**Exhibit 14-16**You are given the following information about x and y.| x (Independent Variable) | y (Dependent Variable) ||--------------------------|------------------------|| 21 | 10 || 8 | 4 || 9 | 8 || 10 | 5 |Refer to Exhibit 14-16. The coefficient of determination equals _____.- ○ .1905- ○ -.638- ○ .639- ○ -.1905**Explanation:**This exhibit presents data for two variables, an independent variable $x$ and a dependent variable $y$. Four pairs of values are provided, showing how changes in $x$ might be associated with changes in $y$. The task is to determine the coefficient of determination, which indicates how well the independent variable explains the variability in the dependent variable. The possible answers are labeled and include both positive and negative values.

X Y X.Y X2 Y2 21 10 210 441 100 8 4 32 64 16 9 8 72 81 64 10 5 50 100 25 ∑X=48 ∑Y=27…

Exhibit 14-16 You are given the following information about x and y. X Independent Variable 21 8 9 10 Dependent Variable O.1905 O-638 .639 O-.1905 10 4 +005 8 Refer to Exhibit 14-16. The coefficient of determination equals

Exhibit 14-16 You are given the following information about x and y. X Independent Variable 21 8 9 10 Dependent Variable O.1905 O-638 .639 O-.1905 10 4 +005 8 Refer to Exhibit 14-16. The coefficient of determination equals

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Question

100%

**Exhibit 14-16**

You are given the following information about x and y.

| x (Independent Variable) | y (Dependent Variable) |
|--------------------------|------------------------|
| 21 | 10 |
| 8 | 4 |
| 9 | 8 |
| 10 | 5 |

Refer to Exhibit 14-16. The coefficient of determination equals _____.

- ○ .1905
- ○ -.638
- ○ .639
- ○ -.1905

**Explanation:**

This exhibit presents data for two variables, an independent variable $x$ and a dependent variable $y$. Four pairs of values are provided, showing how changes in $x$ might be associated with changes in $y$. The task is to determine the coefficient of determination, which indicates how well the independent variable explains the variability in the dependent variable. The possible answers are labeled and include both positive and negative values.

Expert Solution

Step 1

X	Y	X.Y	$X^{2}$	$Y^{2}$
21	10	210	441	100
8	4	32	64	16
9	8	72	81	64
10	5	50	100	25
$\sum_{} X = 48$	$\sum_{} Y = 27$	$\sum_{} X Y = 364$	$\sum_{} X^{2} = 686$	$\sum_{} Y^{2} = 205$