Calculate the value of sum xy.

here are the solutions for questions 14, 15, 16, and 17.

14. Calculate the value of $\sum xy$.

Step 1: Identify the given regression equation and statistical values.
The regression equation is $y = 11.37395 + 2.82773x$.
This is in the form $y = a + bx$, where $a = 11.37395$ and $b = 2.82773$.
Given: $\sum y = 255$, $\sum y^2 = 8621$, $\sum x^2 = 480$, $n = 8$.

Step 2: Use the normal equation $\sum y = na + b \sum x$ to find $\sum x$.

$$255 = (8)(11.37395) + (2.82773) \sum x$$ $$255 = 90.9916 + 2.82773 \sum x$$ $$255 - 90.9916 = 2.82773 \sum x$$ $$164.0084 = 2.82773 \sum x$$ $$\sum x = \frac{164.0084}{2.82773}$$ $$\sum x \approx 58$$

Step 3: Use the normal equation $\sum xy = a \sum x + b \sum x^2$ to find $\sum xy$.

$$\sum xy = (11.37395)(58) + (2.82773)(480)$$ $$\sum xy = 659.6901 + 1357.3104$$ $$\sum xy = 2017.0005$$

Rounding to the nearest integer, $\sum xy = 2017$.

The correct option is C.
The value of $\sum xy$ is $\boxed{\text{C. } \textbf{2017}}$.

15. For the data in Question 14, calculate the correlation coefficient.

Step 1: State the formula for the correlation coefficient ($r$).

$$r = \frac{n \sum xy - (\sum x)(\sum y)}{\sqrt{[n \sum x^2 - (\sum x)^2][n \sum y^2 - (\sum y)^2]}}$$

Step 2: Substitute the known values into the formula.
From Question 14, we have:
$n = 8$
$\sum xy = 2017.0005$
$\sum x = 58$
$\sum y = 255$
$\sum x^2 = 480$
$\sum y^2 = 8621$

Calculate the numerator:

$$n \sum xy - (\sum x)(\sum y) = 8(2017.0005) - (58)(255)$$ $$= 16136.004 - 14790$$ $$= 1346.004$$

Calculate the first part of the denominator:

$$n \sum x^2 - (\sum x)^2 = 8(480) - (58)^2$$ $$= 3840 - 3364$$ $$= 476$$

Calculate the second part of the denominator:

$$n \sum y^2 - (\sum y)^2 = 8(8621) - (255)^2$$ $$= 68968 - 65025$$ $$= 3943$$

Step 3: Calculate $r$.

$$r = \frac{1346.004}{\sqrt{(476)(3943)}}$$ $$r = \frac{1346.004}{\sqrt{1877068}}$$ $$r = \frac{1346.004}{1369.9007}$$ $$r \approx 0.98255$$

Rounding to three decimal places, $r \approx 0.983$. The closest option is 0.982.

The correct option is B.
The correlation coefficient is $\boxed{\text{B. } \textbf{0.982}}$.

16. Which team's points scored shows greater variability throughout the season.

Step 1: Understand that variability relative to the mean is measured by the Coefficient of Variation (CV).
The formula for the Coefficient of Variation is:

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