question 42 points 3

the following data best fits a line. find the slope of the line.

$\begin{array}{|c|c|}\hline x & y \\\hline 10 & 110 \\\hline 20 & 150 \\\hline 30 & 118 \\\hline 40 & 130 \\\hline 50 & 127 \\\hline 60 & 161 \\\hline\end{array}$

0.37
0.57

Question

question 42 points 3

the following data best fits a line. find the slope of the line.

$\begin{array}{|c|c|}\hline x & y \\\hline 10 & 110 \\\hline 20 & 150 \\\hline 30 & 118 \\\hline 40 & 130 \\\hline 50 & 127 \\\hline 60 & 161 \\\hline\end{array}$

0.37
0.57

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Line of Best Fit", "Least Squares Method" ], "new_concepts": [], "current_concepts": [ "Line of Best Fit", "Least Squares Method", "Linear Modeling" ] } ## Calculate summary statistics Using the **Least Squares Method** knowledge point $$ \begin{aligned} n &= 6\ \sum x &= 10 + 20 + 30 + 40 + 50 + 60 = 210\ \bar{x} &= \frac{210}{6} = 35\ \sum y &= 110 + 150 + 118 + 130 + 127 + 161 = 796\ \bar{y} &= \frac{796}{6} \approx 132.667 \end{aligned} $$ ## Compute sum of squares for x Using the **Least Squares Method** knowledge point $$ \begin{aligned} \sum x^2 &= 10^2 + 20^2 + 30^2 + 40^2 + 50^2 + 60^2\ &= 100 + 400 + 900 + 1600 + 2500 + 3600 = 9100\ SS_{xx} &= \sum x^2 - \frac{(\sum x)^2}{n} = 9100 - \frac{210^2}{6} = 9100 - 7350 = 1750 \end{aligned} $$ ## Compute sum of products Using the **Least Squares Method** knowledge point $$ \begin{aligned} \sum xy &= (10)(110) + (20)(150) + (30)(118) + (40)(130) + (50)(127) + (60)(161)\ &= 1100 + 3000 + 3540 + 5200 + 6350 + 9660 = 28850\ SS_{xy} &= \sum xy - \frac{(\sum x)(\sum y)}{n} = 28850 - \frac{(210)(796)}{6} = 28850 - 27860 = 990 \end{aligned} $$ ## Calculate the slope Using the **Line of Best Fit** knowledge point $$ \begin{aligned} m &= \frac{SS_{xy}}{SS_{xx}} = \frac{990}{1750} \approx 0.5657 \end{aligned} $$ Rounding to two decimal places yields $0.57$.

(A) 0.37

(B) 0.57

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Line of Best Fit" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate summary statistics

Compute sum of squares for x

Compute sum of products

Calculate the slope

Answer: