38 Questions
What is the main purpose of partial correlation analysis?
To control the effect of multiple independent variables on the dependent variable
What is the characteristic of linear correlation?
The ratio of change between two variables is constant
What is the primary objective of correlation analysis?
To determine the degree of relationship between two or more variables
Which of the following is an example of perfect positive correlation?
If 10% rise in price of a commodity results in 10% rise in its supply
What is the benefit of correlation analysis in business?
It enables business executives to estimate cost, price and other variables
What is the range of the correlation coefficient?
-1 to +1
What is the significance of correlation analysis in practical life?
It is of immense use in understanding economic behavior
What is the purpose of controlling for the effect of other independent variables in partial correlation analysis?
To isolate the effect of one independent variable on the dependent variable
What is the main difference between linear and non-linear correlation?
Linear correlation has a constant ratio of change, while non-linear correlation has a varying ratio of change
What is the characteristic of non-linear correlation?
The ratio of change between two variables is not constant
What is the relationship between correlation and regression analysis?
Correlation analysis can be used as a basis for the study of regression
Which type of correlation analysis is used to study the relationship between yield of rice and rainfall, while controlling for the effect of fertilizer used?
Partial correlation analysis
Which of the following is NOT a type of correlation?
Causal correlation
What is the advantage of using correlation analysis in decision making?
It reduces the range of uncertainty associated with decision making
What do Boddington and Lunchou agree on regarding correlation analysis?
Correlation analysis deals with the association between two or more variables
What do Simpson and Kafka say about correlation analysis?
Correlation analysis deals with the association between two or more variables
What is the characteristic of perfect negative correlation?
An increase in one variable is followed by the same proportion of decrease in another variable.
What is the term used to describe a correlation where an increase in one variable is followed by a non-proportional increase in another variable?
Limited degree of positive correlation
What is the term used to describe a correlation where an increase in one variable is followed by a non-proportional decrease in another variable?
Limited degree of negative correlation
What is the characteristic of zero correlation?
There is no correlation between variables.
If a 10% rise in price results in a 5% fall in demand, what type of correlation is this?
Limited degree of negative correlation
If a 10% rise in price results in a 10% fall in demand, what type of correlation is this?
Perfect negative correlation
If a 10% fall in price results in a 5% increase in demand, what type of correlation is this?
Perfect negative correlation
What is the main difference between perfect negative correlation and limited degree of negative correlation?
The proportion of the correlation
What can be inferred from the direction and closeness of the two curves in the correlation graph?
Whether the variables are related or not
What is a limitation of the correlation graph method?
It cannot establish the exact degree of relationship between the variables
What is Karl Pearson's Co-efficient of Correlation also known as?
Product moment correlation coefficient
What is the formula for Karl Pearson's Co-efficient of Correlation?
r = Covariance of X and Y / (SD of X) x (SD of Y)
What is a merit of the correlation graph method?
It is a simple method of studying relationship between the variables
What is not possible with the correlation graph method?
To calculate a numerical value of correlation
What is the name of the method that plots all the values of two variables in a chart in the form of dots?
Scatter Diagram
What is the advantage of using a scatter diagram to study correlation?
It is a non-mathematical method that requires no calculations
What is the purpose of creating a scatter diagram?
To form an idea about the relationship between the variables
What is a limitation of using a scatter diagram to study correlation?
It only gives a rough idea about the correlation between variables
What type of correlation is indicated by a scatter of dots in a scatter diagram?
Low correlation
What is the name of the method that involves plotting individual values of two variables on a graph paper?
Correlation Graph
Which of the following is a characteristic of a scatter diagram?
It is easy to understand and does not require mathematical calculations
What is the first step in investigating the relationship between two variables?
Making a scatter diagram
Study Notes
Correlation Analysis
- Correlation analysis is a statistical technique used to study the relationship between two or more variables.
- It helps to determine the degree of relationship between variables.
Types of Correlation
- Partial Correlation: A correlation analysis that considers one dependent variable and one independent variable, while keeping the other independent variables constant.
- Linear Correlation: A correlation where the ratio of change between two sets of variables is the same.
- Non-Linear Correlation: A correlation where the amount of change in one variable does not bring the same ratio of change in the other variable.
Degrees of Correlation
- Perfect Positive Correlation: A correlation where an increase in one variable is followed by the same proportion of increase in the other variable.
- Perfect Negative Correlation: A correlation where an increase in one variable is followed by the same proportion of decrease in the other variable.
- Limited Degree of Positive Correlation: A correlation where an increase in one variable is followed by a non-proportional increase in the other variable.
- Limited Degree of Negative Correlation: A correlation where an increase in one variable is followed by a non-proportional decrease in the other variable.
- Zero Correlation: A correlation where there is no correlation between variables.
Correlation Coefficient
- The correlation coefficient is a numerical value that expresses the degree of correlation between two or more variables.
- It ranges from -1 to +1.
Significance of Correlation Analysis
- Correlation analysis is useful in practical life because it helps to:
- Find a single figure to measure the degree of relationship between variables.
- Understand economic behavior.
- Estimate cost, price, and other variables.
- Reduce the range of uncertainty associated with decision making.
- Provide a basis for the study of regression.
Methods of Measuring Correlation
-
Graphic Methods:
- Scatter Diagram: A method that plots the values of two variables in a chart to form an idea of whether the variables are related or not.
- Correlation Graph Method: A method that plots the individual values of two variables on a graph paper to infer whether the variables are related or not.
-
Algebraic Methods:
- Karl Pearson's Co-efficient of Correlation: A method that calculates the correlation coefficient using the covariance between X and Y and the product of their standard deviations.
- Spearman's Rank Correlation Method: A method that calculates the correlation coefficient using the rank of the variables.
- Concurrent Deviation Method: A method that calculates the correlation coefficient using the deviations of the variables from their means.
Merits and Demerits of Correlation Methods
-
Scatter Diagram Method:
- Merits: Simple, non-mathematical, easy to understand, and not influenced by extreme items.
- Demerits: Only gives a rough idea, cannot calculate correlation coefficient, and cannot establish exact degree of relationship.
-
Correlation Graph Method:
- Merits: Simple, easy to understand, and does not require mathematical calculations.
- Demerits: Cannot calculate correlation coefficient, only a pictorial presentation, and cannot establish exact degree of relationship.
-
Karl Pearson's Co-efficient of Correlation:
- Merits: Most popular method, widely used, and provides a precise measure of correlation.
- Demerits: Requires mathematical calculations and can be complex.
This quiz covers the basics of correlation analysis, including types of correlation such as partial and linear correlation, and its application in statistical analysis.
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