Curve Fitting and Machine Learning Analysis

This assignment delves into the application of curve fitting and machine learning algorithms to analyze three distinct datasets. It covers various techniques like quadratic equations and exponential values for curve fitting, as well as sequential model operations and optimization strategies. The analysis encompasses error detection and correction, with a focus on generating interpretable models and achieving computational efficiency across all datasets.

Software
Processes

Table of Contents
1. Question 1................................................................................................................................2
1.1 Models Used.....................................................................................................................2
1.2 Analysis Technique Used..................................................................................................3
1.3 Reasons for Choosing Analysis Technique......................................................................4
2. Question 2................................................................................................................................4
2.1 Model Fits- General Polynomial.......................................................................................4
2.2 Curve fitting......................................................................................................................5
3. Question 3................................................................................................................................6
3.1 Learning phase..................................................................................................................6
3.2 Testing phase.....................................................................................................................7
4. Question 4................................................................................................................................7
5. Question 5................................................................................................................................8
6. Question 6................................................................................................................................8

1. Question 1
The curve fitting models are used as it fits the requirements. It has many models and they are
described below.
Curve Fitting techniques and Models
The linear fit, Gaussian peak fit, exponential fit, power fit and logarithm fit models are used to
compute the curve fitting function in mathematical format. In addition, the following VIs used to
analyze and compute the curve fitting function. There are given below,
1) General Linear Fit VI
2) General Polynomial VI
3) Nonlinear Curve Fit VI
4) Cubic Spline Fit VI
In this General Linear Fit VI and General Polynomial VI is used for implementation work. Those
two models are described below.
The values taken for a, b and c are constant values. The graph is generated according to the
requirements. MS-EXCEL is the software tool used for implementing the curve.
1.1 Models Used
General Polynomial Fit
Use of common polynomial fit VI in curve fitting, fits data set to polynomial. The overall form
of the polynomial fit model is,
F(x) =a+bx+cx2+…..
The user initially need to set polynomial input when use the polynomial model fit VI. The
polynomial order could not assure good fitting output and it can cause oscillation. The lower
polynomial order can fulfill the best applications. Default value of the polynomial order is 2.
General Linear Fit

The Linear Fit VI in curve fitting used to suits data set according to the subsequent calculation
and equation.
The variable y provides the linear grouping of the coefficients such as a0, a1, a2,……,ak-
k denotes the sum of coefficients.
The analysis chosen for this is predictive analysis
1.2 Analysis Technique Used
Data analysis is a process in which the following is done. They are
 Inspecting
 Cleaning
 Transforming
 Modeling
Predictive analytics are necessary to distinguish and to interpret the result set and to make better
decisions further.
Data:

The good data is needed to perform the process of analysis. The attributes in dataset are
analyzed
Statistics:
For the statistics, the regression analysis is used. The statistical process are analyzed by
using the statistics. The effects in variable are examined and the analysis report is made for
further investigation
Assumptions:
The assumptions needs to be monitored and the predictive analysis is done for the
dataset. More attention is given the secondary variables and the external variables. The dataset
relationship is assumed, identified and is examined in better way. The assumptions are then
validated from multiple resource and modified accordingly.
1.3 Reasons for Choosing Analysis Technique
The analysis chosen for this is predictive analysis. This is because
 This is chosen as it to perform the process of analysis in better way.
 Suitable procedures related to requirements are followed in predictive analysis
 The effects in variable are examined and the analysis report is made effectively.
 In predictive analysis, the dataset relationship is assumed, identified and is
examined in better way. (Oravecz & Muth, 2017)
2. Question 2
.
The best fit model is provided below.
Model 1: Effort = (a + bct) / (bt +1)
The above model fits well for the set of programs in generating P1LA, P2LA, P1LB.
General polynomial is used because it uses common polynomial function in curve fitting
technique. The general description for General polynomial is provided below.

2.1 Model Fits- General Polynomial
The uses of common polynomial fit VI in curve fitting, fits data set to a polynomial function.
The over-all form of the polynomial fit model is,
F(x) =a+bx+cx2+…..
The user initially needs to set the polynomial order input when use the polynomial model fit VI.
The higher polynomial order could not assure a good fitting output and it can be a reason for
oscillation. The lower polynomial order satisfies the best applications. The default value of the
polynomial order is 2. ("Curve Fitting and Method of Least Squares | eMathZone", 2017)
The plots are provided in this.
Learning of curve fitting from the previous projects helped in summarizing the curve fitting in
different way. The new of understanding curve fitting is provided below.
2.2 Curve Fitting Technique
Generally, the curve fitting is used to find a mathematical function which is represented as f(x) in
a function class ɵ for the statistics ("Curve Fitting Software | NCSS Statistical Software | NCSS",
2017)
The below graph is generated from the dataset-

7 students are selected. The screenshot of table which include data of 7 students is shown below.
Model 4:
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
0
2
4
6
8
10
12
0
5
10
15
20
25
30
35
40f(x) = 0
Attempt
Effort(mins)
From the data in P1LA, P2LA and P1LB are generated.

The graphs are created according to the requirements.
MODEL1:P1LA
Model 1:P2LA

Model 1:P1LB

MODEL 3:
P1LA:
P2LA:

P1LB:

( xi, yi )
I=0, 1, 2, 3,…., n-1. (Wade, Walker & Petrone, 2013)
The mathematical function which is represented as f(x) reduces the residual under weight W. in
geometric, curve fitting is a curve y=f(x) that fits the data ( xi, yi ).
I=0, 1, 2, 3,…., n-1.
The various VI functions are used to calculate the curve fitting functions. There are given below
1) Exponential fit VI
2) Gaussian fit VI
3) Linear fit VI
4) Logarithm fit VI

5) Power fit VI
These VI function generate various kinds of the curve fitting models for the data set. The user
must choose which fitting model to use after fitting the dataset. For instance, the linear model is
used to fit logarithm data and leads to an improper fitting output. The output incorrectly regulates
the features and characteristics of the data set. So, the user must select a suitable fitting model
and it’s fully grounded on the data scattering shape. If the given model appropriate for according
to output result ("How to Use Curve Fitting in Predictive Analytics - dummies", 2017).
The curve fitting technique learning is the extent. The different fitting model for the project is
analyzed and learnt. The observations form learning are provided below.
Each fitting model in VI takes a weighted input. The default value of weighted input is 1.
It actually means every statistics values have similar influence fits output result. The user
compute the outliers at the similar weight as like data samples. But it is a difficult task while
fitting. So, the user change the weights of the outliers in the dataset even fix the weights to zero
and it avoids the negative influence result.
3. Question 3
1) The estimated time taken for the models are,
2) The model 1 takes less time. Additionally, it fits the real time requirement exactly
when comparing to the other models provided.
3) The time taken for the model 1 is half an hour.
4) When implementing model 3, we faced errors, so it took more time. When
comparing to model 1 it is complex and suits less for the scenario.
The estimated results of operating data set is generated as the optimization of error is
done in greater extend. In addition with that, few features are used in aim of developing finer
results.

There are two process is followed. The phases are described below.
3.1 Learning phase
The training data sets are separated and is learned individually and made analysis with
the help of various models and methods.
The similarities are then recognized and with the help of individual data analyses is validated
using the testing phase which is described below.
3.2 Testing phase
After the learning phase, the methods, models and the rules are now tested in the testing
phase. The new data is generated as per the modifications made. The performance measures are
clearly identified and are computed.
The computational learning theory grows with mathematical models to describe the knowledge
data size in addition with number of training in the machine learning. This can also be useful for
the small data set learning. Though, it leaves certain practical difficulties. Although it proposals a
probably approximately correct which is called (PAC) model. It is used for the estimation, the
relation is all about the predict accuracy. It also have sample size, it is tough to estimate the
sample space in the model. But, it indeed shapes a theoretical based model to describe the
machine learning problem.
The analysis made is predictive analysis. The predictive analysis is chosen as it captures the
similarities by viewing and observing it in different ways.
4. Question 4
Yes. The learning pattern is similar in operating the data set.
The following explains few similarities between the operating data set.
 Similar set words appeared,
 Similar basic techniques are used and implemented in the software process.
 The basic techniques are used for monitoring the locations doe the sampling code. The
data is then extracted randomly in the same way.

 Machine learning algorithms are used
 Sequential model operations are used for implementing.
 Some more additional features are added for generating finer results.
 the data set contains both the input value and the output value
 The optimization of error is measured as same for the three data sets.
 Easy interpreting models are used for implementation of analysis purpose of those three
data.
 The computational efficiency is reached its average range for all the three dataset.
5. Question 5
It took 5 hours for each.
I. The Model 1 took half an hour as mentioned above. Model 1 curve fitting has
simpler calculations when comparing to the other models.
II. Model 3 took more time as exponential values calculations are there.
III. Model 4 is much simpler and it took less than half an hour.
The knowledge encoding techniques includes different methods. With the help of the
methods, the code is generated. The efficiency is also examined for the code.
6. Question 6
The analysis techniques for dataset is learnt. The interpreting models for the code are
examined and is learnt. The curve fitting process is learnt. Relevant models and the operations
are used for implementation. Model 1 and model 3 are taken and generated curve fitting graph
according to that requirements. Model 1 is easier to generate the curve fitting. But model 3 takes
additional time to implement the curve fitting graph than model 1. The optimization technique
for model 1 is different from model 3 as the quadratic equations vary. More focus is made on the

statistics of the student’s data and provided the best results. From the dataset provided, curve
fitting has the exact relation with the data provided.
The optimization techniques for error detection and correction techniques are
investigated and learnt. The additional features are also learnt for generating the finer results.
References
Curve Fitting and Method of Least Squares | eMathZone. (2017). eMathZone. Retrieved 27
September 2017, from http://www.emathzone.com/tutorials/basic-statistics/curve-fitting-
and-method-of-least-squares.html
Curve Fitting Software | NCSS Statistical Software | NCSS. (2017). Ncss.com. Retrieved 27
September 2017, from https://www.ncss.com/software/ncss/curve-fitting-in-ncss/
How to Use Curve Fitting in Predictive Analytics - dummies. (2017). dummies. Retrieved 27
September 2017, from http://www.dummies.com/programming/big-data/data-science/how-
to-use-curve-fitting-in-predictive-analytics/
Oravecz, Z., & Muth, C. (2017). Fitting growth curve models in the Bayesian
framework. Psychonomic Bulletin & Review. http://dx.doi.org/10.3758/s13423-017-1281-0
Wade, S., Walker, S., & Petrone, S. (2013). A Predictive Study of Dirichlet Process Mixture
Models for Curve Fitting. Scandinavian Journal Of Statistics, 41(3), 580-605.
http://dx.doi.org/10.1111/sjos.12047