leastsquaresregression-文庫吧資料
2025-07-23 15:26本頁面
【正文】 y yyyy b b x???? ? ?the r es i du al i s the v er ti c al de v i ati on of theda ta po i nt fr om the l i ne :r es i du al = ob s er v ed pr ed i c tedResiduals: graphically G r a p h i c a l D i s p l a y o f R e s i d u a l sXX iY i ei =Y i Y iY ip o s i t i v e re s i d u a ln e g a t i v e re s i d u a lCriterion for choosing what line to draw: method of least squares ? The method of least squares chooses the line that makes the sum of squares of the residuals as small as possible ? This line has slope b1 and intercept b0 that minimizes 2011[ ( ) ] ( , )niiiiiy b b xxy????fo r th e gi v en ob s er v at i on sLeast Squares Line y = b0 + b1x: Slope b1 and Intercept b0 10211221121()i s the sta nda r d d e v i a t i on of , , .. .,1()i s the sta nda r d d e v i a t i on of , , .. .,1( ) ( )(yxniixnniiynniiissbxxs x x xnyys y y ynx x y yrbry bx???????????????????1 1 2 2 n n( x , y ) , ( x , y ) , , ( x , y )s l o p e y i n t e rc e p tw h e re2011 1 1i s the c or r e l a t i on be t w e e n a nd1)xyn n ni i i ii i ixyn s sSSE y b y b x y? ? ??? ? ?? ? ?Example: Ine vs Consumption Expenditure Inc om e (x)Cons um ptio nEx pe ndi ture (y )1 75 69 913 817 10Questions ? Construct scatterplot。 it responds to changes in the x variable. (dependent variable) Examples ? Fertilizer (x ) corn yield (y ) ? Advertising $ (x ) store ine (y ) ? Drug dose (x ) blood pressure (y ) ? Daily temperature (x ) natural gas demand (y ) ? change in min wage(x) unemployment rate (y) Simplest Relationship ? Simplest equation that describes the dependence of variable y on variable x y = b0 + b1x ? linear equation ? graph is line with slope b1 and yintercept b0 Graph y x 0 b0 y=b0 +b1x run rise Slope b=rise/run Notation ? (x1, y1), (x2, y2), . . . , (xn, yn) ? draw the line y= b0 + b1x through the scatterplot , the point on the line corresponding to xi is 010 1 ii垐 。Least Squares Regression Fitting a Line to Bivariate Data Linear Relationships Avg. occupants per car ? 1980: 6/car ? 1990: 3/car ? 2022: ? By the year 2022 every fourth car will have nobody in it! Food for Thought ? Kind of mathematical relationship between year and avg. no. of occupants per car? ? Why might relation ship break down by 2022? Basic Terminology ? Scatterplots, correlation: interested in association between 2 variables (assign x and y arbitrarily) ? Least squares regression: does one quantitative variable explain or c
范文總結(jié)相關(guān)推薦
鄂ICP備17016276號-1