document.write( "Question 466807: Given are five observation for two variables,X and Y\r
\n" ); document.write( "\n" ); document.write( " Xi 1 2 3 4 5
\n" ); document.write( " Yi 3 7 5 11 14
\n" ); document.write( "a- Develop a scatter diagram for these data ?
\n" ); document.write( "b- What does the scatter diagram developed in part (a) indicate about the relationship between the two variables ?
\n" ); document.write( "c- Try to approximate the relationship between X and Y by drawing a straight line through the data .
\n" ); document.write( "d- Develop the estimated regression equation by computing the values of b0 and b1 using equation (1.46)and(1.47) .
\n" ); document.write( "e- Use the estimated regression equation to predict the value of Y when X=4 . \n" ); document.write( "
Algebra.Com's Answer #320156 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( " xi     1  2  3   4    5\r\n" );
document.write( " yi     3  7  5  11   14\r\n" );
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\n" ); document.write( "a- Develop a scatter diagram for these data
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\n" ); document.write( "b- What does the scatter diagram developed in part (a) indicate about the relationship between the two variables ?
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document.write( "It indicates that those points aren't too far off a straight line.\r\n" );
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\n" ); document.write( "c- Try to approximate the relationship between X and Y by drawing a straight line through the data .
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\n" ); document.write( "d- Develop the estimated regression equation by computing the values of b0 and b1 using equation (1.46)and(1.47)
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document.write( "I can't see your book, but most books use this formula for\r\n" );
document.write( "the slope b1:\r\n" );
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document.write( "Or this, when we multiply top and bottom by n:\r\n" );
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document.write( "Then from that the y-intercept, b0, is calculated:\r\n" );
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document.write( "\"b%5B0%5D=%28+sum%28y%5B1%5D%29+-b%5B1%5Dsum%28x%5Bi%5D%29%29%2Fn\"\r\n" );
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document.write( "i        xi    yi   xiyi   xi²\r\n" );
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document.write( "1         1     3     3     1\r\n" );
document.write( "2         2     7    14     4\r\n" );
document.write( "3         3     5    15     9\r\n" );
document.write( "4         4    11    44    16 \r\n" );
document.write( "5         5    14    70    25\r\n" );
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document.write( "sums:    15    40   146    55\r\n" );
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document.write( "n = 5\r\n" );
document.write( "\"sum%28x%5Bi%5D%29=15\"\r\n" );
document.write( "\"sum%28y%5Bi%5D%29=40\"\r\n" );
document.write( "\"sum%28x%5Bi%5Dy%5B1%5D%29=146\"\r\n" );
document.write( "\"sum%28%28x%5Bi%5D%5E2%29%29=55\" \r\n" );
document.write( "Substituting in \r\n" );
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document.write( "Then we substitute into:\r\n" );
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document.write( "\"b%5B0%5D=%28+sum%28y%5B1%5D%29+-b%5B1%5Dsum%28x%5Bi%5D%29%29%2Fn\"\r\n" );
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document.write( "\"b%5B0%5D=%2840+-2.6%2A15%29%2F5=%2840-39%29%2F5=1%2F5=.2\"\r\n" );
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document.write( "Therefore the equation of the regression line is\r\n" );
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document.write( "\"y=b%5B1%5Dx%2Bb%5B0%5D\"\r\n" );
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document.write( "\"y=2.6x%2B.2\"\r\n" );
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document.write( "Actually the line drawn above in part c is this \r\n" );
document.write( "regression line. \r\n" );
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\n" ); document.write( "e- Use the estimated regression equation to predict the value of Y when X=4
\n" ); document.write( "\"y=2.6x%2B.2\"
\n" ); document.write( "\"y=2.6%284%29%2B.2\"
\n" ); document.write( "\"y=2.6x%2B.2\"
\n" ); document.write( "\"y=10.4%2B.2\"
\n" ); document.write( "\"y=10.6\"
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document.write( "Notice that the actual value of y in the data when x=4 is 11,\r\n" );
document.write( "which is close.\r\n" );
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document.write( "Edwin
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