Mathematics > EXAM REVIEW > Linear Regression University of PennsylvaniaESE 402402 Final Review (All)

Linear Regression University of PennsylvaniaESE 402402 Final Review

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upervised Learning, Linear Regression Simple linear regression ↳ straightforward approach for predicting a quantitative response Y on the basis of a single predictor variable X ↳ assumes an ap... proximate linear relationship between X and Y Ya Bo +B , X - - coefficients / parameters we don't know the actual coeffs , so we estimate using our training data ↳ estimate D= Bot § , x ( least squares line) Our goat is to obtain coefficient estimates Bo and B, so that the linear model fits the data well : y , x BotBix, for u -- I , - - , n Let Ji -- Bot Bix-u be the prediction for Y based on ith value of X ↳ then e.i-y-u-y.ie ( difference btw observed response and response withresidual predicted by our linear model ) RSS = et t et t - - - ten ( Residual sum of squares) → sum of all errors squared RSS = ( y , -Bo -Bix ,)'t ( ya - Bo - B . xz)'t . . . t ( yn - Bo -B, xn)' = ly i - (Bo t B, x))' §, = Lxi -E)(Yi -g) Bo = g- - B, I 1- least squares coefficient estimates - E. Hi - IT n D= th Z Yi 1=1 I -- thIz x,y mean - zero ACCURACY OF COEFFICIENT ESTIMATES [Show More]

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