Category Archives: Masters of Science

Pattern Oriented Software Engineering Course

Here I will put all the class lectures and exercises of pattern oriented software architectures.

Protected: Introductory Data Analysis: winter 2020 by Andersson

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Linear Regression: Influential Observations

https://www.youtube.com/watch?v=fJSXS4oVf88

Confusion matrix

https://www.dataschool.io/simple-guide-to-confusion-matrix-terminology/#:~:text=A%20confusion%20matrix%20is%20a,the%20true%20values%20are%20known.&text=The%20classifier%20made%20a%20total,the%20presence%20of%20that%20disease).

https://towardsdatascience.com/understanding-confusion-matrix-a9ad42dcfd62

Hypothesis Testing

Outliers in DM

Variable Rejection

 

 

 

Exercise 10: Solving for problem

K={1, 1.1, 5, 5.1, 1.5, 5.2, 7.9, 1.2, 8.1, 9}
Total item=10

iter1:
m1=5 m2=9
K1={1, 1.1, 5, 5.1, 1.5, 5.2, 1.2} K2={7.9, 8.1, 9}
m1=2.87==approx(3) m2=8.333==approx(9)

iter(2):
K1={1, 1.1, 5, 5.1, 1.5, 5.2, 1.2} ; K2={7.9, 8.1, 9}
m1=approx(3) m2=approx(9)
So, here same mean twice. so we have to stop.

Data Mining: Cluster analysis doing manually chapter 10

K-means clustering Algorithm for manually finding from observation:

Step 1: Take mean value

Step 2: Find nearest number of mean and put in cluster

Step 3: Repeat one and two until we get same mean

K={2,3,4,10,11,12,20,25,30}

k=2 [it means we have to create 2 clusters]

iter1:

m1=4   m2=12

k1={2,3,4}   [according to nearest distance of 4]

so mean m1=3

k2={10,11,12,20,25,30}

m2=108/6=18

iter2:

k1={2,3,4,10}

m1=4.75==approc(5)

k2={11,12,20,25,30}

m2=19.6==approx(20)

Iter 3:
K1={2,3,4,10,11,12} K2={20,25,30}
m1=7 m2=25

k1={2,3,4,10,11,12} k2={20,25,30}

m1=7, m2=25

Same mean twice. Thus we are getting same mean we have to stop.

Data Mining: Unit 9

Ensemble Models:

Basics
Boosting
Ranmdom Forests

Support Vector Machines
Basics
Linear Classification
Nonlinear Classification
Properties of SVMs

Discriminant Analysis
Basics

 

Exercise:

We are going to create some data mining models for classification and compare their performance. The goal with our models is still.

 

Data Mining: Exercise 8

Design of network topology

Determine:

Number of input nodes
Too few nodes => misclassification
Too many nodes=> overfitting

 

Problems with dollar sign:

https://stackoverflow.com/questions/42560090/what-is-the-meaning-of-the-dollar-sign-in-r-function

Problem with tilde sign:

https://stackoverflow.com/questions/14976331/use-of-tilde-in-r-programming-language?noredirect=1&lq=1

 

 

Unit 5- Multiple Linear Regression

iT IS HAPPEN WHEN MORE THAN ONE POSSIBLE PREDICTOR VARIABLE.

including more than one independent variable in the regression model, makes us extend the simple linerar regression model to a multiple linear regression model.

Advantages:
Relationship between response variables and several predictors simultaneously.

Disadvantages:
Model building , interpration difficulties due to complexity.

Multiple linear regression with two predictors:

Y=beta0+beta1X1+beta2X2+epsylon
where, Y is the dependent variable.
X1,X2…Xk are predictors(independent variables)
Epsylon is the random error
beta1, beta2, beta0 are unknown regression coefficients

Example=> oil consumption:

Y=oil consumption(per month)
X1=outdoor temperature

X2=size of house(in meter square)

Model:

Y=beta0+beta1X1+beta2X2+epsylon

now beta1 is expected change in Y(oil consiumption) at one unit increase in X1(outdoor temperature), when all other predictors are kept constant, i.e. in this case the size of the house is not changed.

beta1 is estimated with beta1=-27.2 degree C

 

Assumptions:

The random error term epsylon is normally distributed and has mean zero. i.e. E(epsylon)=0

Epsylon has (unknown) variance sigma epsylon^2. i.e. all random errors have the same variance.

Adjusted R^2
R^2adj=1- SSE/(n-k-1)/SST/(n-1)

 

 

As for simple linear regression:

plots of residual against y prime
plots of residuals against xi
normal probability plot of residuals
plots of residuals in observation order
Cook’s distance
Studentized residuals
Standardized residuals
Dffits

Collinearity:
Can only occur for multiple regression.
Predictors explaining the same variation of the response variabl.

Oil consumption continued:
One predictor measuring house size in cm^2 and another predictor in m^2
Variance inflation factor

VIFi=1/1-Ri^2

Condition Index for collinearity:
between 10 and 30=>weak collinearity
between 30 and 100=>moderate
collinearity>100=>strong collinearity

Example of Oil consumption continued:
Assume that we would like to use outdoor temperature X1 and house size X2 as predictors. Additionally, we want to use a third predictor:

X3={1 if extra-thick walls, 0 otherwise

Model:
Y=beta0+beta1X1+beta2X2+beta3X3+epsylon

Model Selection Strategies:
Mldel ranked using R^2, adjusted R^2 or mallow’s Cp
Stepwise selection methods:
Backward, forward, stepwise selection

r^2 Selection
In a data set with 7 possible predictors, there would be 2^7-1=127 possible regression models.
For every model size(k=1,2,…..,p) look at, let say, m models, chosen

Mallow’s Cp:
Large Cp=>biased model
it’s a formula.
where MSEp=mean squared error for a model with p parametes
mean squared error for the full model
n=number of observations

Beta Error

https://www.khanacademy.org/math/ap-statistics/tests-significance-ap/error-probabilities-power/v/introduction-to-type-i-and-type-ii-errors

https://www.google.com/search?q=%CE%B2+error&rlz=1C1CHBF_enBD864BD864&oq=%CE%B2+error&aqs=chrome..69i57j0l7.10568j0j8&sourceid=chrome&ie=UTF-8

 

Some quick excel tips

Exercise Sheet 5

1d theke clear na , eta clear korte hobe , In Sha Allah.

 

Lagle onno kono tutorial ba example dekhte hobe.