find the $y$-intercept of the line of best fit for the given data.

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

$\bigcirc$ 112.87

$\bigcirc$ 98.87

Question

find the $y$-intercept of the line of best fit for the given data.

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

$\bigcirc$ 112.87

$\bigcirc$ 98.87

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 Equation Parameters" ] } ## Calculate summary statistics Using the *Least Squares Method* and *Line of Best Fit* knowledge points $$ \begin{aligned} n &= 6 \ \sum x &= 10 + 20 + 30 + 40 + 50 + 60 = 210 \ \sum y &= 110 + 150 + 118 + 130 + 127 + 161 = 796 \ \bar{x} &= \frac{210}{6} = 35 \ \bar{y} &= \frac{796}{6} \approx 132.6667 \end{aligned} $$ ## Calculate sum of squares Using the *Least Squares Method* knowledge point $$ \begin{aligned} \sum x^2 &= 10^2 + 20^2 + 30^2 + 40^2 + 50^2 + 60^2 \ &= 100 + 400 + 900 + 1600 + 2500 + 3600 = 9100 \ \sum xy &= 10(110) + 20(150) + 30(118) + 40(130) + 50(127) + 60(161) \ &= 1100 + 3000 + 3540 + 5200 + 6350 + 9660 = 28850 \end{aligned} $$ ## Calculate slope of the line Using the *Least Squares Method* and *Linear Equation Parameters* knowledge points $$ \begin{aligned} m &= \frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2} \ m &= \frac{6(28850) - (210)(796)}{6(9100) - (210)^2} \ m &= \frac{173100 - 167160}{54600 - 44100} \ m &= \frac{5940}{10500} \approx 0.5657 \end{aligned} $$ ## Calculate y-intercept Using the *Least Squares Method* and *Linear Equation Parameters* knowledge points $$ \begin{aligned} b &= \bar{y} - m\bar{x} \ b &= 132.6667 - (0.5657)(35) \ b &= 132.6667 - 19.7995 \ b &\approx 112.87 \end{aligned} $$

(A) 112.87

(B) 98.87

{ "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

Calculate sum of squares

Calculate slope of the line

Calculate y-intercept

Answer: