[Stata Program] input p s be ba new 48.5 1.10 3 1 0 55.0 1.01 3 2 0 68.0 1.45 3 2 0 137.0 2.40 3 3 0 309.4 3.30 4 3 1 17.5 .40 1 1 0 19.6 1.28 3 1 0 24.5 .74 3 1 0 34.8 .78 2 1 0 32.0 .97 3 1 0 28.0 .84 3 1 0 49.9 1.08 2 2 0 59.9 .99 2 1 0 61.5 1.01 3 2 0 60.0 1.34 3 2 0 65.9 1.22 3 1 0 67.9 1.28 3 2 0 68.9 1.29 3 2 0 69.9 1.52 3 2 0 70.5 1.25 3 2 0 72.9 1.28 3 2 0 72.5 1.28 3 1 0 72.0 1.36 3 2 0 71.0 1.20 3 2 0 76.0 1.46 3 2 0 72.9 1.56 4 2 0 73.0 1.22 3 2 0 70.0 1.40 2 2 0 76.0 1.15 2 2 0 69.0 1.74 3 2 0 75.5 1.62 3 2 0 76.0 1.66 3 2 0 81.8 1.33 3 2 0 84.5 1.34 3 2 0 83.5 1.40 3 2 0 86.0 1.15 2 2 1 86.9 1.58 3 2 1 86.9 1.58 3 2 1 86.9 1.58 3 2 1 87.9 1.71 3 2 0 88.1 2.10 3 2 0 85.9 1.27 3 2 0 89.5 1.34 3 2 0 87.4 1.25 3 2 0 87.9 1.68 3 2 0 88.0 1.55 3 2 0 90.0 1.55 3 2 0 96.0 1.36 3 2 1 99.9 1.51 3 2 1 95.5 1.54 3 2 1 98.5 1.51 3 2 0 100.1 1.85 3 2 0 99.9 1.62 4 2 1 101.9 1.40 3 2 1 101.9 1.92 4 2 0 102.3 1.42 3 2 1 110.8 1.56 3 2 1 105.0 1.43 3 2 1 97.9 2.00 3 2 0 106.3 1.45 3 2 1 106.5 1.65 3 2 0 116.0 1.72 4 2 1 108.0 1.79 4 2 1 107.5 1.85 3 2 0 109.9 2.06 4 2 1 110.0 1.76 4 2 0 120.0 1.62 3 2 1 115.0 1.80 4 2 1 113.4 1.98 3 2 0 114.9 1.57 3 2 0 115.0 2.19 3 2 0 115.0 2.07 4 2 0 117.9 1.99 4 2 0 110.0 1.55 3 2 0 115.0 1.67 3 2 0 124.0 2.40 4 2 0 129.9 1.79 4 2 1 124.0 1.89 3 2 0 128.0 1.88 3 2 1 132.4 2.00 4 2 1 139.3 2.05 4 2 1 139.3 2.00 4 2 1 139.7 2.03 3 2 1 142.0 2.12 3 3 0 141.3 2.08 4 2 1 147.5 2.19 4 2 0 142.5 2.40 4 2 0 148.0 2.40 5 2 0 149.0 3.05 4 2 0 150.0 2.04 3 3 0 172.9 2.25 4 2 1 190.0 2.57 4 3 1 280.0 3.85 4 3 0 end label variable p "selling price in thousands" label variable s "size in thousands" label variable be "number bedrooms" label variable ba "number bathrooms" label variable new "new-1 or old-0" summarize s ba p corr s ba p stem s stem ba stem p graph p s ba, matrix half regress p s ba, beta pcorr p ba s rvfplot rvpplot s rvpplot ba vif collin p s ba /* user written program: findit collin */ predict sresid, rstandard sort sresid list p s ba sresid in 1/10 list p s ba sresid in -10/l summarize sresid, detail stem sresid pnorm sresid qnorm sresid regress p s regress p s ba regress p ba regress p s ba be test be sw regress p s ba be, pe(.05) [Stata Output] label variable p "selling price in thousands" label variable s "size in thousands" label variable be "number bedrooms" label variable ba "number bathrooms" label variable new "new-1 or old-0" summarize s ba p Variable | Obs Mean Std. Dev. Min Max ---------+----------------------------------------------------- s | 93 1.649677 .5252607 .4 3.85 ba | 93 1.956989 .4147807 1 3 p | 93 99.53333 44.18413 17.5 309.4 corr s ba p (obs=93) | s ba p ---------+--------------------------- s | 1.0000 ba | 0.6625 1.0000 p | 0.8988 0.7137 1.0000 stem s Stem-and-leaf plot for s (size in thousands) s rounded to nearest multiple of .01 plot in units of .01 0** | 40 0** | 74,78 0** | 84,97,99 1** | 01,01,08,10,15,15 1** | 20,22,22,25,25,27,28,28,28,28,29,33,34,34,34,36,36 1** | 40,40,40,42,43,45,45,46,51,51,52,54,55,55,55,56,56,57,58,58,58 1** | 62,62,62,65,66,67,68,71,72,74,76,79,79 1** | 80,85,85,88,89,92,98,99 2** | 00,00,00,03,04,05,06,07,08,10,12,19,19 2** | 25 2** | 40,40,40,40,57 2** | 2** | 3** | 05 3** | 30 3** | 3** | 3** | 85 stem ba Stem-and-leaf plot for ba (number bathrooms) 0* | 1111111111 0* | 222222222222222222222222222222222222222222222222222222222222222 ... (77) 0* | 333333 stem p Stem-and-leaf plot for p (selling price in thousands) p rounded to integers 0** | 18 0** | 20,25,28,32,35 0** | 49,50,55 0** | 60,60,62,66,68,68,69,69,70,70,71,71,72,73,73,73,73,76,76,76,76 0** | 82,84,85,86,86,87,87,87,87,88,88,88,88,90,90,96,96,98,99 1** | 00,00,00,02,02,02,05,06,07,08,08,10,10,10,11,13,15,15,15,15,15,16,18 1** | 20,24,24,28,30,32,37,39,39 1** | 40,41,42,43,48,48,49,50 1** | 73 1** | 90 2** | 2** | 2** | 2** | 2** | 80 3** | 09 graph p s ba,matrix half regress p s ba, beta Source | SS df MS Number of obs = 93 ---------+------------------------------ F( 2, 90) = 224.11 Model | 149573.054 2 74786.527 Prob > F = 0.0000 Residual | 30032.8082 90 333.697869 R-squared = 0.8328 ---------+------------------------------ Adj R-squared = 0.8291 Total | 179605.862 92 1952.23763 Root MSE = 18.267 ------------------------------------------------------------------------------ p | Coef. Std. Err. t P>|t| Beta ---------+-------------------------------------------------------------------- s | 63.86315 4.840401 13.194 0.000 .7592047 ba | 22.44845 6.129679 3.662 0.000 .2107359 _cons | -49.75164 9.183284 -5.418 0.000 . ------------------------------------------------------------------------------ pcorr p ba s (obs=93) Partial correlation of p with Variable | Corr. Sig. -------------+------------------ ba | 0.3601 0.000 s | 0.8119 0.000 rvfplot, yline(0) rvpplot s, yline(0) rvpplot ba, yline(0) vif Variable | VIF 1/VIF ---------+---------------------- ba | 1.78 0.561117 s | 1.78 0.561117 ---------+---------------------- Mean VIF | 1.78 collin p s ba Collinearity Diagnostics SQRT Cond R- Variable VIF VIF Tolerance Eigenval Index Squared ------------------------------------------------------------------------ s 1.78 1.33 0.5611 1.6625 1.0000 0.4389 ba 1.78 1.33 0.5611 0.3375 2.2194 0.4389 ------------------------------------------------------------------------ Mean VIF 1.78 Condition Number 2.2194 Determinant of correlation matrix 0.5611 predict sresid,rstandard sort sresid list p s ba sresid in 1/10 p s ba sresid 1. 149 3.05 2 -2.41815 2. 88.1 2.1 2 -2.279348 3. 69 1.74 2 -2.051483 4. 19.6 1.28 1 -1.990447 5. 137 2.4 3 -1.933392 6. 76 1.66 2 -1.384791 7. 97.9 2 2 -1.379334 8. 124 2.4 2 -1.368973 9. 75.5 1.62 2 -1.271868 10. 69.9 1.52 2 -1.229592 list p s ba sresid in -10/l p s ba sresid 84. 105 1.43 2 1.022334 85. 106.3 1.45 2 1.023229 86. 72.5 1.28 1 1.031645 87. 114.9 1.57 2 1.073262 88. 17.5 .4 1 1.10068 89. 129.9 1.79 2 1.125482 90. 120 1.62 2 1.17789 91. 59.9 .99 1 1.361192 92. 172.9 2.25 2 1.896437 93. 309.4 3.3 3 4.734716 summarize sresid, detail Standardized residuals ------------------------------------------------------------- Percentiles Smallest 1% -2.41815 -2.41815 5% -1.933392 -2.279348 10% -1.229592 -2.051483 Obs 93 25% -.6306399 -1.990447 Sum of Wgt. 93 50% .0940549 Mean .0024452 Largest Std. Dev. 1.020772 75% .7050466 1.17789 90% 1.022334 1.361192 Variance 1.041976 95% 1.125482 1.896437 Skewness .6291919 99% 4.734716 4.734716 Kurtosis 6.807695 stem sresid Stem-and-leaf plot for sresid (Studentized residuals) sresid rounded to nearest multiple of .01 plot in units of .01 sresid rounded to nearest multiple of .01 plot in units of .01 -2** | 42,28,05 -1** | 99,93 -1** | 38,38,37,27,23,20,15,11,09 -0** | 93,91,87,80,80,79,73,68,68,63,55,50,50,50,50 -0** | 48,45,34,33,32,26,25,24,23,22,15,08,06,04,02 0** | 00,07,09,09,10,11,12,14,21,26,27,32,33,38,41,45,46,47,49 0** | 53,53,61,69,69,70,71,73,73,74,77,82,87,87,88,91,91,96,97 1** | 01,02,02,03,07,10,13,18,36 1** | 90 2** | 2** | 3** | 3** | 4** | 4** | 73 qnorm sresid qnorm sresid regress p s Source | SS df MS Number of obs = 93 ---------+------------------------------ F( 1, 91) = 382.63 Model | 145097.459 1 145097.459 Prob > F = 0.0000 Residual | 34508.4029 91 379.213218 R-squared = 0.8079 ---------+------------------------------ Adj R-squared = 0.8058 Total | 179605.862 92 1952.23763 Root MSE = 19.473 ------------------------------------------------------------------------------ p | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------+-------------------------------------------------------------------- s | 75.60684 3.865208 19.561 0.000 67.92908 83.2846 _cons | -25.19356 6.68845 -3.767 0.000 -38.47935 -11.90778 ------------------------------------------------------------------------------ regress p s ba Source | SS df MS Number of obs = 93 ---------+------------------------------ F( 2, 90) = 224.11 Model | 149573.054 2 74786.527 Prob > F = 0.0000 Residual | 30032.8082 90 333.697869 R-squared = 0.8328 ---------+------------------------------ Adj R-squared = 0.8291 Total | 179605.862 92 1952.23763 Root MSE = 18.267 ------------------------------------------------------------------------------ p | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------+-------------------------------------------------------------------- s | 63.86315 4.840401 13.194 0.000 54.24685 73.47945 ba | 22.44845 6.129679 3.662 0.000 10.27078 34.62613 _cons | -49.75164 9.183284 -5.418 0.000 -67.99584 -31.50744 ------------------------------------------------------------------------------ regress p ba Source | SS df MS Number of obs = 93 ---------+------------------------------ F( 1, 91) = 94.47 Model | 91484.3965 1 91484.3965 Prob > F = 0.0000 Residual | 88121.4656 91 968.367754 R-squared = 0.5094 ---------+------------------------------ Adj R-squared = 0.5040 Total | 179605.862 92 1952.23763 Root MSE = 31.119 ------------------------------------------------------------------------------ p | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------+-------------------------------------------------------------------- ba | 76.02581 7.821818 9.720 0.000 60.48873 91.5629 _cons | -49.24837 15.64364 -3.148 0.002 -80.32253 -18.17421 ------------------------------------------------------------------------------ regress p s ba be Source | SS df MS Number of obs = 93 -------------+------------------------------ F( 3, 89) = 148.03 Model | 149621.203 3 49873.7345 Prob > F = 0.0000 Residual | 29984.6586 89 336.906277 R-squared = 0.8331 -------------+------------------------------ Adj R-squared = 0.8274 Total | 179605.862 92 1952.23763 Root MSE = 18.355 ------------------------------------------------------------------------------ p | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- s | 62.35406 6.292024 9.91 0.000 49.85194 74.85617 ba | 22.91549 6.281753 3.65 0.000 10.43378 35.3972 be | 1.63579 4.326989 0.38 0.706 -6.961846 10.23343 _cons | -53.38249 13.31866 -4.01 0.000 -79.84638 -26.91861 ------------------------------------------------------------------------------ test be ( 1) be = 0.0 F( 1, 89) = 0.14 Prob > F = 0.7063 sw regress p s ba be, pe(.05) begin with empty model p = 0.0000 < 0.0500 adding s p = 0.0004 < 0.0500 adding ba Source | SS df MS Number of obs = 93 -------------+------------------------------ F( 2, 90) = 224.11 Model | 149573.054 2 74786.527 Prob > F = 0.0000 Residual | 30032.8082 90 333.697869 R-squared = 0.8328 -------------+------------------------------ Adj R-squared = 0.8291 Total | 179605.862 92 1952.23763 Root MSE = 18.267 ------------------------------------------------------------------------------ p | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- s | 63.86315 4.840401 13.19 0.000 54.24685 73.47945 ba | 22.44845 6.129679 3.66 0.000 10.27078 34.62613 _cons | -49.75164 9.183284 -5.42 0.000 -67.99584 -31.50744 ------------------------------------------------------------------------------