Question

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

Adults and Adolescents only, United States

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

1.) Graph “year” versus “# AIDS cases diagnosed” (plot the scatter plot). Do not include pre-1981 data. In excel using formula's

2.) Find the regression equation, Interpret slope, Find r. and Describe linear correlation.

3.) When x = 1985, ŷ = _____

When x = 1990, ŷ =_____

When x = 1970, ŷ =______ Why doesn’t this answer make sense?

4.)  What does the correlation imply about the relationship between time (years) and the number of diagnosed AIDS cases reported in the U.S.?

Answer 1

1) Scatter diagram:

2) Regression equation: y = 1,749.8x - 3,448,225

Formula Ref:

3.) When x = 1985, ŷ

y = 1,749.78x - 3,448,225.05

y = 1,749.78x - 3,448,225.05

y =1749.78*1985-3448225.05

y = 25088

When x = 1990, ŷ

y =1749.78*1990-3448225.05

y = 33837

When x = 1970, ŷ

y =1749.78*1990-3448225.05

y = -1158

It doesn't make sense because pre 1981 values are consolidated and added as total 91. but here when we calcualate for the 1970, getting negative value which is not possible

4.)  What does the correlation imply about the relationship between time (years) and the number of diagnosed AIDS cases reported in the U.S.?

There is moderate relationship between Years and the diagnosed AIDS cases reported. because t value shows 0.45

correlations between 0.45 and 0.75 are moderate, and those below 0.45 are considered weak.