document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=63314>Question 63314</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0072868244/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Major help needed in figuring this one out?  Respectfully thank you for your help!\r<BR>\n" );
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document.write( "What is the difference between an independent and a dependent variable? Can independent and dependent variables be interchangeable? Why or why not?       Provide an example of this use. \r<BR>\n" );
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document.write( "      For example, cost accountant Linda Thomas provided the following sampling data for observations obtained during an investigation of the relationship between the volume of an ingredient X and the weight of a production batch Y. \r<BR>\n" );
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document.write( "Volume X. Weight Y<BR>\n" );
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document.write( "10          61<BR>\n" );
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document.write( "24          110<BR>\n" );
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document.write( "13          75<BR>\n" );
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document.write( "7           47<BR>\n" );
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document.write( "9           78<BR>\n" );
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document.write( "25          102<BR>\n" );
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document.write( "6            38<BR>\n" );
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document.write( "10           42<BR>\n" );
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document.write( "16           75<BR>\n" );
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document.write( "15           91<BR>\n" );
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document.write( "Note:  When submitting this question the columns all come together.  There are two columns going down but they don't seem to line up when submitting the question.<BR>\n" );
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document.write( "1)       determine the estimated regression equation\r<BR>\n" );
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document.write( "2)       compute, for batch weight, (a) the sample standard deviation and (b) the standard error of the estimate. Does a comparison of these two values indicate that the  regression line would be useful in predicting batch weight? Why or why not? \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #44070 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=44070\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What is the difference between an independent and a dependent variable?<BR>\n" );
document.write( "An independent variable is given an arbitrary value; the dependent <BR>\n" );
document.write( "variable is then calculated based on the rule and the independent <BR>\n" );
document.write( "variable value.\r<BR>\n" );
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document.write( " Can independent and dependent variables be interchangeable? Why or why not? <BR>\n" );
document.write( "Yes.  It is a matter of point of view.<BR>\n" );
document.write( "Provide an example of this use.<BR>\n" );
document.write( "If y=3x+6 the x is considered to be the independent variable.<BR>\n" );
document.write( "The same equation states x=(y-6)/3; the y could be considered to<BR>\n" );
document.write( "be the independent variable.<BR>\n" );
document.write( "--------------- \r<BR>\n" );
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document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "      For example, cost accountant Linda Thomas provided the following sampling data for observations obtained during an investigation of the relationship between the volume of an ingredient X and the weight of a production batch Y. \r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "Volume X. Weight Y<BR>\n" );
document.write( " <BR>\n" );
document.write( "10          61<BR>\n" );
document.write( " 24          110<BR>\n" );
document.write( " 13          75<BR>\n" );
document.write( " 7           47<BR>\n" );
document.write( " 9           78<BR>\n" );
document.write( " 25          102<BR>\n" );
document.write( " 6            38<BR>\n" );
document.write( " 10           42<BR>\n" );
document.write( " 16           75<BR>\n" );
document.write( " 15           91<BR>\n" );
document.write( " <BR>\n" );
document.write( "Note:  When submitting this question the columns all come together.  There are two columns going down but they don't seem to line up when submitting the question.<BR>\n" );
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document.write( "1)       determine the estimated regression equation<BR>\n" );
document.write( "y=3.32x+26.99 (Gotten using TI-83 Linear Regression function)<BR>\n" );
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document.write( "2)       compute, for batch weight:<BR>\n" );
document.write( "(a) the sample standard deviation = s =  6.6207<BR>\n" );
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document.write( "(b) the standard error of the estimate\r<BR>\n" );
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document.write( "SE=s/sqrt(10)= 2.09365\r<BR>\n" );
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document.write( ". Does a comparison of these two values indicate that the  regression line would be useful in predicting batch weight? Why or why not?<BR>\n" );
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document.write( "The smaller the standard error the better the predictability of the <BR>\n" );
document.write( "regression line.  I don't know what criteria you are using for \"small\"<BR>\n" );
document.write( "so I'll let you decide wether 2.09365 is small enough.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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