313307 STATISTICAL MODELLING FOR MACHINE LEARNING K scheme syllabus

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Lists of unit of Statistical Modelling for machine learning

Unit – I Statistical Techniques
Unit – II Statistical Methods
Unit – III Probability of Random Variable
Unit – IV Interpolation
Unit – V Sampling Methods

Unit – I Statistical Techniques

1.1 Frequency Distribution: Definition, Basic terms.
1.2 Classification of Data: Raw, Ungroup and Group data.
1.3 Measures of Central Tendency: Mean, Median and Mode for all types of data.
1.4 Concept of Quartiles, Deciles and Percentiles for all types of data.
1.5 Geometric mean and Harmonic mean and Combined mean for given data.
1.6 Graphical Representation to find Mode (Histogram) and Median (Ogive curve ).
1.7 Measures of Dispersion: Range, Mean Deviation, Standard Deviation, Variance.
1.8 Skewness: Types of skewness, Test of skewness, Co-efficient of skewness-Karl Pearson’s and Bowley’s coefficient.
1.9 Types of skewness in terms of Mean and Mode.
1.10 Measures of Kurtosis using central moment.

Unit – II Statistical Methods

2.1 Fitting of Straight Line y = a+bx using method of least square.
2.2 Fitting of second degree polynomial y=a+bx+cx² using method of least square.
2.3 Covariance of the data.
2.4 Correlations, Types of Correlations.
2.5 Scatter Or Dot-Diagram.
2.6 Karl-Pearson’s and Spearman’s Rank Coefficient of Correlation.
2.7 Regression Equation of line in two variables.

Unit – III Probability of Random Variable

3.1 Probability : Definition, Terminologies.
3.2 Theorem of Probability: Addition, Multiplication.
3.3 Conditional probability.
3.4 Bayes’ theorem.

Unit – IV Interpolation

4.1 Introduction.
4.2 Lagrange’s Interpolation formula.
4.3 Finite Differences: Forward difference, Backward difference, Shift operator, Inverse shift operator.
4.4 Relation between forward, backward, shift and inverse shift operator.
4.5 Newton’s Gregory forward and backward difference Interpolation Formula.
4.6 Concept of Extrapolation.

Unit – V Sampling Methods

5.1 Population, Sampling, Aim of Sampling, Parameters and Statistic, Types of Sampling, Standard Error.
5.2 Hypothesis: Null Hypothesis and Alternating Hypothesis.
5.3 Level of Significance, Test of Significance and Confidence Limits.
5.4 Test of Significance of Large Samples (N>30).
5.5 Sample Distribution of the proportion.
5.6 Comparison of Large Samples.
5.7 The t-Distribution (For Small Samples).
5.8 Chi-Square Distribution, Condition for Chi Square test.
5.9 Degree of freedom.
5.10 Chi-Square Test of Goodness of fit and Chi-Square test as a test of Independence.

Laboratory Experiment / Practical Titles / Tutorial Titles

Download R Studio.Install and configure R studio and R Packages.
Write Program to-
a. Demonstrate the use of R-Numbers. (numeric, integer, complex).
b. Convert number from one type to other using functions.
c. Perform following operations.
i. Addition and Subtraction on numbers.
ii. Find Square root using of number using built-in function.
Write Program to-
a. Print any built-in data set of R.
b. Get information about the data set.
c. Find the dimensions of the data set and view the names of the variables.
Hint: Use dim( ) and names( ) function.
d. Find the name of each row in the first column.
Hint: Use the rownames( ) function.
e. Print all values that belong to a variable.
f. Sort the values of variable.
g. Get the statistical summary of the data.
Write a program to-
a. Find the lowest or highest value in a data set.
Hint: Use min( ) and max( ) functions.
b. Find the index position of the max and min value in the table.
Hint: use which.max( ) and which.min( ) functions.
Write programs to calculate Measures of Central tendency.
a. Import data into R.
b. Calculate the Mean (Average value) of a variable from the given data set.
c. Find the Median (Mid-Point value) of the variable from the given data set.
d. Calculate the mode for the variable from the given data set.( by sorting the column of the dataframe and by using the ‘modest’ package).
e. Calculate the Percentile of the variable from the given data set.
Write programs to-
a. Print Original Data Frame, Modified Frequency Table, Cumulative Frequency Table, Relative Frequency Table.
b. Create the Frequency Table by using multiple arguments.
c. Plot the frequency table using ggplot function.
Write programs to calculate-Variance, Standard Deviation, Range, Mean Deviation for the given data.
* Write Programs to graphically represent mode and median of the given data.
a. Draw Histogram for the given data.
b. Draw Ogive Curve for the given data.
Write a Program to calculate Skewness for the given data.
Write a Program to draw a scatterplot for two variables for the given dataset.
Write Program to perform the correlation test to evaluate the association between two or more variables.
a. Install and load required R packages.
b. Compute correlation in R.
c. Visualize your data using scatter plots.
d. Perform Preliminary test to check the test assumptions.
Write Program to perform the correlation test to evaluate the association between two or more variables.
a. Pearson correlation test.
b. Interpretation of the result.
c. Use Spearman rank correlation coefficient to estimate a rank-based measure of association.
Write a Program based on Line of Regression using two variables.
Write Programs to-
a. Calculate the probability of getting heads when flipping a fair coin.
b. Calculate the probability of drawing a spade from a standard deck of 52 cards.
Write a program to compute probability using prob( ) function.
Write a program to calculate the probability of rolling a 3 on a fair six-sided die.
Write a program to calculate the conditional probability.
Write a program to use Bayes’ Theorem in R-Programming.
Write a Program to interpolate using newton forward interpolation.
Write a Program to interpolate using newton backward interpolation.
Write a program for the implementation of extrapolation.
Write a program to generate Samples using the Sampling Functions.
Write programs to perform following types of sampling-
a. Simple Random Sampling.
b. Stratified Sampling.
c. Systematic Sampling.
d. Biased Sampling.
Write a program to generate a Sampling Distribution proportion.
Write a program based on t-Distribution using dt, pt, qt & rt functions.
Write a program based on Chi-Square Distribution using dchisq, pchisq, qchisq & rchisq functions.

Unitwise weightage of statistical modelling for machine learning

Sr.No	Units	Weightage
1	Unit – I Statistical Techniques	20
2	Unit – II Statistical Methods	14
3	Unit – III Probability of Random Variable	8
4	Unit – IV Interpolation	14
5	Unit – V Sampling Methods	14