Introduction to Statistics, Lecture 11 - Regression Analysis (Chapter ...
Introduction to Statistics, Lecture 11 - Regression Analysis (Chapter ...
Introduction to Statistics, Lecture 11 - Regression Analysis (Chapter ...
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Correlations computationsCorrelation<strong>Regression</strong> <strong>Analysis</strong> (kap <strong>11</strong>)<strong>Regression</strong> <strong>Analysis</strong> (<strong>Chapter</strong> <strong>11</strong>)We assume that Y is a s<strong>to</strong>chastic variable. We areinterested in modelling Y ’s dependency on anexplana<strong>to</strong>ry variable xWe look at a linear relationship between Y and x, thatis a regression model on the formY = α + βx + εPer Bruun Brockhoff (pbb@imm.dtu.dk) <strong>Introduction</strong> <strong>to</strong> <strong>Statistics</strong>, <strong>Lecture</strong> <strong>11</strong> Fall 2012 7 / 32Per Bruun Brockhoff (pbb@imm.dtu.dk) <strong>Introduction</strong> <strong>to</strong> <strong>Statistics</strong>, <strong>Lecture</strong> <strong>11</strong> Fall 2012 9 / 32<strong>Regression</strong> <strong>Analysis</strong> (kap <strong>11</strong>)Simple Linear <strong>Regression</strong><strong>Regression</strong> <strong>Analysis</strong> (kap <strong>11</strong>)Simple Linear <strong>Regression</strong>Y = α + βx} {{ }model+ ε }{{}residual**Y dependent variable**x independent variableα intercept with Y-axisβ slope*** **ε residual (random error)Per Bruun Brockhoff (pbb@imm.dtu.dk) <strong>Introduction</strong> <strong>to</strong> <strong>Statistics</strong>, <strong>Lecture</strong> <strong>11</strong> Fall 2012 10 / 32Per Bruun Brockhoff (pbb@imm.dtu.dk) <strong>Introduction</strong> <strong>to</strong> <strong>Statistics</strong>, <strong>Lecture</strong> <strong>11</strong> Fall 2012 <strong>11</strong> / 32
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