Which is correct to find the value of the coefficient of determination (r2)?

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The coefficient of determination is presented by R² is mostly used in the analysis of regression where it is the proportion of the variance in the dependent variable that is predictable from the independent variable. The range of values between the predicted scores and the actual scores is between 0 to 1. The closer the value to 1, the greater is the relationship between variables and has lesser errors. For example, if there is an R² of 0.80, then it means that 80% is predictable. R² can be obtained using excel as trendline or with the use of formula.

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Let F of x equals the integral from 1 to 3 times x of the natural logarithm of t squared. Use your calculator to find F″(1).

eduard

Reading that as

$F(x)=\displaystyle\int_1^{3x}(\ln t)^2\,\mathrm dt$

By the fundamental theorem of calculus, the first derivative is

$F'(x)=3(\ln(3x))^2$

and so the second derivative would be

$F''(x)=\dfrac{6\ln(3x)}x$

which means

$F''(1)=6\ln3$