Suppose the average remaining lifetime for women in a given country is given in the following table. $$\begin{array} { | c | c | }
\hline \text { Age } & \text { Years } \
\hline 5 & 75.2 \
\hline 30 & 54.3 \
\hline 50 & 37.5 \
\hline 65 & 25.4 \
\hline 75 & 17.0 \
\hline
\end{array}$$ Compute the linear regression equation for these data, where x is the age, in years, and A is the remaining lifetime, in years. Round parameters to the nearest hundredth.
A) $A ( x ) = - 14.53 x + 44.37$
B) $A ( x ) = - 0.83 x + 44.37$
C) $A ( x ) = - 14.53 x + 85.47$
D) $A ( x ) = - 14.53 x + 79.27$
E) $A ( x ) = - 0.83 x + 79.27$

Question

Suppose the average remaining lifetime for women in a given country is given in the following table. $$\begin{array} { | c | c | } 
\hline \text { Age } & \text { Years } \
\hline 5 & 75.2 \
\hline 30 & 54.3 \
\hline 50 & 37.5 \
\hline 65 & 25.4 \
\hline 75 & 17.0 \
\hline
\end{array}$$ Compute the linear regression equation for these data, where x is the age, in years, and A is the remaining lifetime, in years. Round parameters to the nearest hundredth.
A) $A ( x ) = - 14.53 x + 44.37$
B) $A ( x ) = - 0.83 x + 44.37$
C) $A ( x ) = - 14.53 x + 85.47$
D) $A ( x ) = - 14.53 x + 79.27$
E) $A ( x ) = - 0.83 x + 79.27$

Quizplus · Accepted Answer

The correct linear regression equation can be found by calculating the slope (m) and y-intercept (b) of the line that best fits the given data points. The slope is calculated using the formula $m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}$, and the y-intercept is calculated using the formula $b = \frac{\sum y - m(\sum x)}{n}$, where n is the number of data points. After performing these calculations with the given data, the equation that fits the criteria, with parameters rounded to the nearest hundredth, is $A(x) = -0.83x + 79.27$.

Suppose the Average Remaining Lifetime for Women in a Given