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1 mwp-037 regress - regress regress. regress mpg weight foreign Source SS df MS Number of obs = 74 F( 2, 71) = Model Prob > F = Residual R squared = Adj R squared = Total Root MSE = mpg Coef. Std. Err. t P> t [95% Conf. Interval] weight foreign _cons c Copyright Math c Copyright StataCorp LP (used with permission) 1

2 Stata Example auto.dta mpg = β 0 + β 1 weight + β 2 foreign + ϵ Stata regress 1.1 regress1.dta 1,000 use 5. list in 1/5 * 1 y x1 x2 x y. generate y = 0.5*x1 + 2*x rnormal(0, 10) x 1 x 2 rnormal(m, s) m s [D] functions y = 0.5x x 2 10 (1) x 1, x 2 x 3 y x 3 *1 Data Describe data List data 2

3 1.2 1,000 regress Statistics Linear models and related Linear regression Model : Dependent variable: y Independent variables: x1 x2 x3 1 regress - Model. regress y x1 x2 x3 Source SS df MS Number of obs = 1000 F( 3, 996) = Model Prob > F = Residual R squared = Adj R squared = Total Root MSE = y Coef. Std. Err. t P> t [95% Conf. Interval] x x x _cons (1) regress n(n 3) 2 rvfplot 3

4 . rvfplot, yline(0) * 2 (x 1i, x 2i,...) ŷ i y i y i ŷ i rvfplot (residual-versus-fitted plot) ŷ i 10 (2) R 2 regress regress ANOVA y SS (sum of squares) y i (i = 1,..., n) ȳ 2 y i ŷ i y (yi ȳ) 2 = (y i ŷ i ) 2 + (ŷ i ȳ) 2 (2) (yi ȳ) 2 TSS (total sum of squares) (ŷi ȳ) 2 MSS (model sum of squares) (yi ŷ i ) 2 RSS (residual sum of squares) TSS MSS RSS *2 Statistics Linear models and related Regression diagnostics Residual-versus-fitted plot 4

5 (coefficient of determination) R 2 = MSS TSS = 1 RSS TSS (3) / = ANOVA R-squared 39% (3) p R-squared 1 p Prob > F (ANOVA: analysis of variance) F H 0 H 0 : β 1 = β 2 = = 0 β 0 (4) ANOVA Coef. (coefficients) β 1 = 0.48 β2 = 1.97 β3 = 0.01 β0 = 8.91 (1) (5) p p β j = 0 t p x 3 p β 3 = 0 β 3 95% CI: confidence interval [ 0.21, 0.22] 0 x 3 x 1, x 2 p 0 regress p x postestimation 1 test Statistics Postestimation Tests Test linear hypotheses Main : Test type for specification 1: Linear expressions are equal Specification 1, linear expression: x1 = 0.5 5

6 2 test - Main. test (x1 = 0.5) ( 1) x1 =.5 F( 1, 996) = 0.62 Prob > F = (6) Coef. (standard error) Std. Err. (standard deviation) x 1 95% CI (degrees of freedom) 996 t invttail(n, p) [D] functions. display invttail(996, 0.025) * % (critical value). display * display * x 1 95% CI [ , ] *3 Data Other utilities Hand calculator 6

7 x 1, x ,000 1/10 resampling seed seed. set seed 111 * sample 100, count * 5 (900 observations deleted) 100 regress. regress y x1 x2 x3. regress y x1 x2 x3 Source SS df MS Number of obs = 100 F( 3, 96) = Model Prob > F = Residual R squared = Adj R squared = Total Root MSE = y Coef. Std. Err. t P> t [95% Conf. Interval] x x x _cons R 2 x x % test *4 [R] set seed *5 Statistics Resampling Draw random sample 7

8 . test (x1 = 0.37). test (x1 = 0.37) ( 1) x1 =.37 F( 1, 96) = 3.65 Prob > F = test (x1 = 0.8). test (x1 = 0.8) ( 1) x1 =.8 F( 1, 96) = 3.74 Prob > F = p 0.05 (significance level) 5% Reporting Confidence level 3 2. Stata Example auto.dta. sysuse auto.dta * 6 (1978 Automobile Data) mpg (miles per gallon) weight 2 weight 2 2 c.weight#c.weight mwp-028. generate weightsq = weight^2 * 7 *6 File Example datasets Example datasets installed with Stata *7 Data Create or change data Create new variable 8

9 . format weightsq %10.0g * 8. list mpg weight weightsq in 1/5 * 9 mpg weight weightsq , , , , , weight K 2 2. regress mpg weight weightsq * 10. regress mpg weight weightsq Source SS df MS Number of obs = 74 F( 2, 71) = Model Prob > F = Residual R squared = Adj R squared = Total Root MSE = mpg Coef. Std. Err. t P> t [95% Conf. Interval] weight weightsq 1.32e e e e 06 _cons mpg = 1.42e-2 weight e-6 weight mpg weight weight weight (normalize) 0 1 beta *8 Variables weightsq Format weightsq *9 Data Describe data List data *10 Statistics Linear models and related Linear regression 9

10 regress : Reporting : Standardized beta coefficients: 3 regress - Reporting. regress mpg weight weightsq, beta Source SS df MS Number of obs = 74 F( 2, 71) = Model Prob > F = Residual R squared = Adj R squared = Total Root MSE = mpg Coef. Std. Err. t P> t Beta weight weightsq 1.32e e _cons beta weight weight

11 3. auto.dta weight length β 0 length = 0 β 0 β 0 = 0 noconstant Statistics Linear models and related Linear regression Model : Dependent variable: weight Independent variables: length Suppress constant term:. regress weight length, noconstant Source SS df MS Number of obs = 74 F( 1, 73) = Model Prob > F = Residual R squared = Adj R squared = Total Root MSE = weight Coef. Std. Err. t P> t [95% Conf. Interval] length Example census9.dta. use clear * 11 (1980 Census data by state) *11 File Example Datasets Stata 11 manual datasets Base Reference Manual [R] regress 11

12 . list state drate pop medage region in 1/5, nolabel * 12 state drate pop medage region 1. Alabama 91 3,893, Alaska , Arizona 78 2,718, Arkansas 99 2,286, California 79 23,667, (drate) (medage) (region) region Northeast, North Central, South, West 1, 2, 3, 4 drate medage pop mwp regress - Weights Analytic weights Frequency weights Alabama 3, 893, *12 region 12

13 Statistics Linear models and related Linear regression Model : Dependent variable: drate Independent variables: medage i.region * 13 Weights : Analytic weights: pop. regress drate medage i.region [aweight = pop] (sum of wgt is e+08) Source SS df MS Number of obs = 50 F( 4, 45) = Model Prob > F = Residual R squared = Adj R squared = Total Root MSE = drate Coef. Std. Err. t P> t [95% Conf. Interval] medage region _cons [aweight = pop] 5. regress 2 (OLS: ordinary least squares) OLS (homoskedasticity) Example auto.dta. sysuse auto, clear (1978 Automobile Data). replace weight = weight/1000 * 14 *13 i. mwp-028 *14 Data Create or change data Change contents of variable K 13

14 . regress mpg weight. regress mpg weight Source SS df MS Number of obs = 74 F( 1, 72) = Model Prob > F = Residual R squared = Adj R squared = Total Root MSE = mpg Coef. Std. Err. t P> t [95% Conf. Interval] weight _cons twoway (scatter mpg weight) (lfit mpg weight), ytitle(mpg) * 15 1 rvpplot (residual-versus-predictor plot). rvpplot weight, yline(0) * 16 *15 Graphics Twoway graph (scatter, line, etc.) *16 Statistics Linear models and related Regression diagnostics Residual-versus-predictor plot 14

15 rvpplot weight (heteroskedasticity) Statistics Postestimation Reports and statistics estat : Reports and statistics: Tests for heteroskedasticity (hettest) 5 estat 15

16 . estat hettest Breusch Pagan / Cook Weisberg test for heteroskedasticity Ho: Constant variance Variables: fitted values of mpg chi2(1) = Prob > chi2 = estat hettest H 0 p H 0 OLS OLS regress SE/Robust SE (standard error) Statistics Linear models and related Linear regression Model : Dependent variable: mpg Independent variables: weight SE/Robust : Robust 6 regress - SE/Robust 16

17 . regress mpg weight, vce(robust) Linear regression Number of obs = 74 F( 1, 72) = Prob > F = R squared = Root MSE = Robust mpg Coef. Std. Err. t P> t [95% Conf. Interval] weight _cons vce(robust) OLS 95% CI OLS Robust weight [ 7.04, 4.98] [ 7.17, 4.84] cons [36.22, 42.66] [35.48, 43.40] SE/Robust Clustered robust 17

18 5 Graphics Twoway graph (scatter, line, etc.) Plots Create Plot 1 Choose a plot category and type: Basic plots Basic plots: Scatter Y variable: mpg X variable: weight Plots Create Plot 2 Choose a plot category and type: Fit plots Fit plots: Linear prediction Y variable: mpg X variable: weight Y axis : Title: mpg. twoway (scatter mpg weight) (lfit mpg weight), ytitle(mpg) 18

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