document.write( "Question 868166: Need help!!!\r
\n" ); document.write( "\n" ); document.write( "Company A is a microcomputer producer. The following data represents Company A’s yearly sales volume and its advertising expenditures over a period of 8 years. Sales in millions of dollars and advertising is in $10,000. \r
\n" ); document.write( "\n" ); document.write( "1993 15 32
\n" ); document.write( "1994 16 33
\n" ); document.write( "1995 18 35
\n" ); document.write( "1996 17 34
\n" ); document.write( "1997 16 36
\n" ); document.write( "1998 19 37
\n" ); document.write( "1999 19 39
\n" ); document.write( "2000 24 42 \r
\n" ); document.write( "\n" ); document.write( "Using the method of least squares, what is the estimated regression line between sales and adverting, and the predicted sales in dollars, with an advertising expenditure of $400K actual dollars as scaled to 40. \r
\n" ); document.write( "\n" ); document.write( "a. Sales=-10.4211 =.7895 Advertising: Sales $315,790
\n" ); document.write( "b. Advertising= 16.7143 + 1.0714 Sales: Sales $59.57 Million
\n" ); document.write( "c. Sales=.7895 + 10.421 Advertising: Sales $416.63 Million
\n" ); document.write( "d. Sales= -10.4211 + .7895 Advertising: Sales= $21.16 Million
\n" ); document.write( "e. None of the Above
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Algebra.Com's Answer #523377 by ewatrrr(24785)\"\" \"About 
You can put this solution on YOUR website!

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document.write( "Hi
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document.write( "Do Like the Excel Scatter Plot for Obtaining a Regression - no muss no fuss
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document.write( " .
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document.write( "However, should know how the method of least squares works..same result
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document.write( "but might be a need to know.
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document.write( "x	y	xy	x^2
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document.write( "32	15	480	1024
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document.write( "33	16	528	1089
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document.write( "35	18	630	1225
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document.write( "34	17	578	1156
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document.write( "36	16	576	1296
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document.write( "36	16	576	1296
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document.write( "39	19	741	1521
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document.write( "42	24	1008	1764
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document.write( "287	141	5117	10371
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document.write( "141 = 8a + 287b		
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document.write( "5117= 287a + 10371b
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document.write( "a= 1322362/74073 and b =-469/4073   	
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document.write( "y = a + bx	
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Solved by pluggable solver: Using Cramer's Rule to Solve Systems with 2 variables

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document.write( "  \"system%288%2Ax%2B287%2Ay=141%2C287%2Ax%2B1037%2Ay=5117%29\"
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document.write( "  First let \"A=%28matrix%282%2C2%2C8%2C287%2C287%2C1037%29%29\". This is the matrix formed by the coefficients of the given system of equations.
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document.write( "  Take note that the right hand values of the system are \"141\" and \"5117\" which are highlighted here: 
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document.write( "  \"system%288%2Ax%2B287%2Ay=highlight%28141%29%2C287%2Ax%2B1037%2Ay=highlight%285117%29%29\"
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document.write( "  These values are important as they will be used to replace the columns of the matrix A.
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document.write( "  Now let's calculate the the determinant of the matrix A to get \"abs%28A%29=%288%29%281037%29-%28287%29%28287%29=-74073\". Remember that the determinant of the 2x2 matrix \"A=%28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29\" is \"abs%28A%29=ad-bc\". If you need help with calculating the determinant of any two by two matrices, then check out this solver.
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document.write( "  Notation note: \"abs%28A%29\" denotes the determinant of the matrix A.
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document.write( "  Now replace the first column of A (that corresponds to the variable 'x') with the values that form the right hand side of the system of equations. We will denote this new matrix \"A%5Bx%5D\" (since we're replacing the 'x' column so to speak).
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document.write( "  \"A%5Bx%5D=%28matrix%282%2C2%2Chighlight%28141%29%2C287%2Chighlight%285117%29%2C1037%29%29\"
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document.write( "  Now compute the determinant of \"A%5Bx%5D\" to get \"abs%28A%5Bx%5D%29=%28141%29%281037%29-%28287%29%285117%29=-1322362\". Once again, remember that the determinant of the 2x2 matrix \"A=%28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29\" is \"abs%28A%29=ad-bc\"
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document.write( "  To find the first solution, simply divide the determinant of \"A%5Bx%5D\" by the determinant of \"A\" to get: \"x=%28abs%28A%5Bx%5D%29%29%2F%28abs%28A%29%29=%28-1322362%29%2F%28-74073%29=1322362%2F74073\"
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document.write( "  So the first solution is \"x=1322362%2F74073\"
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document.write( "  We'll follow the same basic idea to find the other solution. Let's reset by letting \"A=%28matrix%282%2C2%2C8%2C287%2C287%2C1037%29%29\" again (this is the coefficient matrix).
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document.write( "  Now replace the second column of A (that corresponds to the variable 'y') with the values that form the right hand side of the system of equations. We will denote this new matrix \"A%5By%5D\" (since we're replacing the 'y' column in a way).
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document.write( "  \"A%5Bx%5D=%28matrix%282%2C2%2C8%2Chighlight%28141%29%2C287%2Chighlight%285117%29%29%29\"
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document.write( "  Now compute the determinant of \"A%5By%5D\" to get \"abs%28A%5By%5D%29=%288%29%285117%29-%28141%29%28287%29=469\".
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document.write( "  To find the second solution, divide the determinant of \"A%5By%5D\" by the determinant of \"A\" to get: \"y=%28abs%28A%5By%5D%29%29%2F%28abs%28A%29%29=%28469%29%2F%28-74073%29=-469%2F74073\"
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document.write( "  So the second solution is \"y=-469%2F74073\"
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document.write( "  ====================================================================================
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document.write( "  Final Answer:
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document.write( "  So the solutions are \"x=1322362%2F74073\" and \"y=-469%2F74073\" giving the ordered pair (1322362/74073, -469/74073)
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document.write( "  Once again, Cramer's Rule is dependent on determinants. Take a look at this 2x2 Determinant Solver if you need more practice with determinants.
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