Statistics is the art of using data to make numerical conjectures about problems. This is an introductory course in statistics designed to provide students with the basic concepts of bivariate data analysis. Topics covered include correlation analysis, which is used to quantify the association between two random variables, regression analysis which is a related technique to access the relationship between an outcome variable, analysis of attributes, and bivariate distribution.

1)

2)

3)

4)

5)

1)

2)

3)

4)

5)

1

Bivariate data, scatter diagram, Bivariate table, Conditional means and variances, Marginal distributions.

10

2

Simple Correlation, Correlation ratio, Rank correlation, Spearman rank correlation, Partial and multiple correlation, Spurious correlation and Non-sense correlation.

15

3

Two variable linear regression, Estimation of parameters with properties, Residual analysis, Three variables regression (without matrix approach).

10

4

Basic ideas, classification, Order of classes and class frequencies, Ultimate class frequencies, Positive attributes, Consistency, Incomplete data, Association of attributes, Independence, Complete association and disassociation, Measures of association, Coefficient of association and colligation, Partial association, Analysis of 2 x 2 and r x c contingency table, Yate’s correction.

15

5

Concept of bivariate probability distribution, Marginal and conditional distributions, Expected values and variances, Moments and cumulants. Moment and cumulant generating functions, Derivation of bivariate normal distribution and study of its properties, Normal regression.

10

Bartoszynski, R., & M. Niewiadomska-Bugaj (2007). Probability and statistical inference. John Wiley & Sons.