A financial analyst wants to determine the relationship between a company's earnings per share (EPS, Y, in dollars) and its revenue (X, in million dollars). Assuming a linear relationship between Y and X, the analyst used the least-squares method and found that the Y-intercept = 1.75 and the slope = 0.42. Also, the sum of squares total (SST) and the error sum of squares (SSE) were equal to 82000.12 and 15200.43, respectively.Based on this information, what is the coefficient of determination? Round your final answer to four decimal places. Note: don't put your answer in percentage form.
Question
A financial analyst wants to determine the relationship between a company's earnings per share (EPS, Y, in dollars) and its revenue (X, in million dollars). Assuming a linear relationship between Y and X, the analyst used the least-squares method and found that the Y-intercept = 1.75 and the slope = 0.42. Also, the sum of squares total (SST) and the error sum of squares (SSE) were equal to 82000.12 and 15200.43, respectively.Based on this information, what is the coefficient of determination? Round your final answer to four decimal places. Note: don't put your answer in percentage form.
Solution
The coefficient of determination, often denoted as R^2, is a statistical measure that shows the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model.
In this case, the coefficient of determination can be calculated using the formula:
R^2 = 1 - (SSE/SST)
Where: SSE = Sum of Squares Error = 15200.43 SST = Total Sum of Squares = 82000.12
Substituting the given values into the formula, we get:
R^2 = 1 - (15200.43/82000.12)
After performing the division and subtraction, we get:
R^2 = 0.8146
So, the coefficient of determination is 0.8146 when rounded to four decimal places. This means that approximately 81.46% of the variation in the company's earnings per share can be explained by its revenue.
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