Plasma Beta-carotene vs Age
. regress beta_pl age
Source | SS df MS Number of obs = 315
---------+------------------------------ F( 1, 313) = 3.23
Model | 107541.346 1 107541.346 Prob > F = 0.0731
Residual | 10408097.0 313 33252.706 R-squared = 0.0102
---------+------------------------------ Adj R-squared = 0.0071
Total | 10515638.3 314 33489.294 Root MSE = 182.35
------------------------------------------------------------------------------
beta_pl | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
age | 1.269719 .7060466 1.798 0.073 -.1194785 2.658917
_cons | 126.2207 36.8661 3.424 0.001 53.684 198.7574
------------------------------------------------------------------------------
Plasma Retinol vs Alcohol
. regress ret_pl alcohol Source | SS df MS Number of obs = 315 ---------+------------------------------ F( 1, 313) = 0.09 Model | 4023.67732 1 4023.67732 Prob > F = 0.7619 Residual | 13698094.5 313 43763.8802 R-squared = 0.0003 ---------+------------------------------ Adj R-squared = -0.0029 Total | 13702118.2 314 43637.319 Root MSE = 209.20 ------------------------------------------------------------------------------ ret_pl | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------+-------------------------------------------------------------------- alcohol | .2904922 .9580339 0.303 0.762 -1.594508 2.175493 _cons | 601.8378 12.1985 49.337 0.000 577.8364 625.8393 ------------------------------------------------------------------------------
Transformations
Plasma Beta-carotene vs Dietary Beta-carotene
log(Plasma Beta-carotene) vs log(Dietary Beta-carotene)
. regress logbeta logbdiet
Source | SS df MS Number of obs = 314 ---------+------------------------------ F( 1, 312) = 11.43 Model | 6.06643516 1 6.06643516 Prob > F = 0.0008 Residual | 165.58489 312 .5307208 R-squared = 0.0353 ---------+------------------------------ Adj R-squared = 0.0322 Total | 171.651325 313 .548406788 Root MSE = .72851 ------------------------------------------------------------------------ logbeta | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------+-------------------------------------------------------------- logbdiet | .2098945 .0620822 3.381 0.001 .0877417 .3320473 _cons | 3.398304 .4663317 7.287 0.000 2.480751 4.315856 ------------------------------------------------------------------------
Regression Diagnostics
Residual plot of Plasma Beta-carotene vs Dietary Beta-carotene
Residual plot of Log(Plasma Beta-carotene) vs Log (Dietary Beta-carotene)
. regress ret_pl sex
Source | SS df MS Number of obs = 315
---------+------------------------------ F( 1, 313) = 10.99
Model | 464927.21 1 464927.21 Prob > F = 0.0010
Residual | 13237191.0 313 42291.3449 R-squared = 0.0339
---------+------------------------------ Adj R-squared = 0.0308
Total | 13702118.2 314 43637.319 Root MSE = 205.65
------------------------------------------------------------------------------
ret_pl | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
sex | -113.0165 34.08592 -3.316 0.001 -180.083 -45.94998
_cons | 813.7546 64.67349 12.583 0.000 686.5048 941.0043
------------------------------------------------------------------------------
Categorical Variable (3 levels)
. regress ret_pl current former
Source | SS df MS Number of obs = 315 ---------+------------------------------ F( 2, 312) = 3.79 Model | 325058.873 2 162529.437 Prob > F = 0.0236 Residual | 13377059.3 312 42875.1901 R-squared = 0.0237 ---------+------------------------------ Adj R-squared = 0.0175 Total | 13702118.2 314 43637.319 Root MSE = 207.06 ------------------------------------------------------------------------------ ret_pl | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------+-------------------------------------------------------------------- current | -20.23597 35.63969 -0.568 0.571 -90.3605 49.88857 former | 60.93775 25.41492 2.398 0.017 10.93144 110.9441 _cons | 583.3057 16.52545 35.297 0.000 550.7903 615.8211 ------------------------------------------------------------------------------
Mixture of Continuous and Categorical Variables
. regress ret_pl female ret_diet
Source | SS df MS Number of obs = 314 ---------+------------------------------ F( 2, 311) = 6.99 Model | 589645.768 2 294822.884 Prob > F = 0.0011 Residual | 13112355.6 311 42161.9151 R-squared = 0.0430 ---------+------------------------------ Adj R-squared = 0.0369 Total | 13702001.4 313 43776.3622 Root MSE = 205.33 ------------------------------------------------------------------------------ ret_pl | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------+-------------------------------------------------------------------- female | -119.3491 34.23946 -3.486 0.001 -186.7194 -51.97878 ret_diet | -.0418489 .0243224 -1.721 0.086 -.0897063 .0060085 _cons | 740.2494 39.13048 18.917 0.000 663.2555 817.2434 ------------------------------------------------------------------------------
Two Qualitative Predictors
. regress ret_pl female current
Source | SS df MS Number of obs = 315 ---------+------------------------------ F( 2, 312) = 6.61 Model | 557326.746 2 278663.373 Prob > F = 0.0015 Residual | 13144791.4 312 42130.7417 R-squared = 0.0407 ---------+------------------------------ Adj R-squared = 0.0345 Total | 13702118.2 314 43637.319 Root MSE = 205.26 ------------------------------------------------------------------------------ ret_pl | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------+-------------------------------------------------------------------- female | -114.7534 34.04135 -3.371 0.001 -181.7331 -47.7738 current | -49.91481 33.70498 -1.481 0.140 -116.2326 16.40299 _cons | 709.0572 32.16627 22.043 0.000 645.767 772.3475 ------------------------------------------------------------------------------
Two Qualitative and One Continuous Predictor
. regress ret_pl female current ret_diet
Source | SS df MS Number of obs = 315 ---------+------------------------------ F( 3, 311) = 5.10 Model | 643034.779 3 214344.926 Prob > F = 0.0018 Residual | 13059083.4 311 41990.6218 R-squared = 0.0469 ---------+------------------------------ Adj R-squared = 0.0377 Total | 13702118.2 314 43637.319 Root MSE = 204.92 ------------------------------------------------------------------------------ ret_pl | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------+-------------------------------------------------------------------- female | -118.4176 34.08134 -3.475 0.001 -185.4768 -51.35848 current | -51.29626 33.66278 -1.524 0.129 -117.5318 14.93933 ret_diet | -.0281254 .0196863 -1.429 0.154 -.0668605 .0106098 _cons | 735.8418 37.18479 19.789 0.000 662.6763 809.0074 ------------------------------------------------------------------------------
. tab smoke,summarize(ret_pl)
| Summary of Plasma Retinol (ng/ml)
smoke | Mean Std. Dev. Freq.
------------+------------------------------------
Current | 563.06977 206.57783 43
Former | 644.24348 231.16762 115
Never | 583.30573 187.6431 157
------------+------------------------------------
Total | 602.79048 208.89547 315
. tab smoke,summarize(age)
| Summary of Age
smoke | Mean Std. Dev. Freq.
------------+------------------------------------
Current | 44.534884 13.507227 43
Former | 50.773913 13.972442 115
Never | 51.22293 15.022461 157
------------+------------------------------------
Total | 50.146032 14.575226 315
. anova ret_pl smoke age,cont(age)
Number of obs = 315 R-squared = 0.0655
Root MSE = 202.91 Adj R-squared = 0.0565
Source | Partial SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 897521.329 3 299173.776 7.27 0.0001
|
smoke | 283599.164 2 141799.582 3.44 0.0332
age | 572462.455 1 572462.455 13.90 0.0002
|
Residual | 12804596.8 311 41172.3371
-----------+----------------------------------------------------
Total | 13702118.2 314 43637.319
. anova, regress detail
Factor Value Value Value Value
----------------------------------------------------------------------
smoke 1 1 2 2 3 3
Source | SS df MS Number of obs = 315
---------+------------------------------ F( 3, 311) = 7.27
Model | 897521.329 3 299173.776 Prob > F = 0.0001
Residual | 12804596.8 311 41172.3371 R-squared = 0.0655
---------+------------------------------ Adj R-squared = 0.0565
Total | 13702118.2 314 43637.319 Root MSE = 202.91
------------------------------------------------------------------------------
ret_pl Coef. Std. Err. t P>|t| [95% Conf. Interval]
------------------------------------------------------------------------------
_cons 431.4374 43.82968 9.843 0.000 345.1972 517.6776
smoke
1 -.4069026 35.32732 -0.012 0.991 -69.91768 69.10387
2 62.26901 24.90767 2.500 0.013 13.26016 111.2779
3 (dropped)
age 2.964851 .7951191 3.729 0.000 1.400358 4.529344
------------------------------------------------------------------------------
. tab smoke female,summarize(ret_pl)
Means, Standard Deviations and Frequencies of Plasma Retinol (ng/ml)
| female
smoke | 0 1 | Total
-----------+----------------------+----------
Current | 598.85714 556.11111 | 563.06977
| 289.61896 191.11265 | 206.57783
| 7 36 | 43
-----------+----------------------+----------
Former | 798.5 607.75269 | 644.24348
| 323.1962 187.98373 | 231.16762
| 22 93 | 115
-----------+----------------------+----------
Never | 590.15385 582.6875 | 583.30573
| 249.30799 182.1824 | 187.6431
| 13 144 | 157
-----------+----------------------+----------
Total | 700.7381 587.72161 | 602.79048
| 307.80878 185.43069 | 208.89547
| 42 273 | 315
. tab smoke female,summarize(age)
Means, Standard Deviations and Frequencies of Age
| female
smoke | 0 1 | Total
-----------+----------------------+----------
Current | 55.142857 42.472222 | 44.534884
| 13.885587 12.609489 | 13.507227
| 7 36 | 43
-----------+----------------------+----------
Former | 62.227273 48.064516 | 50.773913
| 11.330245 13.184153 | 13.972442
| 22 93 | 115
-----------+----------------------+----------
Never | 60.615385 50.375 | 51.22293
| 16.630987 14.636803 | 15.022461
| 13 144 | 157
-----------+----------------------+----------
Total | 60.547619 48.545788 | 50.146032
| 13.469391 14.093135 | 14.575226
| 42 273 | 315
. anova ret_pl smoke female
Number of obs = 315 R-squared = 0.0523
Root MSE = 204.337 Adj R-squared = 0.0432
Source | Partial SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 716808.852 3 238936.284 5.72 0.0008
|
smoke | 251881.643 2 125940.821 3.02 0.0504
female | 391749.979 1 391749.979 9.38 0.0024
|
Residual | 12985309.3 311 41753.4062
-----------+----------------------------------------------------
Total | 13702118.2 314 43637.319
. anova, regress detail
Factor Value Value Value Value
----------------------------------------------------------------------
smoke 1 1 2 2 3 3
female 1 0 2 1
Source | SS df MS Number of obs = 315
---------+------------------------------ F( 3, 311) = 5.72
Model | 716808.852 3 238936.284 Prob > F = 0.0008
Residual | 12985309.3 311 41753.4062 R-squared = 0.0523
---------+------------------------------ Adj R-squared = 0.0432
Total | 13702118.2 314 43637.319 Root MSE = 204.34
------------------------------------------------------------------------------
ret_pl Coef. Std. Err. t P>|t| [95% Conf. Interval]
------------------------------------------------------------------------------
_cons 574.6167 16.55271 34.714 0.000 542.0472 607.1861
smoke
1 -28.62971 35.27696 -0.812 0.418 -98.0414 40.78198
2 49.55186 25.3542 1.954 0.052 -.3356008 99.43932
3 (dropped)
female
1 104.9373 34.25874 3.063 0.002 37.5291 172.3456
2 (dropped)
------------------------------------------------------------------------------
. anova ret_pl smoke female age,cont(age)
Number of obs = 315 R-squared = 0.0785
Root MSE = 201.82 Adj R-squared = 0.0666
Source | Partial SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 1075395.83 4 268848.957 6.60 0.0000
|
smoke | 229636.971 2 114818.485 2.82 0.0612
female | 177874.501 1 177874.501 4.37 0.0375
age | 358586.977 1 358586.977 8.80 0.0032
|
Residual | 12626722.3 310 40731.3624
-----------+----------------------------------------------------
Total | 13702118.2 314 43637.319
. anova, regress detail
Factor Value Value Value Value
----------------------------------------------------------------------
smoke 1 1 2 2 3 3
female 1 0 2 1
Source | SS df MS Number of obs = 315
---------+------------------------------ F( 4, 310) = 6.60
Model | 1075395.83 4 268848.957 Prob > F = 0.0000
Residual | 12626722.3 310 40731.3624 R-squared = 0.0785
---------+------------------------------ Adj R-squared = 0.0666
Total | 13702118.2 314 43637.319 Root MSE = 201.82
------------------------------------------------------------------------------
ret_pl Coef. Std. Err. t P>|t| [95% Conf. Interval]
------------------------------------------------------------------------------
_cons 451.4028 44.62898 10.115 0.000 363.5888 539.2169
smoke
1 -9.73225 35.41985 -0.275 0.784 -79.42597 59.96147
2 54.01194 25.08704 2.153 0.032 4.649529 103.3744
3 (dropped)
female
1 73.99278 35.40764 2.090 0.037 4.323086 143.6625
2 (dropped)
age 2.455465 .8275627 2.967 0.003 .8271144 4.083815
------------------------------------------------------------------------------
|Data Sources|
Course Topics|Examples|