or the data $(0,1000),(1,1500),(2,2000),(3,2500),(4,3000),(5,3500)$, where the first number in parenthesis is $t$ and the second number is the actual demand, if we fit a trend line of the form $y t=a+b t$, the value of a obtained using the appropriate formulae is
A) 0
B) 500
C) 1000
D) 1500
E) 2000

Question

Quizplus · Accepted Answer

The value of $a$ can be found using the formula for the intercept in a simple linear regression, which is $a = \bar{y} - b\bar{x}$, where $\bar{y}$ is the average of the $y$ values (demand), $\bar{x}$ is the average of the $x$ values (time $t$), and $b$ is the slope of the line. Given the data, the average demand ($\bar{y}$) is $2250$ and the average time ($\bar{x}$) is $2.5$. The slope $b$ can be calculated or inferred to be $500$ based on the consistent increase in demand over time. Thus, substituting these values into the formula for $a$ gives $a = 2250 - 500(2.5) = 1000$.

Or the Data (0,1000),(1,1500),(2,2000),(3,2500),(4,3000),(5,3500)(0,1000),(1,1500),(2,2000),(3,2500),(4,3000),(5,3500)(0,1000),(1,1500),(2,2000),(3,2500),(4,3000),(5,3500) , Where the First Number in Parenthesis Is

Or the Data $(0,1000),(1,1500),(2,2000),(3,2500),(4,3000),(5,3500)$ , Where the First Number in Parenthesis Is