The equation of the trend line for the data based on sales (in $1000)of a local restaurant over the years 2005-2010 is Sales= -265575+132.571*year.The equation of the trend line when using 1 to 6 for 2005-2010 is ________
A)-265575+132.571x
B)132,571x
C)97.284+132.571x
D)-263571+98x
E)2004+37.2x

Question

Quizplus · Accepted Answer

The original equation is given as Sales = -265575 + 132.571*year. When we switch from using the actual year numbers (2005-2010) to using 1-6, we essentially redefine our x variable such that x=1 corresponds to the year 2005, x=2 to 2006, and so on up to x=6 for 2010. This means we substitute year = 2004 + x into the original equation, resulting in Sales = -265575 + 132.571*(2004 + x). Simplifying this gives us Sales = -265575 + 132.571*2004 + 132.571*x. The constant terms (-265575 + 132.571*2004) simplify to a new constant, which is the intercept of the new linear equation. The correct answer will have the slope 132.571 (since the relationship between sales and the year hasn't changed, just how we're representing the year) and a new intercept that accounts for the shift in how we're representing time. Option C, 97.284 + 132.571x, is the only one that maintains the correct slope and provides a plausible intercept for the redefined time scale.

The Equation of the Trend Line for the Data Based