select the correct answer.

this table contains data on the number of people visiting a historical landmark over a period of one week.

\begin{array}{|c|c|}
\hline
\text{day} & \text{number of visitors} \\
\hline
1 & 120 \\
\hline
2 & 124 \\
\hline
3 & 130 \\
\hline
4 & 131 \\
\hline
5 & 135 \\
\hline
6 & 132 \\
\hline
7 & 135 \\
\hline
\end{array}

sketch a scatter plot. which of these values comes closest to the correlation coefficient for this data?

\bigcirc\ 0.0
\bigcirc\ 0.3
\bigcirc\ 0.9
\bigcirc\ -0.3
\bigcirc\ -0.9

Question

select the correct answer.

this table contains data on the number of people visiting a historical landmark over a period of one week.

\begin{array}{|c|c|}
\hline
\text{day} & \text{number of visitors} \\
\hline
1 & 120 \\
\hline
2 & 124 \\
\hline
3 & 130 \\
\hline
4 & 131 \\
\hline
5 & 135 \\
\hline
6 & 132 \\
\hline
7 & 135 \\
\hline
\end{array}

sketch a scatter plot. which of these values comes closest to the correlation coefficient for this data?

\bigcirc\ 0.0
\bigcirc\ 0.3
\bigcirc\ 0.9
\bigcirc\ -0.3
\bigcirc\ -0.9

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Correlation Coefficient Calculation" ], "new_concepts": [], "current_concepts": [ "Correlation Coefficient Calculation", "Scatter Plot Analysis" ] } ## Calculate summary statistics for the data $$ \begin{aligned} n &= 7 \ \sum x &= 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28 \ \bar{x} &= 4 \ \sum y &= 120 + 124 + 130 + 131 + 135 + 132 + 135 = 907 \ \bar{y} &\approx 129.57 \ \sum (x - \bar{x})^2 &= 9 + 4 + 1 + 0 + 1 + 4 + 9 = 28 \end{aligned} $$ ## Calculate the sum of products and standard deviation of y $$ \begin{aligned} \sum (x - \bar{x})(y - \bar{y}) &= (-3)(-9.57) + (-2)(-5.57) + (-1)(0.43) + (0)(1.43) + (1)(5.43) + (2)(2.43) + (3)(5.43) \ &= 28.71 + 11.14 - 0.43 + 0 + 5.43 + 4.86 + 16.29 = 66 \ \sum (y - \bar{y})^2 &= (-9.57)^2 + (-5.57)^2 + (0.43)^2 + (1.43)^2 + (5.43)^2 + (2.43)^2 + (5.43)^2 \ &\approx 91.58 + 31.02 + 0.18 + 2.04 + 29.48 + 5.90 + 29.48 = 189.68 \end{aligned} $$ ## Calculate the correlation coefficient r $$ \begin{aligned} r &= \frac{\sum (x - \bar{x})(y - \bar{y})}{\sqrt{\sum (x - \bar{x})^2 \sum (y - \bar{y})^2}} \ r &= \frac{66}{\sqrt{28 \times 189.68}} = \frac{66}{\sqrt{5311.04}} \approx \frac{66}{72.88} \approx 0.906 \end{aligned} $$

(A) 0.0

(B) 0.3

(C) 0.9

(D) -0.3

(E) -0.9

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QUESTION IMAGE

Question

Explanation:

Calculate summary statistics for the data

Calculate the sum of products and standard deviation of y

Calculate the correlation coefficient r

Answer: