Question

Math

Posted 4 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 $=1.91$ & R-sq $=92.8 \%$ & & & \\
\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 4 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 $Life Expectancy = Constant + (Fertility \times Coef_{Fertility})$

step 3

Substitute the given values into the equation: $Life Expectancy = 89.70 + (2 \times -5.97)$

step 4

Calculate the predicted life expectancy: $Life Expectancy = 89.70 + (2 \times -5.97) = 89.70 - 11.94 = 77.76$

step 5

Round the predicted life expectancy to the nearest whole number: $78$ 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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