Asked by Dallas Thompson on Jun 29, 2024
Verified
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: Variable Coefficient Constant 1509.5 Year −0.725\begin{array} { | l | l | } \hline \text { Variable } & \text { Coefficient } \\\hline \text { Constant } & 1509.5 \\\hline \text { Year } & - 0.725 \\\hline\end{array} Variable Constant Year Coefficient 1509.5−0.725 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
First-Birth Rate
The frequency at which first births occur within a defined population.
Regression Analysis
A statistical method used for estimating the relationships among variables, often to predict the value of a dependent variable based on independent variables.
Coefficient
An algebraic expression is multiplied and preceded by a constant or numerical quantity known as the coefficient.
- Acquire knowledge on the interpretation and application of regression analysis and its coefficient values.
- Utilize predictive modeling through regression to interpret data for forecasting.
Verified Answer
NM
Nathan MillerJun 29, 2024
Final Answer :
B
Explanation :
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.
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.
Learning Objectives
- Acquire knowledge on the interpretation and application of regression analysis and its coefficient values.
- Utilize predictive modeling through regression to interpret data for forecasting.