Question

The table below contains real data for the first two decades of AIDS reporting.

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

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	489064	43813	5138905993	885.5	982572.00
mean	22230.18	1991.50	SSxx	SSyy	SSxy

sample size ,   n =   22          
here, x̅ = Σx / n=   22230.18   ,     ȳ = Σy/n =   1991.50  
                  
SSxx =    Σ(x-x̅)² =    5138905993.2727          
SSxy=   Σ(x-x̅)(y-ȳ) =   982572.0          
                  
b =estimated slope , ß1 = SSxy/SSxx =   982572.0   /   5138905993.273   =   0.0002
                  
a = intercept,   ß0 = y̅-ß1* x̄ =   1987.2495          
                  
so, regression line is   Ŷ =   1987.2495   +   0.0002   *x
                  
SSE=   (SSxx * SSyy - SS²xy)/SSxx =    697.630          
                  
std error ,Se =    √(SSE/(n-2)) =    5.906          
                  
r = correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.4606          
                  
R² =    (Sxy)²/(Sx.Sy) =    0.2122

Please revert in case of any doubt.

Please upvote. Thanks in advance