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In: Statistics and Probability

The following data set provides information on the lottery sales, proceeds, and prizes by year in...

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+ ___

Solutions

Expert Solution

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

orchestra answered 1 year ago
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