Question

"Correlation/Regrision QB"

A researcher wants to determine the relationship between Father’s IQ (X) and Son’s IQ (Y). The researcher selects 16 fathers and measures their IQ and one of each of their son’s IQ. The data are presented below.
Father’s IQ: 144,   136,   132,   125,   119,   117,   115,   112,   108,   101,   98,    97,   91,   90,   88,   87
Son’s IQ:      134,   142,   122,   130,   115,   117,   110,     95,   112,   100,   83, 106,   87,   89,   89,   97

1) What is the value of the relationship between Father’s IQ and Son’s IQ (Round to three decimal places)?  

4) What is the value of the observed test statistic (t) used to determine whether, in the population, this relationship is significantly different from zero (Round to three decimal places)?  

5) Assuming that you want to maximize the power of the test and are interested in whether the relationship is positive or negative, what is the critical value used to compare the observed test statistic (t) in order to determine whether this relationship is significantly different from zero?

8)If appropriate, calculate the proportion of variation in Son's IQ that is accounted for by Father's IQ (Round to two decimal places). If it is not appropriate to calculate this, input 999.

Answer 1

1. r = 0.900

4. t = 7.726

5. 2.145

8. 0.81

The output is:

	r²	0.810
	r	0.900
	Std. Error	8.077
	n	16
	k	1
	Dep. Var.	Y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	3,894.6502	1	3,894.6502	59.70	2.05E-06
Residual	913.3498	14	65.2393
Total	4,808.0000	15
Regression output				confidence interval
variables	coefficients	std. error	t (df=14)	p-value	95% lower	95% upper
Intercept	9.6502
X	0.8941	0.1157	7.726	2.05E-06	0.6459	1.1423

X	Y
144	134
136	142
132	122
125	130
119	115
117	117
115	110
112	95
108	112
101	100
98	83
97	106
91	87
90	89
88	89
87	97