Week: Unit VI: Regression and Correlation | AST1231: Introduction to Statistics (CoL) | University of Rwanda

Section outline

Aims of the unit:
This Unit deals only with statistical practice or how to apply statistics in the real life, such that in agriculture, industry, and in any services: banks, tourism, restaurants, hostels, and so on. We are often interested in finding whether a relationship exists between two variables. For example, we would expect there to be a relationship between advertising costs and sales, the more a company spends on advertising, the greater the sales it could expect. To investigate this relationship, we could take a random sample of companies, and ask the companies to state the amount spent on advertising and the corresponding sales of the product.

Learning Outcomes:
After successful completion of the unit, you will be expected to be able to:

Explain the concepts regarding this unit,

Demonstrate the mechanism and the technics that help you to manipulate the necessary formulae, and arrive to execute any possible calculations,

To do any application required and get the true solutions without difficulty

Indicative content:

Determination of the coefficient of correlation(Degree of correlation),

Fit the regression model.

Reference:

Read textbooks,

Published papers, and

Articles, materials on the statistical practices in different domains through the University of Rwanda Library website: https:/library.ur.ac.rw/ and materials uploaded below.

Unit outline of this unit:
Attached is the course outline of the coefficient of variation and it describes the sub-units covered by the unit and practice to be conducted in the unit.
- Select activity Source 1: Lecture note
  
  Source 1: Lecture note File PDF
  
  Students must
  
  Mark as done
  
  266.6 KB
- Select activity E-tivity 6.1: Regression between two variables X and Y
  
  E-tivity 6.1: Regression between two variables X and Y Forum
  
  6.1 A: From a set of observations of the variables x and y, it is found that the regression line y on x passes through the point (0; 1.8).
  If the means of the x and y values are 5.0 and 8.3 respectively, find the equation of the regression line of y on x in the form: y= a + bx.
  
  6.1 B: The table below with two variables X and Y is given.
  
  X 9 8 7 6 5 4 3 2 1
  
  Y 15 16 14 13 11 12 10 8 9
  
  Find the coefficient of correlation between the variables X, Y, and comment on its value.
  
  Calculate the regression line of Y on X and X on Y. Give the intersection of two variables
  
  Students have to know well that a regression line is a straight line, which represents the linear relationship between two variables on average. In this step, you have to distinguish their natures (dependent and Independent variables), before their calculation and interpretation of their meanings. You will illustrate this (e-tivity 6.2) with examples in real life.
  
  Not available unless: The activity E-tivity 5.3: Assignment on the prices stability in the ... ...
  
  Not available unless: The activity E-tivity 5.3: Assignment on the prices stability in the Markets is marked complete
- Select activity E-tivity 6.2: Correlation Coefficient of Spearman
  
  E-tivity 6.2: Correlation Coefficient of Spearman Forum
  
  Students must
  
  Mark as done
  
  A random sample of five (5) college students is selected and their grades in mathematics and statistics are found to be calculated by Spearman’s rank correlation coefficient.
  
  Maths 85 60 73 40 90
  
  Statistics 93 75 65 50 80
  
  Before doing this e-tivity 6.2, read deeply the given materials related to the determination of superman’s rank correlation coefficient through Lecture notes, and other resources given that contribute more to this e-tivity.
- Select activity Source 2: Regression and Correlation
  
  Source 2: Regression and Correlation URL
  
  Students must
  
  Mark as done
- Select activity E tivity 6.3: Correlation between variables of two teams A and B
  
  E tivity 6.3: Correlation between variables of two teams A and B Forum
  
  Students must
  
  Mark as done
  
  The Goals scored by two teams A and B in a football season were as follows.
  
  Team A 27 9 8 5 4
  
  Team B 17 9 6 5 3
  
  You (student) have to read the materials provide to you in different resources under your position.
  
  In addition, arrive to understand the concept of the simple correlation as the degree of association between two or more variables. For example, the relationships between price and demand, price and supply, age and husband and age of wife, height and weight of individuals, intelligence quotient, and marks secured by students in an examination are some of the examples of a correlation that student must be able to distinguish very well. You have also to distinguish the difference between regression, correlation, and their meaning in life. By reading carefully the materials, you arrive to understand well that correlation is “a statistical tool used to measure the degree of relationship between two or more variables”