose ranks are unaffected can be skipped altogether.
Levelwise PageRank with Loop-Based Dead End Handling Strategy : SHORT REPORT ...Subhajit Sahu
Abstract — Levelwise PageRank is an alternative method of PageRank computation which decomposes the input graph into a directed acyclic block-graph of strongly connected components, and processes them in topological order, one level at a time. This enables calculation for ranks in a distributed fashion without per-iteration communication, unlike the standard method where all vertices are processed in each iteration. It however comes with a precondition of the absence of dead ends in the input graph. Here, the native non-distributed performance of Levelwise PageRank was compared against Monolithic PageRank on a CPU as well as a GPU. To ensure a fair comparison, Monolithic PageRank was also performed on a graph where vertices were split by components. Results indicate that Levelwise PageRank is about as fast as Monolithic PageRank on the CPU, but quite a bit slower on the GPU. Slowdown on the GPU is likely caused by a large submission of small workloads, and expected to be non-issue when the computation is performed on massive graphs.
4. Terminologies
• Predictors and Target variable:
• Target variable usually denoted by Y, is the variable being predicted and is also
called dependent variable, output variable, response variable or outcome
variable
• Predictor, usually denoted by X, sometimes called an independent or
explanatory variable, is a variable that is being used to predict the
target variable
• Correlation:
• Correlation is a statistical measure that indicates the extent to which two
variables fluctuate together
5. Terminologies (Continued...)
• Isotonic Constraints/Thresholds:
• These are the data points where we can estimate a set a linear model in
between each of the thresholds to minimize the error regarding the training
data
6. Terminologies (Continued...)
• Monotonic Constraints:
• These are either increasing or decreasing set of values which are typically
considered to be increasing in case of isotonic regression.
7. ● xi is observed responses and
X=x1, x2,..., xn
• OBJECTIVE:
It is a variant of linear regression and allows
us to build model in piecewise linear manner
i.e., breaking up the problem into few or
many linear segments and perform linear
interpolation of each function.
• BENEFIT:
o Unlike linear regression this model is not
biased and is flexible.
o Helps in multidimensional scaling.
• MODEL:
o Isotonic regression is the technique of
fitting a free-form line to a sequence of
observations such that the fitted line that
lies close to the observations as possible.
● yi is a finite set of real
numbers Y=y1, y2,...,yn
● wi are positive weights
Introduction
8. Example: Isotonic Regression
Let’s conduct the Isotonic Regression Analysis on Admission Regression Data set on Independent Variables: CGPA, LOR, GRE_Score, TOEFL_Score and
Target Variable: Chance_of_Admit as shown below:
Independent
variables (Xi)
Target
Variable (Y)
Chance_of_admit CGPA LOR GRE_Score TOEFL_Score
0.46 8.0 3.0 308 110
0.64 8.18 3.0 312 98
0.72 8.79 2.5 319 110
0.45 7.46 2.5 290 104
0.57 7.46 2.5 311 98
Model is a an
excellent fit when
Adjusted R-Squared
> 0.7
R-Squared 0.782
Adjusted R-Squared 0.781
R-Squared: It shows the goodness of fit of the model. It
lies between 0 to 1 and closer the value to 1, better the
model.
Adjusted R-Squared: The adjusted R-squared is a
modified version of R-squared that has been adjusted
for the number of predictors in the model. It shows
whether adding additional predictors improve a
regression model or not.
9. Select the Target Variable
Chance_of_Admit
CGPA
LOR
GRE_Score
TOEFL_Score
Step
1
Select the Predictor Variable
Chance_of_Admit
CGPA
LOR
GRE_Score
TOEFL_Score
Step
2
More than one
predictors can be
selected
Step 3
isotonic = true
(This indicates the default value that is based
on the target variable, typically denoting the
increasing property of the isotonic regression).
By default, these parameters
should be set with the values
mentioned
Step 4
Display the output window containing following:
o Model Summary
o Line Fit Plot
o Residual Versus Fit Plot
Note:
▪ Categorical predictors should be auto detected and converted to dummy/binary variables before applying regression
▪ Decision on selection of predictors depends on business knowledge and the correlation value between the target variable and predictors
Standard Input/Tuning Parameters & Sample UI
10. Sample Output: 1. Model Summary
● R-Squared: It shows the goodness of fit of the model. It lies
between 0 to 1 and closer the value to 1, better the model.
Root Mean Square Error (RMSE) 0.066
Mean Absolute Error (MAE) 0.048
Mean_Absolute_Percentile_Error (MAPE) 0.0762619
Mean Percentage Error (MPE) -0.0111406
● Adjusted R-Squared: The adjusted R-squared is a modified
version of R-squared that has been adjusted for the number of
predictors in the model. It shows whether adding additional
predictors improve a regression model or not.
R-Squared 0.782
Adjusted R-Squared 0.781
11. Sample Output: 1. Model Summary (Continued)...
● Root Mean Square Error (RMSE): Square root of the average of squared differences between prediction
and actual observation. It is standard deviation of residual error.
● Mean Absolute Error (MAE): Average of the absolute differences between prediction and actual
observation.
● Mean_Absolute_Percentile_Error (MAPE): Mean Absolute Percentage ratio of residual over actual
observations.
● Mean Percentage Error (MPE): Mean Percentage Error conveys if there is more positive errors than
negative errors or vice-versa based upon its sign.
RMSE, MAE, MAPE and MPE are used to identify the variation in terms of errors from predicted to
actual values.
Lower the values, represent a better fit of the regression model.
12. Sample Output: 2. Interpretation
CGPA
LOR
GRE_Score
TOEFL_Score
Influencer's Importance
Influencer’s Importance chart is used to show impact of each predictor on target variable.
Target Variable: Chance_of_Admit
13. Sample Output: 3. Plots
CGPA Predicted Chance_of_Admit
Line Fit Plot Residual versus Fit Plot
Line fit plots are used to check the assumption of
linearity between each Xi & Y
Residual versus fit plot is used to check the
assumption of equal error variances & outliers
The line plot is plotted between Chance_of_Admit against CGPA.
The residual versus Fit plot is plotted between Predicted Chance_of_Admit and Standard Residuals.
14. Interpretation of Important Model Summary Statistics
RMSE R Squared
RMSE R-Squared
R-Squared: Adjusted R-Squared: RMSE:
• R-squared between 0 to 0.7
represents a model not fit well
and assumptions of normality
and linearity should be checked
for better fitment of a model.
• It shows the goodness of fit of
the model. It lies between 0 to 1
and closer this value to 1, better
the model
• The adjusted R-squared is a
modified version of R-squared
that has been adjusted for the
number of predictors in the
model. It shows whether adding
additional predictors improve a
regression model or not
• If the value is > 0.7, the model
shows a better correlation
between the dependent and
independent variables
• The more the variables, the
lesser is the adjusted R-squared
score
• Square root of the average of
squared differences between
prediction and actual
observation. It is standard
deviation of residual error.
• Lower values of RMSE indicate
a better fit. The value ranges 0
to ∞.
15. Interpretation of Important Model Summary Statistics
(Continued…)
RMSE R Squared
RMSE R-Squared
MAE: MAPE: MPE:
• Average of the absolute
differences between prediction
and actual observation
• Lower values of MAE indicate a
better fit. The value ranges 0 to
∞
• Like RMSE, it is a negatively
oriented score
• Mean Absolute Percentage
ratio of residual over actual
observations
• Lower the MAPE, better the
performance of the model
• Mean Percentage Error conveys
if there is more positive errors
than negative errors or vice-
versa based upon its sign
• In case of more negative errors
the system underestimates, and
in case of more positive errors
the system overestimates
16. Interpretation of Plots: Line Fit Plot
• This plot is used to plot the relationship between
each Xi (predictor) & Y (target variable) with Y-on-y
axis and each Xi on x axis
• As shown in the figure 1 in right, as temperature(X)
increases, so does the Yield(Y), hence there is a
linear relationship between X and Y and isotonic
regression is applicable on this data
• If line doesn’t display linearity as shown in figures 2
& 3 in right, then transformation can be applied on
that particular variable before proceeding with
model building
• If data transformation doesn’t help, then either
that variable(Xi) can be dropped from the analysis
or nonlinear model should be chosen depending
on the distribution pattern of scatter plot.
Figure 2
Figure 3
Figure 1 CGPA
Chance_of_Admit
Figure 2
Figure 3
17. Interpretation of Plots: Residual Versus Fit Plot
• It is the scattered plot of standardized residuals on
Y axis and predicted (fitted) values on X axis
• It is used to detect the unequal residual variances
and outliers in data
• Here are the characteristics of a well-behaved
residual vs. fits plot:
• The residuals should "bounce randomly" around
the 0 line and should roughly form a "horizontal
band" around the 0 line as shown in figure 1. This
suggests that the variances of the error terms are
equal
• No one residual should "stands out" from the
basic random pattern of residuals. This suggests
that there are no outliers.
⮚ Plots shown in
figures 2 & 3 above
depict unequal
error variances,
which is not
desirable for linear
regression analysis
Figure 1
Figure 2
Figure 3
18. Limitations
Time independent error
( fairly constant over time & lying within certain range)
Time dependent error (decreasing with time)
• Isotonic Regression is limited to predicting
numeric output i.e., dependent variable must be
numeric in nature
• Minimum sample size should be at least 20 cases
per independent variable
• Significant risk of overfitting for larger number of
isotonic constraints/thresholds.
• Isotonic Regression is monotonic and hence it is
not appropriate for fitting distributions that have
left and right tails.
19. Limitations (Continued…) Figure 1
Figure 2
• It does not fit derivatives, so it will not approximate
smooth curves like most distribution functions. It may be
useful to approximate heuristically the predicted values,
but would not be especially useful for extrapolation
beyond the extreme values of the x-axis data.
• Target/independent variables should be normally
distributed
• A normal distribution is an arrangement of a data set in
which most values cluster in the middle of the range and
the rest taper off symmetrically toward either extreme. It
will look like a bell curve as shown in figure 1 in right
• Outliers(observations lying outside overall pattern of
distribution) in data, both target as well as independent
variables can affect the analysis, hence outliers need to
be removed as shown in Figure 2 in right.
20. Business Use Case 1
Business Problem: Decide Loan Eligibility based on Applicant’s Annual income, Employment Period,
Debt to Income Ratio etc.
Input Data: Predictor/Independent Variable(s) to determine Applicant’s Loan Eligibility:
• House Ownership Status
• Job Grade
• Employment Length
• Annual Income
• Loan Verification Status
• Debt to Income Ratio
Business Benefit: Loan applicant’s can discover what predictors can lead towards the required loan
amount to be eligible for further proceedings in turn ensuring systematic banking approach and
also assist banks to check the loan eligibility criteria before sanctioning a loan to the applicant.
21. Business Use Case 2
Business Problem: Predicting diamond prices using basic measurement metrics.
Input Data: Predictor/Independent Variable(s) to determine the price of a Diamond:
• Carat weight of Diamond
• Quality of the Cut
• Diamond Color
• Clarity
• Depth
• The width of the diamond’s table
Business Benefit:
The predictive model will provide details on the pricing of diamonds and enable analysis of the most
prominent factors and trends in the diamond market.
22. Want to
Learn More?
Get in touch with us @
support@Smarten.com
And Do Checkout the Learning section
on
Smarten.com
September 2021