this table contains data on the number of people visiting a historical landmark over a period of one week. using technology, find the equation of the regression line for the following data. round values to the nearest tenth if necessary.

\begin{tabular}{|l|l|}
\hline
day (x) & number of visitors (y) \\
\hline
1 & 120 \\
\hline
2 & 124 \\
\hline
3 & 130 \\
\hline
4 & 131 \\
\hline
5 & 135 \\
\hline
6 & 132 \\
\hline
7 & 135 \\
\hline
\end{tabular}

$y = 4x + 116$
$y = 0.3x - 41.1$
$y = 0.3x - 29$
$y = 2.4x + 120.1$

Question

this table contains data on the number of people visiting a historical landmark over a period of one week. using technology, find the equation of the regression line for the following data. round values to the nearest tenth if necessary.

\begin{tabular}{|l|l|}
\hline
day (x) & number of visitors (y) \\
\hline
1 & 120 \\
\hline
2 & 124 \\
\hline
3 & 130 \\
\hline
4 & 131 \\
\hline
5 & 135 \\
\hline
6 & 132 \\
\hline
7 & 135 \\
\hline
\end{tabular}

$y = 4x + 116$
$y = 0.3x - 41.1$
$y = 0.3x - 29$
$y = 2.4x + 120.1$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Line of Best Fit Selection" ], "new_concepts": [ "Linear Regression Equation" ], "current_concepts": [ "Line of Best Fit Selection", "Linear Regression Equation" ] } ## Calculate summary statistics for the data points $$ \begin{aligned} n &= 7 \ \sum x &= 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28 \ \bar{x} &= \frac{28}{7} = 4 \ \sum y &= 120 + 124 + 130 + 131 + 135 + 132 + 135 = 907 \ \bar{y} &= \frac{907}{7} \approx 129.57 \ \sum x^2 &= 1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 + 7^2 = 140 \ \sum xy &= (1)(120) + (2)(124) + (3)(130) + (4)(131) + (5)(135) + (6)(132) + (7)(135) \ &= 120 + 248 + 390 + 524 + 675 + 792 + 945 = 3694 \end{aligned} $$ ## Compute the slope and y-intercept of the regression line $$ \begin{aligned} m &= \frac{n\sum xy - \sum x \sum y}{n\sum x^2 - (\sum x)^2} \ m &= \frac{7(3694) - (28)(907)}{7(140) - (28)^2} = \frac{25858 - 25396}{980 - 784} = \frac{462}{196} \approx 2.357 \approx 2.4 \ b &= \bar{y} - m\bar{x} \ b &= 129.57 - (2.357)(4) \approx 129.57 - 9.43 = 120.14 \approx 120.1 \end{aligned} $$ ## Match with the given options $$ y = 2.4x + 120.1 $$

(A) $y = 4x + 116$

(B) $y = 0.3x - 41.1$

(C) $y = 0.3x - 29$

(D) $y = 2.4x + 120.1$

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

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QUESTION IMAGE

Question

Explanation:

Calculate summary statistics for the data points

Compute the slope and y-intercept of the regression line

Match with the given options

Answer: