I'm trying to regress some simple pooled data. My data has 60 observations and three columns: Weight, Height, and Sex (female=1, male=0).
If I regress thus, Weight ~ Height + Sex, my model is fairly satisfactory, but the residuals are not homoscedastic (green errors are male, blue female):
I tried regressing on the log of Weight and/or Height, but that didn't do much. What should I do to make the residuals homescedastic and/or make my model more accurate? Any help would be appreciated.
Doing a generalized regression model gives the following.
Generalized least squares fit by REML Model: Weight ~ h + s Data: P149 AIC BIC logLik 514.2221 524.4374 -252.1111 Variance function: Structure: Different standard deviations per stratum Formula: ~1 | Sex Parameter estimates: 0 1 1.0000000 0.6685307 Coefficients: Value Std.Error t-value p-value (Intercept) 27.197499 51.88129 0.524226 0.6022 h 1.852382 0.75634 2.449128 0.0174 s -25.284478 5.53300 -4.569755 0.0000 Correlation: (Intr) h h -0.997 s -0.524 0.466 Standardized residuals: Min Q1 Med Q3 Max -1.6655243 -0.6879858 -0.1839396 0.5628971 3.9857544 Residual standard error: 22.13369 Degrees of freedom: 60 total; 57 residual
With this s. residual plot:
Could someone please explain how precisely this model is different from a standard multiple regression model? Thanks.