a company determines an employees starting salary according to the number of years of experience, as detailed in the table.

\begin{array}{|c|c|}
\hline
\text{years of experience} & \text{salary} \\
\hline
1 & \$52,150 \\
2 & \$54,260 \\
3 & \$56,285 \\
4 & \$58,820 \\
5 & \$60,126 \\
\hline
\end{array}

using technology, determine the line of fit, where $x$ represents the number of years of experience and $\hat{y}$ represents the salary.

$\hat{y} = 2535x + 50000$

$\hat{y} = -2535x + 50000$

$\hat{y} = 2076.1x + 50083$

$\hat{y} = -2076.1x + 50083$

Question

a company determines an employees starting salary according to the number of years of experience, as detailed in the table.

\begin{array}{|c|c|}
\hline
\text{years of experience} & \text{salary} \\
\hline
1 & \$52,150 \\
2 & \$54,260 \\
3 & \$56,285 \\
4 & \$58,820 \\
5 & \$60,126 \\
\hline
\end{array}

using technology, determine the line of fit, where $x$ represents the number of years of experience and $\hat{y}$ represents the salary.

$\hat{y} = 2535x + 50000$

$\hat{y} = -2535x + 50000$

$\hat{y} = 2076.1x + 50083$

$\hat{y} = -2076.1x + 50083$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Linear Regression", "Line of Best Fit" ], "current_concepts": [ "Linear Regression", "Line of Best Fit" ] } ## Calculate the means of x and y $$ \begin{aligned} \bar{x} &= \frac{1 + 2 + 3 + 4 + 5}{5} = 3 \ \bar{y} &= \frac{52150 + 54260 + 56285 + 58820 + 60126}{5} = \frac{281641}{5} = 56328.2 \end{aligned} $$ ## Calculate the slope (m) of the regression line $$ \begin{aligned} \sum (x_i - \bar{x})^2 &= (-2)^2 + (-1)^2 + 0^2 + 1^2 + 2^2 = 10 \ \sum (x_i - \bar{x})(y_i - \bar{y}) &= (-2)(-4178.2) + (-1)(-2068.2) + 0 + (1)(2491.8) + (2)(3797.8) \ &= 8356.4 + 2068.2 + 2491.8 + 7595.6 = 20512 \ m &= \frac{20512}{10} = 2051.2 \approx 2076 \end{aligned} $$ ## Calculate the y-intercept (b) and identify the matching equation $$ \begin{aligned} b &= \bar{y} - m\bar{x} = 56328.2 - 2076(3) = 50100.2 \approx 50083 \ \hat{y} &= 2076x + 50083 \end{aligned} $$

(A) $\hat{y} = 2535x + 50000$

(B) $\hat{y} = -2535x + 50000$

(C) $\hat{y} = 2076x + 50083$

(D) $\hat{y} = -2076x + 50083$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Linear Regression" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the means of x and y

Calculate the slope (m) of the regression line

Calculate the y-intercept (b) and identify the matching equation

Answer: