Choose the one alternative that best completes the statement or answers the question.
-In an area of Russia, records were kept on the relationship between the rainfall (in inches) and the yield of wheat (bushels per acre). The data for a 9 year period is as follows:
$\begin{array}{l|ccccccccc}
\text { Rain Fall, x } & 13.1 & 11.4 & 16.0 & 15.1 & 21.4 & 12.9 & 9.6 & 18.2 & 18.6 \
\hline \text { Yield, y } & 48.5 & 44.2 & 56.8 & 80.4 & 47.2 & 29.9 & 74.0 & 74.0 & 76.8
\end{array}$

The equation of the line of least squares is given as $\mathrm { y } = - 9.12 + 4.38 \mathrm { x }$. What would be the expected number of inches of rain if the yield is 60 bushels of wheat per acre?
A) $15.78$
B) $253.68$
C) $11.62$
D) $64.74$

Question

Choose the one alternative that best completes the statement or answers the question.
-In an area of Russia, records were kept on the relationship between the rainfall (in inches) and the yield of wheat (bushels per acre). The data for a 9 year period is as follows:
$\begin{array}{l|ccccccccc}
\text { Rain Fall, x } & 13.1 & 11.4 & 16.0 & 15.1 & 21.4 & 12.9 & 9.6 & 18.2 & 18.6 \
\hline \text { Yield, y } & 48.5 & 44.2 & 56.8 & 80.4 & 47.2 & 29.9 & 74.0 & 74.0 & 76.8
\end{array}$

The equation of the line of least squares is given as $\mathrm { y } = - 9.12 + 4.38 \mathrm { x }$. What would be the expected number of inches of rain if the yield is 60 bushels of wheat per acre?
A) $15.78$
B) $253.68$
C) $11.62$
D) $64.74$

Quizplus · Accepted Answer

To find the expected number of inches of rain for a yield of 60 bushels of wheat per acre, we need to rearrange the equation of the line of least squares to solve for $x$ (rainfall) when $y$ (yield) is 60. The equation given is $y = -9.12 + 4.38x$. Rearranging for $x$, we get $x = \frac{y + 9.12}{4.38}$. Substituting $y = 60$, we get $x = \frac{60 + 9.12}{4.38} = 15.78$.

Choose the One Alternative That Best Completes the Statement or Answers