// Numbas version: exam_results_page_options {"name": "Identifying Parts of Equations: b", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["change", "changes", "r", "change2", "correct"], "name": "Identifying Parts of Equations: b", "tags": [], "advice": "", "rulesets": {}, "parts": [{"maxAnswers": 0, "prompt": "

Which of the following is equivalent to the given equation for $b$?

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$b = \\frac{ \\sum(xy)-\\frac{\\sum{x} \\sum{y}}{n}}{\\sum(x^2)-\\frac{(\\sum{x})^2}{n}}\\\\ $

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$b = \\frac{n \\sum(xy)-\\sum{x} \\sum{y}}{n\\sum(x^2)-(\\sum{x})^2}\\\\ $

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$b = \\dfrac{\\sum(y_i-\\bar{y})}{\\sum(x_i-\\bar{x})}\\\\ $

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$b = \\dfrac{\\sum(x_iy_i-\\overline{xy})}{\\sum(x_i-\\bar{x})^2}\\\\ $

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$b = \\dfrac{\\sum(x_iy_i-\\bar{x}\\bar{y})}{\\sum(x_i-\\bar{x})^2}\\\\ $

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What is $\\bar{y}$?

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Sample mean of the $y$ values

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Population mean of the $y$ values

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Sample variance of the $y$ values

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Estimation of the $y$ values

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If every value $y_i$ is the same, what is $b$?

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Given that

\n

\\[ b = \\dfrac{\\sum(x_i-\\bar{x})(y_i-\\bar{y})}{\\sum(x_i-\\bar{x})^2}, \\]

\n

answer the following questions.

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Identify parts of a statistical formula from a linear regression model

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