what is the coefficient of determination 
the coefficient of determination is a statistical measurement that examines how differences in one variable can be explained by the difference in a second variable when predicting the outcome of a given event this coefficient is more commonly known as r squared or r2 it assesses how strong the linear relationship is between two variables and it s heavily relied upon by investors when conducting trend analysis this coefficient generally answers a key question what percentage of a stock s price movement is attributed to the index s price movement if it s listed on an index and experiences price movements investopedia julie bangunderstanding the coefficient of determinationthe coefficient of determination is a measurement that s used to explain how much the variability of one factor is caused by its relationship to another factor this correlation is represented as a value between 0 0 and 1 0 or 0 to 100 a value of 1 0 indicates a 100 price correlation and is a reliable model for future forecasts a value of 0 0 suggests that the model shows that prices aren t a function of dependency on the index 1a value of 0 20 suggests that 20 of an asset s price movement can be explained by the index a value of 0 50 indicates that 50 of its price movement can be explained by it the coefficient of determination is the square of the correlation coefficient also known as r in statistics the value r can result in a negative number but r2 can t result in a negative number because r squared is the result of r multiplied by itself or squared the square of a negative number is always a positive value 2calculating the coefficient of determinationcalculating the coefficient of determination is achieved by creating a scatter plot of the data and a trend line you d collect the prices as shown in this table if you were to plot the closing prices for the s p 500 and apple aapl stock for trading days from dec 21 to jan 20 apple is listed on the s p 500 34you d then create a scatter plot how well the data fits the regression model on a graph is referred to as the goodness of fit it measures the distance between a trend line and all the data points that are scattered throughout the diagram most spreadsheets use the same formula to calculate the r2 of a dataset if the data reside in columns a and b on your sheet you get an r2 of 0 347 using this formula and highlighting the corresponding cells for the s p 500 and apple prices suggesting that the two prices are less correlated than if the r2 was between 0 5 and 1 0 calculating the coefficient of determination manually involves several steps first gather the data as in the previous table then calculate all the values you need as shown in this table 43use this formula and substitute the values for each row of the table where n equals the number of samples taken that s 20 in this case r 2 n x y x y n x 2 x 2 n y 2 y 2 2 begin aligned r 2 big frac n sum xy sum x sum y sqrt n sum x 2 sum x 2 times sqrt n sum y 2 sum y 2 big 2 end aligned r2 n x2 x 2 n y2 y 2 n xy x y 2 