Question

The following table gives projections of the U.S. population from 2000 to 2100.

Answer 1

The equation of best fit is $f(X) = 2.91964X + 265.86364$.

$f(65) = 455.64024$. It means that the population, in millions, after $65$ years from $2000$ is $455.64024$.

The slope of the line is $2.91964$ which means population is increasing at the rate of $2.91964$ per year.

Sum of $X = 550$

Sum of $Y = 4530.3$

Mean $X = 50$

Mean $Y = 411.8455$

Sum of squares (SSX) $= 11000$

Sum of products (SP) $= 32116$

Regression Equation $= y = bX + a$

$b = \frac{SP}{SSX} = \frac{32116}{11000} = 2.91964$

$a = MY - bMX = 411.85 - (2.92*50) = 265.86364$

$y = 2.91964X + 265.86364$

$f(X) = 2.91964X + 265.86364$

$f(65) = 2.91964\times 65 + 265.86364$

$f(65) = 189.7766 + 265.86364$

$f(65) = 189.7766 + 265.86364$

$f(65) = 455.64024$

It means that the population, in millions, after $65$ years from $2000$ is $455.64024$.

From the equation, $f(X) = 2.91964X + 265.86364$

the slope of the line is $2.91964$ which means population is increasing at the rate of $2.91964$ per year.

Learn more about line of best fit here:

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