Karl Pearson's Coefficient - 2 Video Lecture | Economics Class 11 - Commerce

Ans. Karl Pearson's coefficient, also known as Pearson's correlation coefficient, is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation. To calculate Pearson's coefficient, you need to have paired observations for two variables. Firstly, calculate the covariance of the two variables by subtracting the mean of each variable from its corresponding observation, then multiplying the differences together, and finally taking the average of these products. Secondly, calculate the standard deviation of each variable. Finally, divide the covariance by the product of the two standard deviations to obtain Pearson's coefficient.

Ans. A value of 0 for Karl Pearson's coefficient indicates no linear relationship between the two variables being examined. In other words, there is no correlation between the variables. This means that changes in one variable do not correspond to changes in the other variable. However, it is important to note that a correlation of 0 does not necessarily imply the absence of any relationship between the variables, as there could still be a non-linear relationship present.

Ans. The interpretation of Karl Pearson's coefficient depends on its value. - A coefficient close to 1 indicates a strong positive linear relationship, meaning that as one variable increases, the other variable also tends to increase proportionally. - A coefficient close to -1 indicates a strong negative linear relationship, meaning that as one variable increases, the other variable tends to decrease proportionally. - A coefficient close to 0 indicates no linear relationship between the variables, as mentioned earlier. It is important to remember that Pearson's coefficient only measures the strength and direction of a linear relationship, and it may not capture non-linear relationships or other types of dependencies between variables.

Ans. No, Karl Pearson's coefficient cannot be used to determine causation between variables. Pearson's coefficient only measures the strength and direction of a linear relationship between two variables. It does not provide any information about the underlying causes or mechanisms that drive the relationship. Causation implies that changes in one variable directly cause changes in the other variable. To establish causation, additional research and experimentation are required, such as controlled experiments or longitudinal studies that account for other potential factors and confounding variables.

Ans. Yes, there are certain limitations and assumptions associated with Karl Pearson's coefficient: - Pearson's coefficient assumes that the relationship between the variables is linear and that the data is normally distributed. - It only measures the strength and direction of a linear relationship, and may not capture non-linear relationships or other types of dependencies. - It is sensitive to outliers, as they can significantly impact the calculation of the coefficient. - Pearson's coefficient measures association but does not imply causation. - It is only applicable for continuous variables and may not be suitable for categorical or ordinal variables. Therefore, it is important to consider these limitations and assumptions when interpreting and applying Pearson's coefficient in statistical analysis.