Correlation combines statistical concepts, namely, variance and standard deviation. Variance is the dispersion of a variable around the mean, and standard deviation is the square root of variance. Because it is so time-consuming, correlation is best calculated using software like Excel. In finance, for example, correlation is used in several analyses including the calculation of portfolio standard deviation. Simplify linear regression by calculating correlation with software such as Excel. The correlation coefficient ( ρ) is a measure that determines the degree to which the movement of two different variables is associated. The most common correlation coefficient, generated by the Pearson product-moment correlation, is used to measure the linear relationship between two variables. However, in a non-linear relationship, this correlation coefficient may not always be a suitable measure of dependence. Calculating the correlation coefficient is time-consuming, so data is often plugged into a calculator, computer, or statistics program to find the coefficient.A negative correlation, or inverse correlation, is a key concept in the creation of diversified portfolios that can better withstand portfolio volatility.A value close to zero indicates a weak relationship between the two variables being compared.A correlation coefficient greater than zero indicates a positive relationship while a value less than zero signifies a negative relationship.Correlation coefficients are used to measure the strength of the linear relationship between two variables.The linear regression below was performed on a data set with a TI calculator. According to the linear regression equation, what would be the approximate value of y when x = 3?.What is the correlation coefficient and the coefficient of determination? Is the linear regression equation a good fit for the data?.What is the linear regression equation?.Use the information shown on the screen to answer the following questions: Which of the following calculations will create the line of best fit on the TI-83?.This means that the linear regression equation is a moderately good fit, but not a great fit, for the data. You can see that r, or the correlation coefficient, is equal to 0.9486321738, while r 2, or the coefficient of determination, is equal to 0.8999030012. After pressing ENTER to choose LinReg(ax + b), press ENTER again, and you should see the following screen: In other words, to find the correlation coefficient and the coefficient of determination, after entering the data into your calculator, press STAT, go to the CALC menu, and choose LinReg(ax + b). The correlation coefficient and the coefficient of determination for the linear regression equation are found the same way that the linear regression equation is found. Is the linear regression equation a good fit for the data? \)ĭetermining the Correlation Coefficient and the Coefficient of Determinationĭetermine the correlation coefficient and the coefficient of determination for the linear regression equation that you found in Example B.
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