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What is equivalent to 2.50 in decimals
What is equivalent to 2.50 in decimals
Final answer:To have a coefficient of determination of at least 0.50, the necessary correlation coefficient must be about +/-0.71. This is because the coefficient of determination is the square of the correlation coefficient, and the square root of 0.50 is approximately 0.7071, rounded to four decimal places.Explanation:Understanding Correlation and Coefficient of Determination:The question posed relates to the statistical concepts of correlation and coefficient of determination. The coefficient of determination, represented as R-squared (R²), is the square of the correlation coefficient and indicates how well data points fit a statistical model or line. In this case, to achieve a coefficient of determination of at least 0.50, one needs to first take the square root of 0.50. The square root of 0.50 is approximately 0.7071, rounded to four decimal places.Since correlation can be positive or negative, and the coefficient of determination is the square of the correlation, any correlation coefficient of about 0.7071 or -0.7071 will yield a coefficient of determination of at least 0.50 when squared. Therefore, the required correlation between two variables to achieve a coefficient of determination of at least 0.50 is approximately +/-0.71 when rounded to two decimal places.To understand this better, imagine a scatter plot of data points with a line of best fit through them. A higher absolute value of the correlation coefficient indicates that the data points are closer to the line. When this coefficient is squared to obtain the coefficient of determination, it tells us what proportion of the variance in the dependent variable is predictable from the independent variable. In this context, a coefficient of determination of 0.50 suggests that 50% of the variance is predictable....