the line of best fit for the scatterplot below passes through which pair of points?

p and q
p and t
r and q
s and q

Question

the line of best fit for the scatterplot below passes through which pair of points?

p and q
p and t
r and q
s and q

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Line of Best Fit", "Scatter Plot Analysis" ], "new_concepts": [], "current_concepts": [ "Line of Best Fit", "Scatter Plot Analysis" ] } ## Identify coordinates of the labeled points $$ \begin{aligned} &P = (1, 5)\ &Q = (8, 7)\ &R = (4, 5)\ &S = (5, 2)\ &T = (9, 5) \end{aligned} $$ ## Evaluate the trend of the scatter plot $$ \begin{aligned} &\text{Data points (excluding outliers): } (1,5), (2,3.5), (3,4), (4,5), (4,6), (5,5.5), (5,7), (6,6.5), (7,7), (8,7), (9,5)\ &\text{General trend: Positive linear correlation with a moderate positive slope.}\ &\text{Outliers: } S(5,2) \text{ is far below the trend; } T(9,5) \text{ is far below the upward trend at the end.} \end{aligned} $$ ## Test the proposed lines of best fit $$ \begin{aligned} &\text{Line through } R(4,5) \text{ and } Q(8,7):\ &\quad m = \frac{7 - 5}{8 - 4} = 0.5\ &\quad y - 5 = 0.5(x - 4) \implies y = 0.5x + 3\ &\text{This line passes centrally through the main cluster of points:}\ &\quad x=1 \implies y=3.5 \quad (\text{near } P(1,5) \text{ and } (2,3.5))\ &\quad x=4 \implies y=5 \quad (\text{exactly } R(4,5))\ &\quad x=8 \implies y=7 \quad (\text{exactly } Q(8,7))\ &\text{Lines involving outliers } S \text{ or } T \text{ do not represent the overall positive trend.} \end{aligned} $$

P and Q

P and T

R and Q

S and Q

{ "elements": [ { "type": "point", "params": [[1, 5]], "properties": { "name": "P", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[2, 3.5]], "properties": { "size": 3, "color": "#583C87", "withLabel": false } }, { "type": "point", "params": [[3, 4]], "properties": { "size": 3, "color": "#583C87", "withLabel": false } }, { "type": "point", "params": [[4, 5]], "properties": { "name": "R", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[4, 6]], "properties": { "size": 3, "color": "#583C87", "withLabel": false } }, { "type": "point", "params": [[5, 5.5]], "properties": { "size": 3, "color": "#583C87", "withLabel": false } }, { "type": "point", "params": [[5, 7]], "properties": { "size": 3, "color": "#583C87", "withLabel": false } }, { "type": "point", "params": [[5, 2]], "properties": { "name": "S", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[6, 6.5]], "properties": { "size": 3, "color": "#583C87", "withLabel": false } }, { "type": "point", "params": [[7, 7]], "properties": { "size": 3, "color": "#583C87", "withLabel": false } }, { "type": "point", "params": [[8, 7]], "properties": { "name": "Q", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[9, 5]], "properties": { "name": "T", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "0.5*x + 3", "latex": "y = 0.5x + 3"}, 0, 10], "properties": { "strokeColor": "#F2557F", "strokeWidth": 2, "name": "Line of Best Fit (R to Q)", "withLabel": true } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Line of Best Fit" ] }

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QUESTION IMAGE

Question

Explanation:

Identify coordinates of the labeled points

Evaluate the trend of the scatter plot

Test the proposed lines of best fit

Answer: