document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=83418>Question 83418</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Decrease in Banks The number of banks in the United<BR>\n" );
document.write( "States has dropped about 30% since 1992. The following<BR>\n" );
document.write( "data are from a survey in which x represents the years<BR>\n" );
document.write( "since 1900 and y corresponded to the number of banks, in<BR>\n" );
document.write( "thousands, in the United States.†\r<BR>\n" );
document.write( "\n" );
document.write( "n=10            the weird E symbol x^2 = 93,205<BR>\n" );
document.write( "werid E x = 965        weird E xy = 9165.10<BR>\n" );
document.write( "weird y = 95.3        weird y^2 = 920.47\r<BR>\n" );
document.write( "\n" );
document.write( "a. Find an equation of the least squares line.<BR>\n" );
document.write( "b. If the trend continues, how many banks will there be in<BR>\n" );
document.write( "2004?<BR>\n" );
document.write( "c. Find and interpret the coefficient of correlation.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #59953 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=59953\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The following data are from a survey in which x represents <BR>\n" );
document.write( "the years since 1900 and y corresponded to the number of <BR>\n" );
document.write( "banks, in thousands, in the United States.†<BR>\n" );
document.write( "---------- <BR>\n" );
document.write( "n=10 the weird E(x^2) = 93,205 ;<BR>\n" );
document.write( "E(x) = 965 ; E(xy) = 9165.10<BR>\n" );
document.write( "E(y) = 95.3 ;E(y^2) = 920.47 <BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "a. Find an equation of the least squares line.<BR>\n" );
document.write( "y-hat = bo + b1x<BR>\n" );
document.write( "bo = [(E(y)(E(x^2)-(E(x))(E(xy))] / [nE(x^2) )- (E(x))^2]<BR>\n" );
document.write( "bo = [95.3*93.205-965*9165.1] / [10*93.205-965^2]<BR>\n" );
document.write( "bo = [-8835439.064] / [-30292.95] = 9.49748...<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "b1 = [nE(xy) -E(x)*E(y)] / [nE(x^2) - (Ex)^2]<BR>\n" );
document.write( "b1 = [10*9165.1 - 965*95.3] / [ 10*93.205 - 965^2]<BR>\n" );
document.write( "b1 = [-313.5] / [ -930292.95]<BR>\n" );
document.write( "b1 = 0.00033699<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "y-hat = 9.49748 + 0.00033699 x<BR>\n" );
document.write( "----------------------------------<BR>\n" );
document.write( "b. If the trend continues, how many banks will there be in<BR>\n" );
document.write( "2004?<BR>\n" );
document.write( "From 1900 to 2004 is 104 years<BR>\n" );
document.write( "Letting x = 104 you get:<BR>\n" );
document.write( "# of banks in 2004 = 9.49748 + 0.0033699(104) = 9.84 thousand banks<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "===============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );