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PPT - Correlation & Co-Efficient - Business Mathematics and Statistics - B Com

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Coefficient of correlation
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Coefficient of correlation
A statistic representing how closely two 
variables co-vary; it can vary from -1 
(perfect negative correlation) through 0 
(no correlation) to +1 (perfect positive 
correlation).
Page 3


Coefficient of correlation
A statistic representing how closely two 
variables co-vary; it can vary from -1 
(perfect negative correlation) through 0 
(no correlation) to +1 (perfect positive 
correlation).
• The correlation coefficient, denoted by r, is a 
measure of the strength of the straight-line or 
linear relationship between two variables. The 
correlation coefficient takes on values ranging 
between +1 and -1. 
• The quantity r, called the linear correlation 
coefficient, measures the strength and the 
direction of a linear relationship between two 
variables
Page 4


Coefficient of correlation
A statistic representing how closely two 
variables co-vary; it can vary from -1 
(perfect negative correlation) through 0 
(no correlation) to +1 (perfect positive 
correlation).
• The correlation coefficient, denoted by r, is a 
measure of the strength of the straight-line or 
linear relationship between two variables. The 
correlation coefficient takes on values ranging 
between +1 and -1. 
• The quantity r, called the linear correlation 
coefficient, measures the strength and the 
direction of a linear relationship between two 
variables
Type of correlation coefficient
1. Perfect Positive correlation
2. Perfect negative correlation 
3. Moderately Positive correlation
4. Moderate negative correlation 
5. Absolute no correlation 
Page 5


Coefficient of correlation
A statistic representing how closely two 
variables co-vary; it can vary from -1 
(perfect negative correlation) through 0 
(no correlation) to +1 (perfect positive 
correlation).
• The correlation coefficient, denoted by r, is a 
measure of the strength of the straight-line or 
linear relationship between two variables. The 
correlation coefficient takes on values ranging 
between +1 and -1. 
• The quantity r, called the linear correlation 
coefficient, measures the strength and the 
direction of a linear relationship between two 
variables
Type of correlation coefficient
1. Perfect Positive correlation
2. Perfect negative correlation 
3. Moderately Positive correlation
4. Moderate negative correlation 
5. Absolute no correlation 
Perfect Positive correlation
• If x and y have a strong positive linear correlation, 
r is close to +1. An r value of exactly +1 
indicates a perfect positive fit. Positive values 
indicate a relationship between x and y variables 
such that as values for x increases, values for y 
also increase. 
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FAQs on PPT - Correlation & Co-Efficient - Business Mathematics and Statistics - B Com

1. What is correlation and coefficient?
Ans. Correlation refers to the statistical measure that determines the relationship between two variables. It measures the strength and direction of the linear relationship between the variables. On the other hand, coefficient refers to the numerical value that quantifies the strength and direction of the correlation between the variables. The coefficient ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation.
2. How is correlation coefficient calculated?
Ans. The correlation coefficient is calculated using the formula: r = (nΣXY - ΣXΣY) / sqrt((nΣX^2 - (ΣX)^2)(nΣY^2 - (ΣY)^2)) where n represents the number of data points, ΣXY represents the sum of the products of the corresponding values of the two variables, ΣX and ΣY represent the sum of the values of the two variables, ΣX^2 and ΣY^2 represent the sum of the squares of the values of the two variables.
3. What does a correlation coefficient of 0 mean?
Ans. A correlation coefficient of 0 indicates no linear relationship between the two variables. It means that there is no statistical association between the variables being analyzed. However, it is important to note that a correlation coefficient of 0 does not necessarily imply the absence of a relationship; it only suggests the absence of a linear relationship.
4. How do you interpret the strength of a correlation coefficient?
Ans. The strength of a correlation coefficient is interpreted based on its absolute value. If the coefficient is close to +1 or -1, it indicates a strong linear relationship between the variables. The closer the coefficient is to 0, the weaker the relationship. Additionally, the sign of the coefficient (+ or -) indicates the direction of the relationship. A positive coefficient indicates a positive relationship, while a negative coefficient indicates a negative relationship.
5. Can correlation coefficient determine causation between variables?
Ans. No, correlation coefficient cannot determine causation between variables. It only measures the strength and direction of the linear relationship between the variables. Causation implies that one variable directly influences the other, which cannot be determined solely based on correlation. Additional research and experimental designs are required to establish causation between variables. Correlation merely suggests an association or relationship between the variables.
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