A Taiwan electronics company exports personal computers (PCs) to the U.S. Their PC sales (in thousands) over the past five years are given below in Table 6.
Table 6
$$\begin{array} { | c | c | }
\hline \text { Year } & \text { Sales } \
\hline 1 & 6 \
\hline 2 & 9 \
\hline 3 & 13 \
\hline 4 & 15 \
\hline 5 & 20 \
\hline
\end{array}$$
-Using the data in Table 6 the forecast for sales in year 6 using the simple regression equation is:
A) less than 20.
B) more than 20 but less than or equal to 25.
C) more than 25 but less than or equal to 30.
D) more than 30 but less than or equal to 35.

Question

A Taiwan electronics company exports personal computers (PCs) to the U.S. Their PC sales (in thousands) over the past five years are given below in Table 6.
Table 6
 $$\begin{array} { | c | c | } 
\hline \text { Year } & \text { Sales } \
\hline 1 & 6 \
\hline 2 & 9 \
\hline 3 & 13 \
\hline 4 & 15 \
\hline 5 & 20 \
\hline
\end{array}$$
-Using the data in Table 6 the forecast for sales in year 6 using the simple regression equation is:
A) less than 20.
B) more than 20 but less than or equal to 25.
C) more than 25 but less than or equal to 30.
D) more than 30 but less than or equal to 35.

Quizplus · Accepted Answer

To forecast sales for year 6 using simple linear regression, we first need to determine the line of best fit for the given data. The line of best fit can be represented by the equation $y = mx + b$, where $y$ is the sales, $x$ is the year, $m$ is the slope of the line, and $b$ is the y-intercept. Without calculating the exact values of $m$ and $b$, we can observe that the sales are increasing each year, indicating a positive slope. The sales in year 5 are 20,000 units, and the trend suggests an increase each year. Therefore, the forecast for year 6 would logically be more than 20,000 units but without exact calculations, it's difficult to precisely determine the range beyond that. However, given the consistent increase, a forecast of more than 20 but less than or equal to 25 is a reasonable estimation based on the pattern of growth shown in the table.

A Taiwan Electronics Company Exports Personal Computers (PCs) to the U.S