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Standard error and R Correlation

# Standard error and R Correlation - correlation coefficient...

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What is an r correlation coefficient and what useful information does it provide? This is a discussion board question and there is no word limit. I know the dictionary meaning but the instructor wants us to interpret or explain the statistics and give an example if possible . SOLUTION: Correlation refers to the strength of linear relationships’ between two variables. It defines a process for establishing whether linear relationships exist between two variables. It is given by: Correlation (r) = Cov(x,y) / σx*σy Correlation coefficient is a single summary number which gives you a brief and a good idea about how close one variable is in relation to the other one. Correlation signifies that two variables are related to each other, it should not be interpreted that one variable causes the other. Correlation tells you that as and when there is a change in one variable the other seems to change in a manner which is predictable. It is basically a numerical way to quantify the relationship between two variables for e.g. X and Y and is represented by the symbol r. A
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Unformatted text preview: correlation coefficient always lies between -1 and +1. If r is negative then an increase in X would result in decrease in Y while if r is positive an increase in X is would amount to increase in Y. if two variables are perfectly positively correlated then r=1, while if two stocks are perfectly negatively correlated then r = -1. Larger correlation coefficients like 0.7, 0.9 would reflect stronger correlation while smaller number like 0.2 will reflect weaker correlation between 2 variables. One application of correlation coefficient is while deciding portfolio of stocks to be invested in order to explore the benefits of diversification. For example while deciding the portfolio one may opt for two stocks which are negatively correlated i.e. if price of one stock goes up the price of the other drops, or for a positively correlated stocks. Lower the correlation greater is the risk reduction. Generally a negatively correlated stock saves one during the recessionary trends....
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