Dimensional Analysis Buckingham Pi Theorem, Slides of Dimensional Analysis

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Business Mathematics and Statistics

(MATH0203)

Chapter 1: Correlation & Regression

Dependent and independent

variables

• The independent variable (x) is the one that is

chosen freely or occur naturally.

• The dependent variable (y) occurs as a

consequence of the value of the independent

variable.

Definition of correlation

Correlation is concerned with describing the

strength of the relationship between two

variables.

Scatter Diagrams

• Visual representation can give an immediate

impression of a set of data. Are these two

variables having strong relationship, moderate

relationship, weak relationship or no

relationship?

Question 1.

• The table below presents the data concerning the

number of hours of training in typewriting and

the speed of typing a given text for 10 randomly

selected typists.

• Draw a scatter diagram. Typist (^) 1 2 3 4 5 6 7 8 9 10 Number of hour of training 120 70 100 50 150 90 30 40 80 20 Speed (word/minute) 30 18 25 14 35 21 10 15 20 10

CORRELATION

To measure how well the regression line fits the

actual data

By:

i. Coefficient of determination ( R

2

ii. Coefficient of correlation (R)

8

Perfect correlation Partial correlation No correlation

11

Positive correlation

• Two variables x and y are moving in the same

direction.

• i.e. If x increases, y will increases. If x decreases,

y decreases.

Examples:

1) Numbers of calls made by salesman and

number of sales obtained.

2) Age of employee and salary.

Negative correlation

• Two variables x and y are moving in the opposite

direction.

• i.e. If x increases, y will decreases. If x decreases, y

increases.

Example:

1) Number of weeks of experience and number of

errors made.

2) Grade obtained and number of hours watching

television.

Question 1.2:

• The data of the following table relates the weekly

maintenance cost (RM) to the age (in months) of

five machines of similar type in a manufacturing

company. Calculate the product moment

correlation coefficient between age and cost.

Machine (^) 1 2 3 4 5 Age 5 10 15 20 30 Cost 10 20 20 30 30

x y xy x² y² r = = __________________ = __________________    2 2 2 2 n x ( x ) n y ( y ) n xy x y          Working

Question 1.3:

• Find relationship between mid test and final

exam using rank correlation.

Person (^) A B C D E F G Mid test score 50 62 85 91 74 59 84 Final Exam score 67 70 80 79 68 67 81

Solution:

Person A B C D E F G x 50 62 85 91 74 59 84 y 67 70 80 79 68 67 81 x r y r 2 ( ) x y r  r ( 1 ) 6 1 2 2     n n d r =