Question

DaughtersHeight is a data set on the height of adult daughters and the heights of their mothers and fathers, all in inches. The data were extracted from the US Department of Health and Human Services, Third National Health and Nutrition Examination Survey (use R studio for graphing).

Gender	daughtersheight	mothersheight	fathersheight
F	58.6	63	64
F	64.7	67	65
F	65.3	64	67
F	61	60	72
F	65.4	65	72
F	67.4	67	72
F	60.9	59	67
F	63.1	60	71
F	60	58	66
F	71.1	72	75
F	62.2	63	69
F	67.2	67	70
F	63.4	62	69
F	68.4	69	62
F	62.2	63	66
F	64.7	64	76
F	59.6	63	69
F	61	64	68
F	64	60	66
F	65.4	65	68

Analyze these data with child height as the dependent variable. What can you conclude? Can female daughter height be related to the height of the father and/or the mother? Conduct a separate analysis with Type I and Type III sum of squares to examine whether any major conclusions rest on correlated explanatory variables.

Answer 1

The regression output is:

	R²	0.675
	Adjusted R²	0.637
	R	0.822
	Std. Error	1.940
	n	20
	k	2
	Dep. Var.	daughtersheight
ANOVA table
Source	SS	df	MS	F	p-value
Regression	132.9973	2	66.4986	17.67	.0001
Residual	63.9747	17	3.7632
Total	196.9720	19
Regression output					confidence interval
variables	coefficients	std. error	t (df=17)	p-value	95% lower	95% upper
Intercept	7.4543
mothersheight	0.7072	0.1289	5.488	4.00E-05	0.4353	0.9791
fathersheight	0.1636	0.1266	1.293	.2134	-0.1035	0.4307

The female daughter's height is related to the height of the father and/or the mother.

There is a significant relationship between the female daughter's height and the mother's height based on the Type I and Type III sum of squares.