Question

Consider a study to relate birthweight (y) to the estriol level(x) of pregnant women. The data is below with 32 observations.

i	Estriol(mg/24hr)	Weight(g/100)	i	Estriol(mg/24hr)	Weight(g/100)
1	7	25	17	17	32
2	9	25	18	25	32
3	9	25	19	27	34
4	12	27	20	15	34
5	14	27	21	15	34
6	16	27	22	15	35
7	16	24	23	16	35
8	14	30	24	19	34
9	16	30	25	18	35
10	17	31	26	17	36
11	19	30	27	18	37
12	21	31	28	20	38
13	24	30	29	22	40
14	15	28	30	25	39
15	15	32	31	24	43
16	16	32	32	27	35

PLEASE SHOW ALL YOUR WORK:

1. Calculate the correlation coefficient r. :   

2. Estimate the equation of the regression line that best describes the relationship between birthweight and the estriol level of pregnant women (Assume that the dependent variable is birthweight). :

3. Is the coefficient(β) of birthweight significantly different than zero at significance

level 0.05? :

Answer 1

Answer,

a)

Using Excel

=correl (array1 ,array2) gives correlation

r = 0.6376

b)

data

estriol	weight
7	25
9	25
9	25
12	27
14	27
16	27
16	24
14	30
16	30
17	31
19	30
21	31
24	30
15	28
15	32
16	32
17	32
25	32
27	34
15	34
15	34
15	35
16	35
19	34
18	35
17	36
18	37
20	38
22	40
25	39
24	43
27	35

Data -> data analysis -> regression

regression result

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.637614732
R Square	0.406552547
Adjusted R Square	0.386770965
Standard Error	3.674949902
Observations	32
ANOVA
	df	SS	MS	F	Significance F
Regression	1	277.5610465	277.5610465	20.55207472	8.66755E-05
Residual	30	405.1577035	13.50525678
Total	31	682.71875
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	21.61409884	2.401184916	9.001430373	4.99722E-10	16.71022502
estriol	0.598837209	0.132093346	4.533439612	8.66755E-05	0.329066606

c)

p-value of slope = 0.00009 < alpha

hence we reject the null hypothesis

we conclude that coefficient if birthweight differ from 0 significantly

p-value of slope = 0.00009 < alpha

hence we reject the null hypothesis

we conclude that coefficient if birthweight differ from 0 significantly