Question

Year # AIDS cases diagnosed # AIDS deaths

Year	# AIDS cases diagnosed	# AIDS deaths
Pre–1981	91	29
1981	319	121
1982	1,170	453
1983	3,076	1,482
1984	6,240	3,466
1985	11,776	6,878
1986	19,032	11,987
1987	28,564	16,162
1988	35,447	20,868
1989	42,674	27,591
1990	48,634	31,335
1991	59,660	36,560
1992	78,530	41,055
1993	78,834	44,730
1994	71,874	49,095
1995	68,505	49,456
1996	59,347	38,510
1997	47,149	20,736
1998	38,393	19,005
1999	25,174	18,454
2000	25,522	17,347
2001	25,643	17,402
2002	26,464	16,371
Total	802,118	489,093

Graph "year" vs. "# AIDS deaths." Do not include pre-1981. Label both axes with words. Scale both axes. Calculate the following. (Round your answers to the nearest whole number. Round the correlation coefficient r to four decimal places.)

a =

b=

r=

n=

Answer 1

X - Mx	Y - My	(X - Mx)2	(X - Mx)(Y - My)
-10.5	-22109.1818	110.25	232146.4091
-9.5	-21777.1818	90.25	206883.2273
-8.5	-20748.1818	72.25	176359.5455
-7.5	-18764.1818	56.25	140731.3636
-6.5	-15352.1818	42.25	99789.1818
-5.5	-10243.1818	30.25	56337.5
-4.5	-6068.1818	20.25	27306.8182
-3.5	-1362.1818	12.25	4767.6364
-2.5	5360.8182	6.25	-13402.0455
-1.5	9104.8182	2.25	-13657.2273
-0.5	14329.8182	0.25	-7164.9091
0.5	18824.8182	0.25	9412.4091
1.5	22499.8182	2.25	33749.7273
2.5	26864.8182	6.25	67162.0455
3.5	27225.8182	12.25	95290.3636
4.5	16279.8182	20.25	73259.1818
5.5	-1494.1818	30.25	-8218
6.5	-3225.1818	42.25	-20963.6818
7.5	-3776.1818	56.25	-28321.3636
8.5	-4883.1818	72.25	-41507.0455
9.5	-4828.1818	90.25	-45867.7273
10.5	-5859.1818	110.25	-61521.4091
		SS: 885.5	SP: 982572

Sum of X = 43813
Sum of Y = 489064
Mean X = 1991.5
Mean Y = 22230.1818
Sum of squares (SS_X) = 885.5
Sum of products (SP) = 982572

Regression Equation = ŷ = bX + a

b = SP/SS_X = 982572/885.5 = 1110

a = M_Y - bM_X = 22230.18 - (1109.62*1991.5) = -2187586

ŷ = 1110X - 2187586

X - Mx	Y - My	(X - Mx)2	(Y - My)2	(X - Mx)(Y - My)
-10.5	-22109.182	110.25	488815920.7	232146.409
-9.5	-21777.182	90.25	474245647.9	206883.227
-8.5	-20748.182	72.25	430487048.8	176359.545
-7.5	-18764.182	56.25	352094519.3	140731.364
-6.5	-15352.182	42.25	235689486.6	99789.182
-5.5	-10243.182	30.25	104922773.8	56337.5
-4.5	-6068.182	20.25	36822830.58	27306.818
-3.5	-1362.182	12.25	1855539.306	4767.636
-2.5	5360.818	6.25	28738371.58	-13402.045
-1.5	9104.818	2.25	82897714.12	-13657.227
-0.5	14329.818	0.25	205343689.1	-7164.909
0.5	18824.818	0.25	354373779.6	9412.409
1.5	22499.818	2.25	506241818.2	33749.727
2.5	26864.818	6.25	721718455.9	67162.045
3.5	27225.818	12.25	741245175.7	95290.364
4.5	16279.818	20.25	265032480	73259.182
5.5	-1494.182	30.25	2232579.306	-8218
6.5	-3225.182	42.25	10401797.76	-20963.682
7.5	-3776.182	56.25	14259549.12	-28321.364
8.5	-4883.182	72.25	23845464.67	-41507.045
9.5	-4828.182	90.25	23311339.67	-45867.727
10.5	-5859.182	110.25	34330011.58	-61521.409
Mx: 1991.500	My: 22230.182	Sum: 885.500	Sum: 5138905993.273	Sum: 982572.000

X Values
∑ = 43813
Mean = 1991.5
∑(X - M_x)² = SS_x = 885.5

Y Values
∑ = 489064
Mean = 22230.182
∑(Y - M_y)² = SS_y = 5138905993.273

X and Y Combined
N = 22
∑(X - M_x)(Y - M_y) = 982572

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = 982572 / √((885.5)(5138905993.273)) = 0.4606

n=22