document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182816>Question 1182816</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello!\r<BR>\n" );
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document.write( "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.\r<BR>\n" );
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document.write( "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.\r<BR>\n" );
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document.write( "Every 7 days starting on July 7, 2021 I will call our union to get an update on my rank. \r<BR>\n" );
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document.write( "The data I have so far is: \r<BR>\n" );
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document.write( "On May 19, 2021 I was rank 345<BR>\n" );
document.write( "On July 7, 2021 I was rank 302<BR>\n" );
document.write( "there are 49 days between May 19 and July 7 (2021).<BR>\n" );
document.write( "Every 7 days I will get an update on my rank.\r<BR>\n" );
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document.write( "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?\r<BR>\n" );
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document.write( "thank you!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #812925 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=812925\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the simplest thing you can do is apply the straight line equation of y = mx + b.<BR>\n" );
document.write( "m is the slope<BR>\n" );
document.write( "b is the y-intercept.\r<BR>\n" );
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document.write( "since your starting point is 345, then the y-intercept is 345.<BR>\n" );
document.write( "each time you get a new data point, revise the equation as follows:\r<BR>\n" );
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document.write( "m = (y2 - y2) / (x2 - x1)\r<BR>\n" );
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document.write( "with the two data points that you currently have, the equation would become:<BR>\n" );
document.write( "m = (302 - 345) / (49 - 0) = -43/49.\r<BR>\n" );
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document.write( "your equation becomes y = -43/49 * x + 345.\r<BR>\n" );
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document.write( "when x = 49, y becomes 302, as you already know.\r<BR>\n" );
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document.write( "to solve for when the rank becomes 0, replace y with 0 to get:\r<BR>\n" );
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document.write( "0 = -43/49 * x + 345\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = -345 / (-43/49) = 393.1395349.\r<BR>\n" );
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document.write( "this indicate a rank of 0 in approximately 393 days.\r<BR>\n" );
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document.write( "as you add data points, you revise the equation with the latest data point.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "in 7 days, the new data point might be (56,295)\r<BR>\n" );
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document.write( "the equation becomes y = (295 - 345) / 56 * x + 345 which becomes y = -50 / 56 * x + 345.<BR>\n" );
document.write( "set y = 0 and solve for x to get:<BR>\n" );
document.write( "x = -345 / -(50/56) = 386.4 days.\r<BR>\n" );
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document.write( "after 14 more days, if your remaining days is 250, your data point becomes (63,250) and your equation becomes:<BR>\n" );
document.write( "y = (250 - 345) / 63 * x + 345 which becomes y = -95/63 * x + 345.<BR>\n" );
document.write( "set y = 0 and solve for x to get:<BR>\n" );
document.write( "x = -345 / (-95/63) = approximately 228 days.\r<BR>\n" );
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document.write( "after 7 more days, if your remaining days is 245, your data point becomes (70,245) and your equation becomes:<BR>\n" );
document.write( "y = (245 - 345) / 70 * x + 345 which becomes y = -100/70 * x + 345.<BR>\n" );
document.write( "set y = 0 and solve for x to get:<BR>\n" );
document.write( "x = -345 / (-100/70) = approximately 241 days.\r<BR>\n" );
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document.write( "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.\r<BR>\n" );
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document.write( "alternatively, you can use a linear regression formula.\r<BR>\n" );
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document.write( "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.\r<BR>\n" );
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document.write( "for example, with the data points i assumed, you would have 5 data points.\r<BR>\n" );
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document.write( "they would be (0,345),(49,301),(56,295),(63,250),(70,245).\r<BR>\n" );
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document.write( "you would need a minimum of 5 points to run the regression formula.\r<BR>\n" );
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document.write( "that i have with my accumptions.\r<BR>\n" );
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document.write( "the data inputs to the regression calculator become:\r<BR>\n" );
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document.write( "0,49,56,63,70 on the first line (these are the x-values).<BR>\n" );
document.write( "345,302,295,250,245 on the second line (these are the y-values).\r<BR>\n" );
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document.write( "the results are shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/070804.jpg\" >\r<BR>\n" );
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document.write( "the equation shown on the linear regression calculator was:\r<BR>\n" );
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document.write( "y=352.10828025478-1.3594176524113x\r<BR>\n" );
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document.write( "it's enough to round 352.... to 352 and to round -1.3594... to -1.40.\r<BR>\n" );
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document.write( "your equation becomes 352 - 1.40 * x\r<BR>\n" );
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document.write( "any greater accuracy is more then likely not requried.\r<BR>\n" );
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document.write( "with y = 352 -1.40 * x, you would set y = 0 and solve for x to get:\r<BR>\n" );
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document.write( "x = -352 / -1.40 = approximately 251 days.\r<BR>\n" );
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document.write( "each time you add another data point, the regression analysis will give you a new forecast.\r<BR>\n" );
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document.write( "the more data points, the more accurate the forecast from the regression formula.\r<BR>\n" );
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document.write( "the regression calculator can be found at <a  rel=nofollow HREF= \"http://www.alcula.com/calculators/statistics/linear-regression/#gsc.tab=0\" target = \"_blank\">http://www.alcula.com/calculators/statistics/linear-regression/#gsc.tab=0</a> </SPAN>\n" );
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