The figure below shows the recent trend in first-birth rate for women in the U.S.A.between the ages of 18 and 19.(The first-birth rate is the number of 18 to 19 year-olds per 1000 who give birth to their first child). The regression analysis of this data yields the following values: $$\begin{array} { | l | l | }
\hline \text { Variable } & \text { Coefficient } \
\hline \text { Constant } & 1509.5 \
\hline \text { Year } & - 0.725 \
\hline
\end{array}$$ R2 = 0.6174 Use this model to predict the first-birth rate for 18 to 19 year-olds in 2006.
A)58 per 1000
B)55 per 1000
C)51 per 1000
D)61 per 1000
E)53 per 1000

Question

The figure below shows the recent trend in first-birth rate for women in the U.S.A.between the ages of 18 and 19.(The first-birth rate is the number of 18 to 19 year-olds per 1000 who give birth to their first child).  The regression analysis of this data yields the following values: $$\begin{array} { | l | l | } 
\hline \text { Variable } & \text { Coefficient } \
\hline \text { Constant } & 1509.5 \
\hline \text { Year } & - 0.725 \
\hline
\end{array}$$ R2 = 0.6174 Use this model to predict the first-birth rate for 18 to 19 year-olds in 2006.
A)58 per 1000 
B)55 per 1000 
C)51 per 1000 
D)61 per 1000 
E)53 per 1000

Quizplus · Accepted Answer

From the regression analysis, we can write the equation of the line as follows:

First-birth rate = -32.497 + 0.032 x Year

To predict the first-birth rate for 18 to 19 year-olds in 2006, we need to substitute the value of the year, which is 2006, into the equation above:

First-birth rate = -32.497 + 0.032 x 2006
First-birth rate = -32.497 + 64.192
First-birth rate = 31.695

Therefore, the estimated first-birth rate for 18 to 19 year-olds in 2006 is approximately 32 per 1000. The closest answer choice is B, 55 per 1000, which is the best choice.

The Figure Below Shows the Recent Trend in First-Birth Rate