Regression Line and Karl Pearson Coefficient of Correlation


The regression line is a straight line that represents the relationship between two variables X and Y. In this case, the regression line is given by Y = X^2. This means that for every increase in the value of X, the value of Y will increase by the square of X.


The Karl Pearson coefficient of correlation, also known as the Pearson correlation coefficient, is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 represents a perfect negative correlation, 0 represents no correlation, and 1 represents a perfect positive correlation. In this case, the coefficient of correlation is 0.5, indicating a moderate positive correlation between X and Y.


Since the coefficient of correlation is positive, we can say that there is a tendency for Y to increase as X increases. However, the correlation is only moderate, which means that not all the variability in Y can be explained by the variability in X. This is because the relationship between X and Y is not perfectly linear, as indicated by the curve Y = X^2. Therefore, we cannot use the regression line to predict Y with a high degree of accuracy.

In conclusion, while there is a positive relationship between X and Y, the correlation is only moderate, and the regression line cannot be used to predict Y accurately.