Problem set 1: Use the following data to answer questions 1-4 (30 points):

There is often thought to be a relationship between a person's educational attainment and the number of children he or she has. The hypothesis is that as one's educational level increases, he or she has fewer children. Investigate this conjecture with 25 cases drawn from the 2020 GSS file. The following table displays educational attainment, in years, and the number of children for each respondent.

Education	Children	Education	Children	Education	Children
18	1	14	2	18	2
12	3	13	2	13	2
14	2	15	1	15	3
8	6	12	2	14	2
15	1	12	3	12	2
14	2	11	3
16	1	12	3
12	4	11	4
24	0	12	4
12	3	12	4

1. Calculate the Pearson correlation coefficient for these two variables. Does its value support the hypothesized relationship (10 pts)?

EDUC	CHILDS	(X-)	(X-)2	(Y-)	(Y-) 2	(X-) (Y-)
18	1
12	3
14	2
8	6
15	1
14	2
16	1
12	4
24	0
12	3
14	2
13	2
15	1
12	2
12	3
11	3
12	3
11	4
12	4
12	4
18	2
13	2
15	3
14	2
12	2
X=341	Y=62	=	=	=	=	=
Mean X = (X /N) =
Mean Y = (Y/ N) =
Variance (X) =S2X = (X-)2 / N-1 = Standard deviation (X) = Sx = square root ( )=
Variance (Y) =S2Y =(Y-)2 / N-1 = Standard deviation (Y) = Sy = square root ( )=
Covariance (X,Y) = Sxy =(X-) (Y-) / N-1 =
r = Sxy / Sx * Sy =
*Answers may differ slightly due to rounding.