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SIMPLE AND MULTIPLE REGRESSION

SIMPLE AND MULTIPLE REGRESSION. Relació entre variables. Entre variables discretes (exemple: veure Titanic ) Entre continues (Regressió !) Entre discretes i continues (Regressió!). Pisa 2003. > Rendiment en Matemàtiques, > Nombre de llibres a casa. Pisa 2003.

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SIMPLE AND MULTIPLE REGRESSION

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  1. SIMPLE AND MULTIPLE REGRESSION

  2. Relació entre variables Entre variables discretes (exemple: veure Titanic) Entre continues (Regressió !) Entre discretes i continues (Regressió!)

  3. Pisa 2003 > Rendiment en Matemàtiques, > Nombre de llibres a casa

  4. Pisa 2003 > Rendiment en Matemàtiques, > Nombre de llibres a casa

  5. Regressió Lineal ? Pisa 2003

  6. Regressió Lineal ? Pisa 2003

  7. Regressió Lineal ? Pisa 2003

  8. Regressió Lineal

  9. * We first load the PISAespanya.sav file and then * this is the sintaxis file for SPSS analysis *Q38 How often do these things happen in your math class *Student dont't listen to what the teacher says CROSSTABS /TABLES=subnatio BY st38q02 /FORMAT= AVALUE TABLES /STATISTIC=CHISQ /CELLS= COUNT ROW . FACTOR /VARIABLES pv1math pv2math pv3math pv4math pv5math pv1math1 pv2math1 pv3math1 pv4math1 pv5math1 pv1math2 pv2math2 pv3math2 pv4math2 pv5math2 pv1math3 pv2math3 pv3math3 pv4math3 pv5math3 pv1math4 pv2math4 pv3math4 pv4math4 pv5math4 /MISSING LISTWISE /ANALYSIS pv1math pv2math pv3math pv4math pv5math pv1math1 pv2math1 pv3math1 pv4math1 pv5math1 pv1math2 pv2math2 pv3math2 pv4math2 pv5math2 pv1math3 pv2math3 pv3math3 pv4math3 pv5math3 pv1math4 pv2math4 pv3math4 pv4math4 pv5math4 /PRINT INITIAL EXTRACTION FSCORE /PLOT EIGEN ROTATION /CRITERIA FACTORS(1) ITERATE(25) /EXTRACTION ML /ROTATION NOROTATE /SAVE REG(ALL) . GRAPH /SCATTERPLOT(BIVAR)=st19q01 WITH fac1_1 /MISSING=LISTWISE . REGRESSION /MISSING LISTWISE /STATISTICS COEFF OUTS R ANOVA /CRITERIA=PIN(.05) POUT(.10) /NOORIGIN /DEPENDENT fac1_1 /METHOD=ENTER st19q01 /PARTIALPLOT ALL /SCATTERPLOT=(*ZRESID ,*ZPRED ) /RESIDUALS HIST(ZRESID) NORM(ZRESID) .

  10. library(foreign) help(read.spss) data=read.spss("G:/DATA/PISAdata2003/ReducedDataSpain.sav", use.value.labels=TRUE,to.data.fram=TRUE) names(data) [1] "SUBNATIO" "SCHOOLID" "ST03Q01" "ST19Q01" "ST26Q04" "ST26Q05" [7] "ST27Q01" "ST27Q02" "ST27Q03" "ST30Q02" "EC07Q01" "EC07Q02" [13] "EC07Q03" "EC08Q01" "IC01Q01" "IC01Q02" "IC01Q03" "IC02Q01" [19] "IC03Q01" "MISCED" "FISCED" "HISCED" "PARED" "PCMATH" [25] "RMHMWK" "CULTPOSS" "HEDRES" "HOMEPOS" "ATSCHL" "STUREL" [31] "BELONG" "INTMAT" "INSTMOT" "MATHEFF" "ANXMAT" "MEMOR" [37] "COMPLRN" "COOPLRN" "TEACHSUP" "ESCS" "W.FSTUWT" "OECD" [43] "UH" "FAC1.1" attach(data) mean(FAC1.1) [1] -8.95814e-16 tabulate(ST19Q01) [1] 106 0 15 1266 1927 2372 3575 1155 375 > table(ST19Q01) ST19Q01 Miss Invalid N/A More than 500 books 106 0 15 1266 201-500 books 101-200 books 26-100 books 11-25 books 1927 2372 3575 1155 0-10 books 375

  11. Efecto de Cultural Possession of the family

  12. Data Variables Y and X observed on a sample of size n: yi , xi i =1,2, ..., n

  13. Covariance and correlation

  14. Scatterplot for various values of correlation

  15. Coeficient de correlació r = 0 , tot i que hi ha una relació funcional exacta (no lineal!) > cbind(x,y) x y [1,] -10 100 [2,] -9 81 [3,] -8 64 [4,] -7 49 [5,] -6 36 [6,] -5 25 [7,] -4 16 [8,] -3 9 [9,] -2 4 [10,] -1 1 [11,] 0 0 [12,] 1 1 [13,] 2 4 [14,] 3 9 [15,] 4 16 [16,] 5 25 [17,] 6 36 [18,] 7 49 [19,] 8 64 [20,] 9 81 [21,] 10 100 >

  16. Regressió Lineal Simple Variables Y X E Y | X = a + b X Var (Y | X ) = s2

  17. Linear relation: y = 1 + .6 X

  18. Linear relation and sample data

  19. Regression Model Yi = a + b Xi + ei ei : mean zero variance s2 normally distributed

  20. Sample Data: Scatterplot

  21. Fitted regression line a= 0.5789 b=0.6270

  22. Fitted and true regression lines: a=1, b=.6 a= 0.5789 b=0.6270

  23. Fitted and true regression lines in repeated (20) sampling a=1, b=.6

  24. OLS estimate of beta (under repeated sampling) Estimate of beta for different samples (100): 0.619 0.575 0.636 0.543 0.555 0.594 0.611 0.584 0.576 ...... > a=1, b=.6 > mean(bs) [1] 0.6042086 > sd(bs) [1] 0.03599894 >

  25. REGRESSION Analysis of the Simulated Data (with R and other software )

  26. Fitted regression line: a=1, b=.6 a= 1.0232203, b= 0.6436286

  27. Regression Analysis regression = lm(Y ~X) summary(regression) Call: lm(formula = Y ~ X) Residuals: Min 1Q Median 3Q Max -6.0860 -2.1429 -0.1863 1.9695 9.4817 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.0232 0.3188 3.21 0.00180 ** X 0.6436 0.0377 17.07 < 2e-16 *** --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 Residual standard error: 3.182 on 98 degrees of freedom Multiple R-Squared: 0.7483, Adjusted R-squared: 0.7458 F-statistic: 291.4 on 1 and 98 DF, p-value: < 2.2e-16 >>

  28. Regression Analysis with Stata . use "E:\Albert\COURSES\cursDAS\AS2003\data\MONT.dta", clear . regress y x Source | SS df MS Number of obs = 100 ---------+------------------------------ F( 1, 98) = 291.42 Model | 2950.73479 1 2950.73479 Prob > F = 0.0000 Residual | 992.280727 98 10.1253135 R-squared = 0.7483 ---------+------------------------------ Adj R-squared = 0.7458 Total | 3943.01551 99 39.8284395 Root MSE = 3.182 ------------------------------------------------------------------------------ y | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------+-------------------------------------------------------------------- x | .6436286 .0377029 17.071 0.000 .5688085 .7184488 _cons | 1.02322 .3187931 3.210 0.002 .3905858 1.655855 ------------------------------------------------------------------------------ . predict yh . graph yh y x, c(s.) s(io)

  29. Regression analysis with SPSS

  30. Estimación

  31. Gráfico de dispersión

  32. Fitted Regression FYi = 1.02 + .64 Xi , R2=.74 s.e.: (.037) t-value: 17.07 Regression coeficient of X is significant (5% significance level), with the expected value of Y icreasing .64 for each unit increase of X. The 95% confidence interval for the regression coefficient is [.64-1.96*.037, . .64+1.96*.037]=[.57, .71] 74% of the variation of Y is explained by the variation of X

  33. Fitted regression line

  34. Residual plot

  35. OLS analysis

  36. Variance decomposition

  37. Properties of OLS estimation

  38. Sampling distributions

  39. Inferences

  40. Student-t distribution

  41. Significance tests

  42. F-test

  43. Prediction of Y

  44. Multiple Regression:

  45. t-test and CI

  46. F-test

  47. Confidence bounds for Y

  48. Interpreting multiple regression by means of simple regression

  49. Adjusted R2

  50. Exemple de l’Anàlisi de Regressió Dades de paisos.sav

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