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

Question

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

Accepted Answer

∻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 $Life Expectancy = Constant + (Fertility imes Coef_{Fertility})$. ‖ ‖ step 3 ⋮ Substitute the given values into the equation: $Life Expectancy = 89.70 + (2 imes -5.97)$. ‖ ‖ step 4 ⋮ Calculate the predicted life expectancy: $Life Expectancy = 89.70 + (2 imes -5.97) = 89.70 - 11.94 = 77.76$. ‖ ‖ 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.⚹◊What is the formula to calculate the residual in a⍭ Generate me a similar question◊

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