A group of students want to determine if a person's height is linearly related to the distance they are able to jump.To determine the relationship between a person's height and the distance they are able to jump, the group of students measured the height, in inches, of each person in their class and then measured the distance, in feet, they were able to jump from a marked starting point.Each student was given three tries at the jump and their longest jump distance was recorded. The data the students collected is shown below.

Question

KashtonW295412 KashtonW295412

31-10-2022
Mathematics

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A group of students want to determine if a person's height is linearly related to the distance they are able to jump.To determine the relationship between a person's height and the distance they are able to jump, the group of students measured the height, in inches, of each person in their class and then measured the distance, in feet, they were able to jump from a marked starting point.Each student was given three tries at the jump and their longest jump distance was recorded. The data the students collected is shown below.

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NicoletteY283387 NicoletteY283387 · Answer 1 · 2022-10-31T02:27:18+01:00

Explanation

We are required to determine the correlation coefficient (r) of the data provided. This should be calculated with the formula:

[tex]r_{xy}=\frac{\sum_{i\mathop{=}1}^n(x_i-\bar{x})(y_i-\bar{y})}{\sqrt{\sum_{i\mathop{=}1}^n(x_i-\bar{x})^2\sum_{i\mathop{=}1}^n(y_i-\bar{y})^2}}[/tex]

The information can be represented in a table as:

From the table, we have:

[tex]\begin{gathered} \sum_{i\mathop{=}1}^n(X-M_X)(Y-M_Y)=\sum_{i\mathop{=}1}^n(x_i-\bar{x})(y_i-\bar{y})=31.800 \\ \\ \sum_{i\mathop{=}1}^n(X-M_X)^2=\sum_{i\mathop{=}1}^n(x-\bar{x})^2=288.438 \\ \\ \sum_{i\mathop{=}1}^n(Y-M_Y)^2=\sum_{i\mathop{=}1}^n(y-\bar{y})^2=4.520 \end{gathered}[/tex]

Therefore, we can calculate the correlation coefficient as:

[tex]\begin{gathered} r_{xy}=\frac{\sum_{i\mathop{=}1}^n(x_i-\bar{x})(y_i-\bar{y})}{\sqrt{\sum_{i\mathop{=}1}^n(x_i-\bar{x})_{i\mathop{=}1}^{2\sum n}(y_i-\bar{y})}}\frac{}{} \\ \\ r_{xy}=\frac{31.800}{\sqrt{288.438\times4.520}} \\ \\ r_{xy}=0.8807 \\ \\ r_{xy}\approx0.88 \end{gathered}[/tex]

Hence, the answer is 0.88.