Bivate Regressions - Updated

Bivariate MTurk Label Regressions

We now consider a set of bivariate regressions of the MTurk labels on release outcome:

Combined male-female regression
subsample female
Subsample male
Subsample black
Subsample not-black

I then also repeat the above regressions on the well-labeled subset of observations with more than 3 MTurkers.

Combined Male-Female

**Multihead(ResNet50)**

	Dependent variable:

	Release Outcome
	(1)	(2)	(3)	(4)	(5)

attractiveness	0.005				0.002
	(-0.002, 0.012)				(-0.008, 0.013)

competence		0.006			0.003
		(-0.002, 0.014)			(-0.010, 0.015)

dominance			-0.003		-0.008
			(-0.011, 0.004)		(-0.017, 0.001)

trustworthiness				0.007^*	0.006
				(0.0001, 0.015)	(-0.005, 0.017)

Constant	0.740^***	0.736^***	0.782^***	0.730^***	0.751^***
	(0.706, 0.774)	(0.695, 0.777)	(0.741, 0.823)	(0.695, 0.765)	(0.702, 0.799)


Observations	7,318	7,318	7,318	7,318	7,318
Adjusted R²	0.0001	0.00005	-0.0001	0.0002	0.0001
F Statistic	1.477 (df = 1; 7316)	1.330 (df = 1; 7316)	0.523 (df = 1; 7316)	2.743^* (df = 1; 7316)	1.193 (df = 4; 7313)

Note:	p<0.1; p<0.05; p<0.01

Subsample Female

**Multihead(ResNet50)**

	Dependent variable:

	Release Outcome
	(1)	(2)	(3)	(4)	(5)	(6)

attractiveness	0.016^**				0.011	0.010
	(0.003, 0.028)				(-0.007, 0.029)	(-0.003, 0.024)

competence		0.012			-0.010
		(-0.002, 0.026)			(-0.033, 0.013)

dominance			0.019^**		0.016	0.014
			(0.005, 0.033)		(-0.0001, 0.032)	(-0.001, 0.030)

trustworthiness				0.014^*	0.006
				(0.001, 0.027)	(-0.014, 0.027)

Constant	0.772^***	0.785^***	0.752^***	0.779^***	0.733^***	0.728^***
	(0.713, 0.832)	(0.713, 0.858)	(0.683, 0.821)	(0.715, 0.844)	(0.651, 0.816)	(0.652, 0.804)


Observations	1,593	1,593	1,593	1,593	1,593	1,593
Adjusted R²	0.002	0.001	0.003	0.001	0.002	0.003
F Statistic	4.473^** (df = 1; 1591)	2.044 (df = 1; 1591)	5.291^** (df = 1; 1591)	3.155^* (df = 1; 1591)	1.853 (df = 4; 1588)	3.419^** (df = 2; 1590)

Note:	p<0.1; p<0.05; p<0.01

Subsample Male

**Multihead(ResNet50)**

	Dependent variable:

	Release Outcome
	(1)	(2)	(3)	(4)	(5)

attractiveness	-0.0002				-0.004
	(-0.008, 0.008)				(-0.016, 0.008)

competence		0.003			0.005
		(-0.006, 0.013)			(-0.009, 0.020)

dominance			-0.002		-0.004
			(-0.012, 0.007)		(-0.014, 0.007)

trustworthiness				0.003	0.004
				(-0.006, 0.011)	(-0.010, 0.017)

Constant	0.742^***	0.725^***	0.754^***	0.727^***	0.738^***
	(0.703, 0.782)	(0.677, 0.773)	(0.704, 0.803)	(0.686, 0.768)	(0.680, 0.796)


Observations	5,725	5,725	5,725	5,725	5,725
Adjusted R²	-0.0002	-0.0001	-0.0001	-0.0001	-0.0005
F Statistic	0.002 (df = 1; 5723)	0.315 (df = 1; 5723)	0.172 (df = 1; 5723)	0.331 (df = 1; 5723)	0.311 (df = 4; 5720)

Note:	p<0.1; p<0.05; p<0.01

Subsample Black

**Multihead(ResNet50)**

	Dependent variable:

	Release Outcome
	(1)	(2)	(3)	(4)	(5)

attractiveness	0.004				0.004
	(-0.006, 0.014)				(-0.010, 0.017)

competence		0.007			0.012
		(-0.004, 0.018)			(-0.005, 0.029)

dominance			-0.005		-0.010
			(-0.015, 0.005)		(-0.022, 0.001)

trustworthiness				0.003	-0.004
				(-0.006, 0.013)	(-0.019, 0.011)

Constant	0.744^***	0.729^***	0.788^***	0.746^***	0.759^***
	(0.699, 0.789)	(0.673, 0.784)	(0.733, 0.844)	(0.700, 0.793)	(0.692, 0.825)


Observations	4,107	4,107	4,107	4,107	4,107
Adjusted R²	-0.0001	0.00001	-0.0001	-0.0002	-0.0002
F Statistic	0.495 (df = 1; 4105)	1.039 (df = 1; 4105)	0.611 (df = 1; 4105)	0.329 (df = 1; 4105)	0.794 (df = 4; 4102)

Note:	p<0.1; p<0.05; p<0.01

Subsample Not-Black

**Multihead(ResNet50)**

	Dependent variable:

	Release Outcome
	(1)	(2)	(3)	(4)	(5)

attractiveness	0.006				0.001
	(-0.004, 0.016)				(-0.015, 0.016)

competence		0.004			-0.009
		(-0.008, 0.016)			(-0.028, 0.010)

dominance			-0.001		-0.005
			(-0.013, 0.010)		(-0.018, 0.009)

trustworthiness				0.012^*	0.019^*
				(0.001, 0.022)	(0.002, 0.036)

Constant	0.737^***	0.747^***	0.774^***	0.710^***	0.743^***
	(0.685, 0.790)	(0.686, 0.808)	(0.712, 0.835)	(0.656, 0.764)	(0.671, 0.814)


Observations	3,211	3,211	3,211	3,211	3,211
Adjusted R²	-0.00003	-0.0002	-0.0003	0.001	0.0002
F Statistic	0.902 (df = 1; 3209)	0.299 (df = 1; 3209)	0.035 (df = 1; 3209)	3.150^* (df = 1; 3209)	1.158 (df = 4; 3206)

Note:	p<0.1; p<0.05; p<0.01

Well labeled subset:

Repeating the above regressions on the well-labeled subset:

Combined Male-Female

**Multihead(ResNet50)**

	Dependent variable:

	Release Outcome
	(1)	(2)	(3)	(4)	(5)

attractiveness	0.024				-0.022
	(-0.009, 0.057)				(-0.074, 0.029)

competence		0.052^**			0.034
		(0.011, 0.094)			(-0.037, 0.104)

dominance			0.012		0.002
			(-0.029, 0.053)		(-0.043, 0.047)

trustworthiness				0.049^**	0.043
				(0.012, 0.085)	(-0.024, 0.110)

Constant	0.647^***	0.499^***	0.696^***	0.535^***	0.489^***
	(0.491, 0.803)	(0.292, 0.705)	(0.479, 0.914)	(0.363, 0.707)	(0.225, 0.752)


Observations	449	449	449	449	449
Adjusted R²	0.001	0.007	-0.002	0.008	0.004
F Statistic	1.426 (df = 1; 447)	4.378^** (df = 1; 447)	0.217 (df = 1; 447)	4.678^** (df = 1; 447)	1.406 (df = 4; 444)

Note:	p<0.1; p<0.05; p<0.01

Subsample Female

**Multihead(ResNet50)**

	Dependent variable:

	Release Outcome
	(1)	(2)	(3)	(4)	(5)	(6)

attractiveness	0.049				0.048	0.043
	(-0.003, 0.100)				(-0.031, 0.127)	(-0.015, 0.102)

competence		0.074			0.100
		(-0.001, 0.149)			(-0.039, 0.238)

dominance			0.039		-0.002	0.014
			(-0.024, 0.103)		(-0.079, 0.075)	(-0.058, 0.086)

trustworthiness				0.035	-0.075
				(-0.028, 0.099)	(-0.196, 0.045)

Constant	0.596^***	0.457^*	0.636^***	0.661^***	0.467^*	0.552^***
	(0.341, 0.851)	(0.073, 0.842)	(0.315, 0.957)	(0.346, 0.975)	(0.056, 0.877)	(0.213, 0.892)


Observations	101	101	101	101	101	101
Adjusted R²	0.014	0.016	0.0004	-0.002	0.001	0.005
F Statistic	2.448 (df = 1; 99)	2.632 (df = 1; 99)	1.043 (df = 1; 99)	0.833 (df = 1; 99)	1.013 (df = 4; 96)	1.265 (df = 2; 98)

Note:	p<0.1; p<0.05; p<0.01

Subsample Male

**Multihead(ResNet50)**

	Dependent variable:

	Release Outcome
	(1)	(2)	(3)	(4)	(5)

attractiveness	0.005				-0.064
	(-0.037, 0.047)				(-0.129, 0.0001)

competence		0.041			0.021
		(-0.008, 0.089)			(-0.061, 0.103)

dominance			0.013		0.021
			(-0.039, 0.066)		(-0.036, 0.079)

trustworthiness				0.045^*	0.078
				(0.001, 0.090)	(-0.001, 0.157)

Constant	0.714^***	0.537^***	0.666^***	0.531^***	0.459^**
	(0.521, 0.908)	(0.295, 0.779)	(0.383, 0.949)	(0.325, 0.737)	(0.122, 0.795)


Observations	348	348	348	348	348
Adjusted R²	-0.003	0.003	-0.002	0.005	0.004
F Statistic	0.034 (df = 1; 346)	1.872 (df = 1; 346)	0.166 (df = 1; 346)	2.771^* (df = 1; 346)	1.385 (df = 4; 343)

Note:	p<0.1; p<0.05; p<0.01

Subsample Black

**Multihead(ResNet50)**

	Dependent variable:

	Release Outcome
	(1)	(2)	(3)	(4)	(5)

attractiveness	0.031				-0.041
	(-0.015, 0.076)				(-0.114, 0.033)

competence		0.074^**			0.080
		(0.020, 0.128)			(-0.017, 0.177)

dominance			0.018		0.009
			(-0.036, 0.072)		(-0.052, 0.069)

trustworthiness				0.055^*	0.031
				(0.007, 0.103)	(-0.058, 0.120)

Constant	0.631^***	0.404^**	0.670^***	0.520^***	0.373^*
	(0.424, 0.838)	(0.136, 0.671)	(0.379, 0.962)	(0.300, 0.739)	(0.012, 0.734)


Observations	267	267	267	267	267
Adjusted R²	0.001	0.015	-0.003	0.010	0.007
F Statistic	1.239 (df = 1; 265)	5.144^** (df = 1; 265)	0.309 (df = 1; 265)	3.592^* (df = 1; 265)	1.495 (df = 4; 262)

Note:	p<0.1; p<0.05; p<0.01

Subsample Not-Black

**Multihead(ResNet50)**

	Dependent variable:

	Release Outcome
	(1)	(2)	(3)	(4)	(5)

attractiveness	0.021				-0.005
	(-0.029, 0.071)				(-0.079, 0.069)

competence		0.027			-0.016
		(-0.038, 0.091)			(-0.122, 0.089)

dominance			-0.002		-0.016
			(-0.066, 0.063)		(-0.089, 0.057)

trustworthiness				0.044	0.065
				(-0.015, 0.103)	(-0.039, 0.169)

Constant	0.643^***	0.609^***	0.750^***	0.535^***	0.626^***
	(0.399, 0.886)	(0.284, 0.935)	(0.415, 1.085)	(0.254, 0.817)	(0.233, 1.019)


Observations	182	182	182	182	182
Adjusted R²	-0.003	-0.003	-0.006	0.003	-0.012
F Statistic	0.471 (df = 1; 180)	0.460 (df = 1; 180)	0.002 (df = 1; 180)	1.513 (df = 1; 180)	0.454 (df = 4; 177)

Note:	p<0.1; p<0.05; p<0.01

Appendix

Subsample Female with race controll

**Multihead(ResNet50)**

	Dependent variable:

	Release Outcome
	(1)	(2)	(3)	(4)	(5)	(6)

race_mturk_2_not_black	-0.057^***	-0.050^***	-0.048^***	-0.051^***	-0.055^***	-0.055^***
	(-0.087, -0.027)	(-0.080, -0.021)	(-0.078, -0.018)	(-0.081, -0.021)	(-0.086, -0.025)	(-0.085, -0.025)

attractiveness	0.020^***				0.017	0.015^*
	(0.008, 0.032)				(-0.001, 0.036)	(0.002, 0.029)

competence		0.014			-0.011
		(-0.00005, 0.028)			(-0.034, 0.012)

dominance			0.019^**		0.014	0.012
			(0.005, 0.033)		(-0.002, 0.030)	(-0.004, 0.027)

trustworthiness				0.016^**	0.005
				(0.003, 0.029)	(-0.015, 0.026)

Constant	0.783^***	0.804^***	0.778^***	0.798^***	0.754^***	0.746^***
	(0.723, 0.843)	(0.731, 0.877)	(0.707, 0.850)	(0.733, 0.863)	(0.671, 0.837)	(0.669, 0.823)


Observations	1,593	1,593	1,593	1,593	1,593	1,593
Adjusted R²	0.008	0.005	0.006	0.006	0.007	0.008
F Statistic	7.094^*** (df = 2; 1590)	4.899^*** (df = 2; 1590)	6.207^*** (df = 2; 1590)	5.571^*** (df = 2; 1590)	3.280^*** (df = 5; 1587)	5.260^*** (df = 3; 1589)

Note:	p<0.1; p<0.05; p<0.01

Skin-tone and race relation (sanity check)