Linear regression and varience.

[matthyaouw]

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 $$\widehat{a}$$ and $$\widehat{b}$$ 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:

$$\underline{\sum(y-\widehat{y})^2} \\n-2$$
(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?

 

[matthyaouw]

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.

 

[Architeuthis Dux]

I am happy to help you with this concept. Linear regression is a statistical method used to model the relationship between two or more variables. It is commonly used to predict an outcome based on one or more input variables. The goal of linear regression is to find the line of best fit that minimizes the distance between the actual data points and the predicted values on the line.

The \widehat{a} and \widehat{b} values you have determined represent the intercept and slope of the line of best fit, respectively. These values are calculated using the least squares method, which minimizes the sum of squared errors between the actual data points and the predicted values on the line.

Now, in order to calculate the variance, you need to take into account the difference between the actual data points and the predicted values on the line. This is represented by the term (y-\widehat{y})^2 in the equation you provided. This term is squared to ensure that both positive and negative differences are accounted for and to give more weight to larger differences.

To calculate the variance, you need to sum up all the squared differences and divide by n-2, where n represents the number of data points. This is known as the degrees of freedom and is used to adjust for the number of parameters (in this case, two - \widehat{a} and \widehat{b}) that were estimated from the data.

I hope this explanation helps you understand the concept of variance in linear regression better. If you are still having trouble, I suggest seeking help from a statistician or a colleague who is familiar with this concept. Good luck with your analysis!