The following information is available for maintenance costs:
$$\begin{array} { l c c }
\text { Month } & \text { Production Volume } & \text { Maintenance Costs } \
\hline\text { January } & 75 & \$ 250 \
\text { February } & 115 & 310 \
\text { March } & 190 & 400 \
\text { April } & 60 & 240 \
\text { May } & 135 & 355
\end{array}$$
-Refer to the figure.Using the method of least squares,what would be the maintenance costs at 100 units of production?
A)$291
B)$321
C)$336
D)$698

Question

The following information is available for maintenance costs:
$$\begin{array} { l c c } 
\text { Month } & \text { Production Volume } & \text { Maintenance Costs } \
\hline\text { January } & 75 & \$ 250 \
\text { February } & 115 & 310 \
\text { March } & 190 & 400 \
\text { April } & 60 & 240 \
\text { May } & 135 & 355
\end{array}$$
-Refer to the figure.Using the method of least squares,what would be the maintenance costs at 100 units of production?
A)$291
B)$321
C)$336
D)$698

Quizplus · Accepted Answer

To predict maintenance costs at 100 units of production using the least squares method, we first calculate the slope (b) and the intercept (a) of the line of best fit using the given data. The formula for the slope (b) is: $$b = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}$$ and the formula for the intercept (a) is: $$a = \frac{\sum y - b(\sum x)}{n}$$ where $n$ is the number of observations, $x$ is the production volume, and $y$ is the maintenance costs. After calculating $a$ and $b$, we use the equation of the line $y = a + bx$ to predict the maintenance costs at 100 units of production. The exact numerical calculations are not provided here, but following these steps with the given data will lead to the prediction.

The Following Information Is Available for Maintenance Costs -Refer to the Figure