Question

If the re-expressed regression line for world population (in millions. is (sqrt) Pop=21.35+(0,566. (years since 1900), then what was the predictedpopulation for 2012?

Answer 1

The expression for the regression is given as

`\sqrt[]{Pop}=21.35+\mleft(0.566.(\text{years since 1900}\mright)`

So, for 1900 to 2012 is

`\begin{gathered} 2012-1900=112\text{ years } \\ so\text{ we will substitute 112 for the years } \end{gathered}`

We will have

`\begin{gathered} \sqrt[]{Pop}=21.35+(0.566.(\text{years since 1900}) \\ \sqrt[]{Pop}=21.35+(0.566.(112) \\ \sqrt[]{Pop}=21.35+(0.566*112) \\ \sqrt[]{Pop}=21.35+63.392 \\ \sqrt[]{Pop}=84.742 \end{gathered}`

Squaring both sides we have

`\begin{gathered} \sqrt[]{Pop}=84.742 \\ (\sqrt[]{Pop})^2=(84.742)^2 \\ Pop=7181.2065 \end{gathered}`

Hence the answer is 7181 to the nearest millions Option d is the correct answer