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Question
Math
Posted 10 months ago

Nkechi took a random sample of 10 countries to study fertility rate (babies per woman) and life expectancy (in years). She noticed a strong negative linear relationship between those variables in the sample data. Here is computer output from a least-squares regression analysis for using fertility rate to predict life expectancy:
\begin{tabular}{lrrrrr} 
Predictor & Coef & SE Coef & T & P \\
\hline Constant & 89.70 & 1.63 & 54.87 & 0.00 \\
Fertility & -5.97 & 0.59 & -10.18 & 0.00 \\
S =1.91=1.91 & R-sq =92.8%=92.8 \% & & & \\
\hline
\end{tabular}

Use this model to predict the life expectancy of a country whose fertility rate is 2 babies per woman.
You may round your answer to the nearest whole number of years.
\square years
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Answer from Sia
Posted 10 months ago
Solution by Steps
step 1
To predict the life expectancy using the regression model, we use the coefficients for Constant and Fertility
step 2
The regression equation is LifeExpectancy=Constant+(Fertility×CoefFertility)Life Expectancy = Constant + (Fertility \times Coef_{Fertility})
step 3
Substitute the given values into the equation: LifeExpectancy=89.70+(2×5.97)Life Expectancy = 89.70 + (2 \times -5.97)
step 4
Calculate the predicted life expectancy: LifeExpectancy=89.70+(2×5.97)=89.7011.94=77.76Life Expectancy = 89.70 + (2 \times -5.97) = 89.70 - 11.94 = 77.76
step 5
Round the predicted life expectancy to the nearest whole number: 7878 years
[1] Answer
78
Key Concept
Linear Regression Prediction
Explanation
To predict a value using a linear regression model, we plug the independent variable(s) into the regression equation and perform the necessary calculations. The result is then rounded to the desired level of precision.

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