question 6 of 25

what is the $r$-value of the following data, to three decimal places?

$\begin{array}{|c|c|}\hline x & y \\\hline 4 & 2 \\\hline 5 & 9 \\\hline 8 & 10 \\\hline 9 & 12 \\\hline 13 & 23 \\\hline\end{array}$

a. $-0.953$
b. $0.953$
c. $0.908$
d. $-0.908$

Question

question 6 of 25

what is the $r$-value of the following data, to three decimal places?

$\begin{array}{|c|c|}\hline x & y \\\hline 4 & 2 \\\hline 5 & 9 \\\hline 8 & 10 \\\hline 9 & 12 \\\hline 13 & 23 \\\hline\end{array}$

a. $-0.953$
b. $0.953$
c. $0.908$
d. $-0.908$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Correlation Coefficient" ], "new_concepts": [], "current_concepts": [ "Correlation Coefficient" ] } ## Calculate summary statistics $$ \begin{aligned} n &= 5 \ \sum x &= 4 + 5 + 8 + 9 + 13 = 39 \ \sum y &= 2 + 9 + 10 + 12 + 23 = 56 \ \bar{x} &= 7.8 \ \bar{y} &= 11.2 \end{aligned} $$ ## Calculate sum of squares and cross-products $$ \begin{aligned} \sum x^2 &= 16 + 25 + 64 + 81 + 169 = 355 \ \sum y^2 &= 4 + 81 + 100 + 144 + 529 = 858 \ \sum xy &= 8 + 45 + 80 + 108 + 299 = 540 \ SS_{xx} &= 355 - \frac{39^2}{5} = 355 - 304.2 = 50.8 \ SS_{yy} &= 858 - \frac{56^2}{5} = 858 - 627.2 = 230.8 \ SS_{xy} &= 540 - \frac{39 \times 56}{5} = 540 - 436.8 = 103.2 \end{aligned} $$ ## Compute correlation coefficient $$ \begin{aligned} r &= \frac{SS_{xy}}{\sqrt{SS_{xx} \times SS_{yy}}} \ r &= \frac{103.2}{\sqrt{50.8 \times 230.8}} \ r &= \frac{103.2}{\sqrt{11724.64}} \ r &\approx \frac{103.2}{108.2804} \approx 0.953 \end{aligned} $$

A. -0.953

B. 0.953

C. 0.908

D. -0.908

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Correlation Coefficient" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate summary statistics

Calculate sum of squares and cross-products

Compute correlation coefficient

Answer: