document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1163400>Question 1163400</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For a sample of 29 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents) as a function of its poverty rate (in %) and its median income (in $1,000s). He finds that SSE = 4,136,781 and SST = 7,662,937.\r<BR>\n" );
document.write( "\n" );
document.write( "Calculate the standard error of the estimate.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #854379 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(2264)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=854379\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To calculate the standard error of the estimate ($S_e$) for a multiple regression model, we use the sum of squared errors ($SSE$) and the degrees of freedom associated with the error.\r<BR>\n" );
document.write( "\n" );
document.write( "### 1. Identify the Given Information<BR>\n" );
document.write( "* **Sample size ($n$):** $29$<BR>\n" );
document.write( "* **Number of independent variables ($k$):** $2$ (Poverty rate and Median income)<BR>\n" );
document.write( "* **Sum of Squared Errors ($SSE$):** $4,136,781$<BR>\n" );
document.write( "* **Total Sum of Squares ($SST$):** $7,662,937$ (Note: $SST$ is not required for this specific calculation)\r<BR>\n" );
document.write( "\n" );
document.write( "### 2. The Formula<BR>\n" );
document.write( "The standard error of the estimate is the square root of the mean square error ($MSE$):<BR>\n" );
document.write( "$$S_e = \sqrt{\frac{SSE}{n - k - 1}}$$\r<BR>\n" );
document.write( "\n" );
document.write( "Where:<BR>\n" );
document.write( "* $n - k - 1$ represents the degrees of freedom for the error ($df_E$).\r<BR>\n" );
document.write( "\n" );
document.write( "### 3. Calculation<BR>\n" );
document.write( "**Step 1: Calculate the degrees of freedom ($df_E$)**<BR>\n" );
document.write( "$$df_E = 29 - 2 - 1 = 26$$\r<BR>\n" );
document.write( "\n" );
document.write( "**Step 2: Calculate the Mean Square Error ($MSE$)**<BR>\n" );
document.write( "$$MSE = \frac{4,136,781}{26} \approx 159,106.9615$$\r<BR>\n" );
document.write( "\n" );
document.write( "**Step 3: Calculate the square root**<BR>\n" );
document.write( "$$S_e = \sqrt{159,106.9615} \approx 398.8821$$\r<BR>\n" );
document.write( "\n" );
document.write( "### Final Answer<BR>\n" );
document.write( "The standard error of the estimate is approximately **$398.88$**. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );