Linear regression and varience.

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SUMMARY

This discussion focuses on calculating variance in the context of linear regression after determining the coefficients \(\widehat{a}\) and \(\widehat{b}\) for the line of best fit. The user is attempting to apply the variance formula \(\frac{\sum(y-\widehat{y})^2}{n-2}\) but encounters issues with LaTeX formatting. The key takeaway is that variance is calculated by summing the squared differences between actual and predicted values, divided by the degrees of freedom (n-2).

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  • Understanding of linear regression concepts, including coefficients \(\widehat{a}\) and \(\widehat{b}\)
  • Familiarity with variance calculation in statistics
  • Basic knowledge of LaTeX for formatting mathematical equations
  • Experience with data sets and their analysis
NEXT STEPS
  • Research the derivation and application of the variance formula in linear regression
  • Learn advanced LaTeX formatting techniques for mathematical expressions
  • Explore statistical software tools like R or Python's NumPy for regression analysis
  • Study the implications of degrees of freedom in statistical calculations
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Data analysts, statisticians, and students studying linear regression and variance calculations, as well as anyone interested in improving their LaTeX skills for mathematical documentation.

matthyaouw
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Im having some trouble with this, and I was hoping someone could help me.
I have a data set from which I've determined the [tex]\widehat{a}[/tex] and [tex]\widehat{b}[/tex] values and determined where the line of best fit should go using linear regression. The next thing I have to do is work out the varience using this equation:

[tex]\underline{\sum(y-\widehat{y})^2}<br /> \\n-2[/tex]
(edit) Sorry, first time using latex, and I can't access the tutorials for some reason.
I've typed :
"\underline{\sum(y-\widehat{y})^2}
\\n-2"
But I'm not getting a new line after ^2}. How do I do this? (/edit)

I'm a bit unsure what to do here. Does that mean that I have to sum up all of my y values, and take away the expected y values that are predicted on my line of best fit which correspond to the actual values I've entered?
 
Last edited:
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Never mind, got it (I think). If someone could still tell me what I'm doing wrong with the Latex I'd appreciate it though.
 

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