Question 1182816: Hello!
I would like an equation or formula to roughly estimate which day I could be called back for rehire at my last job in which I was laid off. The call back right's are determined by seniority and employees are given a "rank". My goal is to reach rank zero (0) in as short amount of time as possible.
My company is slowly calling it's laid-off employees back and I want to determine their daily rate of call backs and which date I could expect a call back myself, assuming that my company maintains the same call back rate.
Every 7 days starting on July 7, 2021 I will call our union to get an update on my rank.
The data I have so far is:
On May 19, 2021 I was rank 345
On July 7, 2021 I was rank 302
there are 49 days between May 19 and July 7 (2021).
Every 7 days I will get an update on my rank.
Is there enough data here to formulate out an equation or formula? Is there any other required data that I would need to complete the equation?
thank you!!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the simplest thing you can do is apply the straight line equation of y = mx + b.
m is the slope
b is the y-intercept.
since your starting point is 345, then the y-intercept is 345.
each time you get a new data point, revise the equation as follows:
m = (y2 - y2) / (x2 - x1)
with the two data points that you currently have, the equation would become:
m = (302 - 345) / (49 - 0) = -43/49.
your equation becomes y = -43/49 * x + 345.
when x = 49, y becomes 302, as you already know.
to solve for when the rank becomes 0, replace y with 0 to get:
0 = -43/49 * x + 345
solve for x to get:
x = -345 / (-43/49) = 393.1395349.
this indicate a rank of 0 in approximately 393 days.
as you add data points, you revise the equation with the latest data point.
for example:
in 7 days, the new data point might be (56,295)
the equation becomes y = (295 - 345) / 56 * x + 345 which becomes y = -50 / 56 * x + 345.
set y = 0 and solve for x to get:
x = -345 / -(50/56) = 386.4 days.
after 14 more days, if your remaining days is 250, your data point becomes (63,250) and your equation becomes:
y = (250 - 345) / 63 * x + 345 which becomes y = -95/63 * x + 345.
set y = 0 and solve for x to get:
x = -345 / (-95/63) = approximately 228 days.
after 7 more days, if your remaining days is 245, your data point becomes (70,245) and your equation becomes:
y = (245 - 345) / 70 * x + 345 which becomes y = -100/70 * x + 345.
set y = 0 and solve for x to get:
x = -345 / (-100/70) = approximately 241 days.
each time you add a new data point, the equation will change and you will get a new estimate as to when your rank will become 0.
alternatively, you can use a linear regression formula.
with that, all you do is add the new data points when they become available and run the regression formula again to get a new equation.
for example, with the data points i assumed, you would have 5 data points.
they would be (0,345),(49,301),(56,295),(63,250),(70,245).
you would need a minimum of 5 points to run the regression formula.
that i have with my accumptions.
the data inputs to the regression calculator become:
0,49,56,63,70 on the first line (these are the x-values).
345,302,295,250,245 on the second line (these are the y-values).
the results are shown below:
the equation shown on the linear regression calculator was:
y=352.10828025478-1.3594176524113x
it's enough to round 352.... to 352 and to round -1.3594... to -1.40.
your equation becomes 352 - 1.40 * x
any greater accuracy is more then likely not requried.
with y = 352 -1.40 * x, you would set y = 0 and solve for x to get:
x = -352 / -1.40 = approximately 251 days.
each time you add another data point, the regression analysis will give you a new forecast.
the more data points, the more accurate the forecast from the regression formula.
the regression calculator can be found at http://www.alcula.com/calculators/statistics/linear-regression/#gsc.tab=0
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