type the correct answer in each box. spell all words correctly, and use numerals instead of words for numbers. if necessary, use / for the fraction bar(s).

the table and scatter plot present rays monthly electricity bills and the amount of time ray spent at home from january through august.

\begin{array}{|c|c|c|}
\hline
\text{month} & \text{time spent at home (hours)} & \text{electricity bill (\$)} \\
\hline
\text{january} & 240 & 128 \\
\hline
\text{february} & 225 & 126 \\
\hline
\text{march} & 212 & 115 \\
\hline
\text{april} & 264 & 144 \\
\hline
\text{may} & 282 & 146 \\
\hline
\text{june} & 198 & 108 \\
\hline
\text{july} & 234 & 142 \\
\hline
\text{august} & 254 & 142 \\
\hline
\end{array}

using the scatter plot, find the correlation coefficient of this data set.

the correlation coefficient (r) is .

the correlation coefficient can be improved by ignoring the bill for the month of .

Question

type the correct answer in each box. spell all words correctly, and use numerals instead of words for numbers. if necessary, use / for the fraction bar(s).

the table and scatter plot present rays monthly electricity bills and the amount of time ray spent at home from january through august.

\begin{array}{|c|c|c|}
\hline
\text{month} & \text{time spent at home (hours)} & \text{electricity bill (\$)} \\
\hline
\text{january} & 240 & 128 \\
\hline
\text{february} & 225 & 126 \\
\hline
\text{march} & 212 & 115 \\
\hline
\text{april} & 264 & 144 \\
\hline
\text{may} & 282 & 146 \\
\hline
\text{june} & 198 & 108 \\
\hline
\text{july} & 234 & 142 \\
\hline
\text{august} & 254 & 142 \\
\hline
\end{array}

using the scatter plot, find the correlation coefficient of this data set.

the correlation coefficient (r) is  .

the correlation coefficient can be improved by ignoring the bill for the month of  .

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear Association", "Bivariate Data Analysis" ], "new_concepts": [ "Correlation Coefficient Calculation", "Outlier Analysis" ], "current_concepts": [ "Linear Association", "Bivariate Data Analysis", "Correlation Coefficient Calculation", "Outlier Analysis" ] } ## Calculate the correlation coefficient (r) $$ \begin{aligned} &n = 8\ &\sum x = 240 + 225 + 212 + 264 + 282 + 198 + 234 + 254 = 1909\ &\sum y = 128 + 126 + 115 + 144 + 146 + 108 + 142 + 142 = 1051\ &\sum x^2 = 240^2 + 225^2 + 212^2 + 264^2 + 282^2 + 198^2 + 234^2 + 254^2 = 460165\ &\sum y^2 = 128^2 + 126^2 + 115^2 + 144^2 + 146^2 + 108^2 + 142^2 + 142^2 = 139469\ &\sum xy = 240(128) + 225(126) + 212(115) + 264(144) + 282(146) + 198(108) + 234(142) + 254(142) = 252446\ &r = \frac{n\sum xy - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}}\ &r = \frac{8(252446) - (1909)(1051)}{\sqrt{[8(460165) - 1909^2][8(139469) - 1051^2]}}\ &r = \frac{2019568 - 2006359}{\sqrt{[3681320 - 3644281][1115752 - 1104601]}}\ &r = \frac{13209}{\sqrt{37039 \times 11151}} = \frac{13209}{\sqrt{413021889}} \approx \frac{13209}{20322.94} \approx 0.65 \end{aligned} $$ ## Identify the outlier month \[ \begin{aligned} &\text{January: } (240, 128) \quad \text{Line value at } 240 \approx 133 \quad \text{Residual} \approx -5\ &\text{February: } (225, 126) \quad \text{Line value at } 225 \approx 124 \quad \text{Residual} \approx +2\ &\text{March: } (212, 115) \quad \text{Line value at } 212 \approx 116 \quad \text{Residual} \approx -1\ &\text{April: } (264, 144) \quad \text{Line value at } 264 \approx 148 \quad \text{Residual} \approx -4\ &\text{May: } (282, 146) \quad \text{Line value at } 282 \approx 159 \quad \text{Residual} \approx -13\ &\text{June: } (198, 108) \quad \text{Line value at } 198 \approx 108 \quad \text{Residual} \approx 0\ &\text{July: } (234, 142) \quad \text{Line value at } 234 \approx 130 \quad \text{Residual} \approx +12\ &\text{August: } (254, 142) \quad \text{Line value at } 254 \approx 142 \quad \text{Residual} \approx 0\ &\text{Outlier is July (point is significantly above the trend line, or May which is significantly below).} \ &\text{Re-evaluating the scatter plot: the point at } (240, 142) \text{ is January's bill plotted incorrectly, or July } (234, 142) \text{ which lies far above the line.}\ &\text{The point furthest from the trend line is July.} \end{aligned} \] ## Question 1 The correlation coefficient ($r$) is 0.65. ## Question 2 The correlation coefficient can be improved by ignoring the bill for the month of July. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Bivariate Data Analysis" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the correlation coefficient (r)

Identify the outlier month

Answer:

Question 1

Question 2