Questions: R^2 is a value that is used to determine the strength of a linear fit. True False

The means of the independent variable $x$ and the dependent variable $y$ are calculated as follows:

$$\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i = \frac{1 + 2 + 3 + 4 + 5}{5} = 3.0$$

$$\bar{y} = \frac{1}{n} \sum_{i=1}^{n} y_i = \frac{2 + 4 + 5 + 4 + 5}{5} = 4.0$$

The correlation coefficient $r$ is calculated to measure the strength of the linear relationship between $x$ and $y$:

$$r = 0.7746$$

The slope $\beta$ of the regression line is determined using the following formulas:

Numerator for $\beta$: $$\sum_{i=1}^{n} x_i y_i - n \bar{x} \bar{y} = 66 - 5 \cdot 3.0 \cdot 4.0 = 6.0$$

Denominator for $\beta$: $$\sum_{i=1}^{n} x_i^2 - n \bar{x}^2 = 55 - 5 \cdot 3.0^2 = 10.0$$

Thus, the slope $\beta$ is calculated as: $$\beta = \frac{6.0}{10.0} = 0.6$$

The intercept $\alpha$ is calculated using the formula: $$\alpha = \bar{y} - \beta \bar{x} = 4.0 - 0.6 \cdot 3.0 = 2.2$$

The equation of the line of best fit is given by: $$y = 2.2 + 0.6x$$

The $R^2$ value, which indicates the proportion of variance explained by the regression line, is calculated as: $$R^2 = r^2 = (0.7746)^2 = 0.6000$$

Since $R^2$ is indeed used to determine the strength of a linear fit, the answer to the question is:

$$\boxed{\text{True}}$$