document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164939>Question 1164939</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The normality assumption implies that:a. the population error u is dependent on the explanatory variables and is normally distributed with mean equal to one and variance 2b. the population error u is independent of the explanatory variables and is normally distributed with mean equal to one and variance c. the population error u is dependent on the explanatory variables and is normally distributed with mean zero and variance d. the population error u is independent of the explanatory variables and is normally distributed with mean zero and variance 2.<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 #853501 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(2189)</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=853501\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Based on the standard Gauss-Markov assumptions for classical linear regression models, the correct answer is **d**.\r<BR>\n" );
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document.write( "The **normality assumption** specifically states that the population error term () is **independent** of the explanatory variables () and is **normally distributed** with a mean of **zero** and a constant variance ().\r<BR>\n" );
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document.write( "### Breakdown of the Assumption:\r<BR>\n" );
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document.write( "* **Independence:** The error term  must not be related to the explanatory variables. If they were dependent, the estimates for your coefficients would be biased.<BR>\n" );
document.write( "* **Mean Zero ():** We assume that, on average, the errors cancel each other out. Any non-zero mean is typically absorbed into the intercept () of the model.<BR>\n" );
document.write( "* **Constant Variance ():** Also known as homoscedasticity, this implies the \"spread\" of the errors remains constant across all levels of the explanatory variables.<BR>\n" );
document.write( "* **Normal Distribution:** This allows us to conduct hypothesis tests (like t-tests and F-tests) because it ensures that the sampling distributions of our estimators are also normal.\r<BR>\n" );
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document.write( "### Why the other options are incorrect:\r<BR>\n" );
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document.write( "* **a & c:** The error term cannot be dependent on the explanatory variables; this violates the assumption of exogeneity.<BR>\n" );
document.write( "* **a & b:** The mean of the error term must be **zero**, not one. If the mean were one, the model would systematically over-predict or under-predict the dependent variable.\r<BR>\n" );
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document.write( "Would you like me to explain how violating this assumption affects the reliability of your p-values? </SPAN>\n" );
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