SOLUTION: The following data is associated with the problem: Year Population (in millions) 1950 6.79 1960 27.81 1970 45.59 1980 69.01 1990 84.39 2000 110.21

Algebra ->  Probability-and-statistics -> SOLUTION: The following data is associated with the problem: Year Population (in millions) 1950 6.79 1960 27.81 1970 45.59 1980 69.01 1990 84.39 2000 110.21      Log On


   

Question 1125291: The following data is associated with the problem:
Year Population (in millions)
1950 6.79
1960 27.81
1970 45.59
1980 69.01
1990 84.39
2000 110.21
A: use x=0 for 1950, x=10 for 1960,....
The linear regression equation that best fits this data in the form y=ax+b is: ______________. Round the constants to the nearest thousandth.
B: Use your regression equation to predict the population if x=5.15
c: Approximate in what year the population reaches 38.05 million.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Year Population (in millions)
x|y
1950|+6.79
1960|+27.81
1970|+45.59
1980|+69.01
1990|+84.39
2000|+110.21
A:
use x=0+ for 1950, x=10 for 1960,....
x|y
0|+6.79
10|+27.81
20|+45.59
30|+69.01
40|+84.39
50|+110.21

The linear regression equation that best fits this data in the form y=ax%2Bb is:
y=ax%2Bb use x=0|+y=6.79
6.79=a%2A0%2Bb
b=6.79
y=ax%2Bb use x=10|+y=27.81 and b=6.79
27.81=10a%2B6.79
27.81-6.79=10a
21.02=10a
a=21.02%2F10
a=2.102

_____ y=2.102x%2B6.79 _________. Round the constants to the nearest thousandth.


B: Use your regression equation to predict the population if x=5.15
y=2.102%2A5.15%2B6.79
y=10.8253%2B6.79
y=17.615
c: Approximate in what year the population reaches 38.05 million.
38.05=2.102x%2B6.79
38.05+-6.79++=2.102x
31.26++=2.102x
31.26+%2F2.102=x
x=14.9....Approximately
since x=10 represents year 1960, x=14.9=10%2B4.9 will represent 1960%2B4.9=1964.9 year which means in year 1964, and almost 11 months which means in November, 1964