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Probable Error - Correlation & Regression, Business Mathematics & Statistics - Business Mathematics and Statistics - B Com

Probable Error
The term probable error is seen only in older statistics literature where it used to denote the product of the standard error and a constant factor 0.6745. Thus,
P.E = 0.6745(S.E)
Here P.E and S.E stand for the probable error and the standard error, respectively. By using the above formula the probable error of any statistic may be determined if we substitute the standard error of that statistic. Hence, for example, the probable error of the correlation coefficient would be 

Probable Error - Correlation & Regression, Business Mathematics & Statistics | Business Mathematics and Statistics - B Com
Definition: The Probable Error of Correlation Coefficient helps in determining the accuracy and reliability of the value of the coefficient that in so far depends on the random sampling.
In other words, the probable error (P.E.) is the value which is added or subtracted from the coefficient of correlation (r) to get the upper limit and the lower limit respectively, within which the value of the correlation expectedly lies.
The probable error of correlation coefficient can be obtained by applying the following formula:
Probable Error - Correlation & Regression, Business Mathematics & Statistics | Business Mathematics and Statistics - B Com
r = coefficient of correlation
N = number of observations

  • There is no correlation between the variables if the value of ‘r’ is less than P.E. This shows that the coefficient of correlation is not at all significant.
  • The correlation is said to be certain when the value of ‘r’ is six times more than the probable error; this shows that the value of ‘r’ is significant.
  • By adding and subtracting the value of P.E from the value of ‘r,’ we get the upper limit and the lower limit, respectively within which the correlation of coefficient is expected to lie. Symbolically, it can be expressed
    Probable Error - Correlation & Regression, Business Mathematics & Statistics | Business Mathematics and Statistics - B Com

where rho denotes the correlation in a population
The probable Error can be used only when the following three conditions are fulfilled:

  1. The data must approximate to the bell-shaped curve, i.e. a normal frequency curve.
  2. The Probable error computed from the statistical measure must have been taken from the sample.
  3. The sample items must be selected in an unbiased manner and must be independent of each other.

Thus, the probable error is calculated to check the reliability of the value of coefficient calculated from the random sampling.

The document Probable Error - Correlation & Regression, Business Mathematics & Statistics | Business Mathematics and Statistics - B Com is a part of the B Com Course Business Mathematics and Statistics.
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FAQs on Probable Error - Correlation & Regression, Business Mathematics & Statistics - Business Mathematics and Statistics - B Com

1. What is correlation and regression in business mathematics and statistics?
Ans. Correlation and regression are statistical techniques used in business mathematics and statistics to examine the relationship between two or more variables. Correlation measures the strength and direction of the relationship, while regression helps in predicting the value of one variable based on the values of other variables.
2. How is correlation calculated?
Ans. Correlation is calculated using a correlation coefficient, typically denoted by "r". It ranges from -1 to +1, where -1 represents a perfect negative correlation, +1 represents a perfect positive correlation, and 0 represents no correlation. The correlation coefficient is calculated by dividing the covariance of the two variables by the product of their standard deviations.
3. What is the difference between correlation and regression?
Ans. Correlation measures the strength and direction of the relationship between two variables, whereas regression helps in predicting the value of one variable based on the values of other variables. Correlation does not imply causation, while regression can establish a cause-and-effect relationship between the variables.
4. How is regression analysis used in business?
Ans. Regression analysis is widely used in business to analyze and predict various outcomes. It helps in understanding the relationship between independent variables (such as price, advertising, and customer satisfaction) and dependent variables (such as sales or profit). Businesses can use regression analysis to make informed decisions, optimize their strategies, and forecast future trends.
5. What are the limitations of correlation and regression analysis?
Ans. While correlation and regression analysis are powerful tools, they also have limitations. These include the assumption of linearity between variables, sensitivity to outliers, inability to establish causation, and reliance on past data to predict future outcomes. It is important to interpret the results carefully and consider other factors that may influence the relationship between variables.
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