Regression analysis and correlation coefficient are the widely practiced processes to analyze the relationship of two quantitative variables with each other. Regression equation calculates the value of the dependent variable from independent variable and correlation coefficient is an estimate of the strength of this relationship.
The best regression would be:
Income = B2 * STOCKS + C2,
As stocks are strongly positively correlated with income as compared to debts, which implies that correlation coefficient would be nearly equal to +1. Strong correlation means that there is a high degree of association between stocks and income, which means that both variables are closely related to each other and would be more tightened on a scatterplot. Hence, it becomes easy to find a line that best fits the data which is highly correlated, and its data points are close to each other on the plot which makes intuitive sense. Since the data points for the scatterplot of stocks and income would be tightly packed hence regression equation representing the linear relationship between these two variables would yield the more accurate results. Moreover, the correlation coefficient is directly related to the slope of the regression line. Hence, a higher value of correlation coefficient makes the value of B2 more reliable.
References
Kean University. Regression and Correlation (extracted from Daniel, W. Wayne. (1999).
Biostatistics: a foundation for analysis in the health sciences. New York: John Wiley and Sons.).Retrieved from http://www.kean.edu/~fosborne/bstat/09rc.html
