In: Statistics and Probability
The following data set provides information on the lottery sales, proceeds, and prizes by year in Iowa.
FYI | Sales | Proceeds | Prizes |
1986 | $85,031,584 | $27,631,613 | $39,269,612 |
1987 | $98,292,366 | $31,157,797 | $47,255,945 |
1988 | $128,948,560 | $40,090,157 | $65,820,798 |
1989 | $172,488,594 | $49,183,227 | $92,563,898 |
1990 | $168,346,888 | $50,535,644 | $90,818,207 |
1991 | $158,081,953 | $44,053,446 | $86,382,329 |
1992 | $166,311,122 | $45,678,558 | $92,939,035 |
1993 | $207,192,724 | $56,092,638 | $116,820,274 |
1994 | $206,941,796 | $56,654,308 | $116,502,450 |
1995 | $207,648,303 | $58,159,175 | $112,563,375 |
1996 | $190,004,182 | $51,337,907 | $102,820,278 |
1997 | $173,655,030 | $43,282,909 | $96,897,120 |
1998 | $173,876,206 | $42,947,928 | $96,374,445 |
1999 | $184,065,581 | $45,782,809 | $101,981,094 |
2000 | $178,205,366 | $44,769,519 | $98,392,253 |
2001 | $174,943,317 | $44,250,798 | $96,712,105 |
2002 | $181,305,805 | $48,165,186 | $99,996,233 |
2003 | $187,829,568 | $47,970,711 | $104,199,159 |
2004 | $208,535,200 | $55,791,763 | $114,456,963 |
2005 | $210,669,212 | $51,094,109 | $113,455,673 |
2006 | $339,519,523 | $80,875,796 | $122,258,603 |
2007 | $235,078,910 | $58,150,437 | $133,356,860 |
2008 | $249,217,468 | $56,546,118 | $144,669,575 |
2009 | $243,337,101 | $60,553,306 | $138,425,341 |
2010 | $256,255,637 | $57,907,066 | $150,453,787 |
2011 | $271,391,047 | $68,001,753 | $158,961,078 |
2012 | $310,851,725 | $78,731,949 | $182,442,447 |
2013 | $339,251,420 | $84,890,729 | $200,801,768 |
2014 | $314,055,429 | $73,972,114 | $186,948,985 |
2015 | $324,767,416 | $74,517,068 | $196,882,289 |
2016 | $366,910,923 | $88,024,619 | $221,767,401 |
You decided to find the linear equation that corresponds to sales and year. Create a graph using the sales and year. Add the linear equation to the graph. What is the y-intercept of the linear equation?
Round each value below to the nearest integer.
Provide your answer below: ____E+ ___
The scatter plot of the year and the sales.
In order to find out the equations, we need the sum and the sum of squares and cross products of year and sales. We form the table below:
Year | Sales | x^2 | y^2 | X*y | |
1986 | 8,50,31,584 | 3944196 | 7.23037E+15 | 1.68873E+11 | |
1987 | 9,82,92,366 | 3948169 | 9.66139E+15 | 1.95307E+11 | |
1988 | 12,89,48,560 | 3952144 | 1.66277E+16 | 2.5635E+11 | |
1989 | 17,24,88,594 | 3956121 | 2.97523E+16 | 3.4308E+11 | |
1990 | 16,83,46,888 | 3960100 | 2.83407E+16 | 3.3501E+11 | |
1991 | 15,80,81,953 | 3964081 | 2.49899E+16 | 3.14741E+11 | |
1992 | 16,63,11,122 | 3968064 | 2.76594E+16 | 3.31292E+11 | |
1993 | 20,71,92,724 | 3972049 | 4.29288E+16 | 4.12935E+11 | |
1994 | 20,69,41,796 | 3976036 | 4.28249E+16 | 4.12642E+11 | |
1995 | 20,76,48,303 | 3980025 | 4.31178E+16 | 4.14258E+11 | |
1996 | 19,00,04,182 | 3984016 | 3.61016E+16 | 3.79248E+11 | |
1997 | 17,36,55,030 | 3988009 | 3.01561E+16 | 3.46789E+11 | |
1998 | 17,38,76,206 | 3992004 | 3.02329E+16 | 3.47405E+11 | |
1999 | 18,40,65,581 | 3996001 | 3.38801E+16 | 3.67947E+11 | |
2000 | 17,82,05,366 | 4000000 | 3.17572E+16 | 3.56411E+11 | |
2001 | 17,49,43,317 | 4004001 | 3.06052E+16 | 3.50062E+11 | |
2002 | 18,13,05,805 | 4008004 | 3.28718E+16 | 3.62974E+11 | |
2003 | 18,78,29,568 | 4012009 | 3.52799E+16 | 3.76223E+11 | |
2004 | 20,85,35,200 | 4016016 | 4.34869E+16 | 4.17905E+11 | |
2005 | 21,06,69,212 | 4020025 | 4.43815E+16 | 4.22392E+11 | |
2006 | 33,95,19,523 | 4024036 | 1.15274E+17 | 6.81076E+11 | |
2007 | 23,50,78,910 | 4028049 | 5.52621E+16 | 4.71803E+11 | |
2008 | 24,92,17,468 | 4032064 | 6.21093E+16 | 5.00429E+11 | |
2009 | 24,33,37,101 | 4036081 | 5.92129E+16 | 4.88864E+11 | |
2010 | 25,62,55,637 | 4040100 | 6.5667E+16 | 5.15074E+11 | |
2011 | 27,13,91,047 | 4044121 | 7.36531E+16 | 5.45767E+11 | |
2012 | 31,08,51,725 | 4048144 | 9.66288E+16 | 6.25434E+11 | |
2013 | 33,92,51,420 | 4052169 | 1.15092E+17 | 6.82913E+11 | |
2014 | 31,40,55,429 | 4056196 | 9.86308E+16 | 6.32508E+11 | |
2015 | 32,47,67,416 | 4060225 | 1.05474E+17 | 6.54406E+11 | |
2016 | 36,69,10,923 | 4064256 | 1.34624E+17 | 7.39692E+11 | |
Total | 62031 | 6713009956 | 1.24E+08 | 1.60351E+18 | 1.34498E+13 |
The linear equation to the graph is
The y-intercept of the equation is -1.3564656279E+10