Question

The table shown to the right gives the national average pupil-teacher ratio in public schools over selected years. a. Find the equation for the least squares line. Let x Correspond to the number of years since 1990 and let y correspond to the average number of pupils per 1 teacher. b. Use the answer from part a to predict the pupil-teacher ratio in 2020. Does this seem realistic? c. Calculate and interpret the correlation coefficient. TTTTT Year 1900 1993 1908 1999 2002 Ratio 18.4 187 169 162 HH 158

Answer 1

Year	Ratio	X	X-Xbar	Y-Ybar	Sxx	Sxy
1990	18.4	0	-2	1.2	4	-2.4
1993	18.7	1	-1	1.5	1	-1.5
1996	16.9	2	0	-0.3	0	0
1999	16.2	3	1	-1	1	-1
2020	15.8	4	2	-1.4	4	-2.8
Sum	86	10	0	1.78E-14	10	-7.7
Mean	17.2	2
a)	intercept	a =	18.74
	slope	b =	-0.77
	Trend line (least square line)
	y = 18.74 -0.77*X
OR	y = 18.74 -0.77*(year - 1990)/3
	if year = 2020
b)	y	=	11.04
c)
	Cor Coeff =		Cov(x,y)/(sx*sy)		-0.93791