How do I calculate the most accurate predictions made based

How do I calculate the most accurate predictions made based on a set of data? The following chart shows the percent of garbage recycles from the years 1990 through 2001. Describe the overall trend in the data. What is the domain of the data set? What is the range of the data set? Use your calculator to find the median-median line for the data set. Meaning of the slope: Meaning of the y-intercept:

Solution

domain is all values of x for which the function exists

domain of data set is { 0,2,3,5,6,8,10,11 }

range is all y values { 8,14,17,23,27,30,33,32 }

year ( x)         percent of garbage recycled (y)

1990                       8

1992                      14

1993                      17

1995                      23

1996                     27

1998                     30

2000                     33

2001                    32

divide the points into 3 equally sized group

finding median of each group

for first group median is 14

2nd group median is 27

3rd group median is 32.5

s1 = (2,14)

s2 = (6,27)

s3 = 10.5 , 32.5)

finding slope of median median line using s1 and s3

slope= y2-y1 / x2-x1

slope = 32.5 - 27 / 10.5 - 6 = 11/9

centroid = ( 2+6+10.5/3 , 14+27+32.5/3 )

centroid = ( 6.16 , 24.5 )

equation of median median line is

y = 11/9x + 16.68

y intercept = 16.68