# MLE and Regression. Insights

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Hiya!

I wanted to know if anyone knows any sites for understanding regression (multiple and simple). I'm finding it all very confusing. I have a book by Hogg & Tanis, but am still a little confused by Regression and MLE, as well as ANOVA. That whole side of statistics is rather confusing for me.

Also, I don't understand how:

1) The arithmetic mean is the MLE of the unknown mean/mew of the normal pdf. How do I prove that or is there proof of that anywhere?

2) And why the arithmetic mean could be a sufficient statistic for the unknown mean and nor do I understand how it's distribution could be that of X(bar)~N(mew, sigma squared/n). Also, if i'm not mistaken, the pdf could be used to show that the arithmetic mean is the MLE of unknown mew, but is there a proof of that? If not, could someone show me how that could be the case?

I have an exam at the beginning of June, so need to get the understanding in there pretty quickly. Also! Hypothesis testing has me confused and how that fits in to all this regression stuff.

I wanted to know if anyone knows any sites for understanding regression (multiple and simple). I'm finding it all very confusing. I have a book by Hogg & Tanis, but am still a little confused by Regression and MLE, as well as ANOVA. That whole side of statistics is rather confusing for me.

Also, I don't understand how:

1) The arithmetic mean is the MLE of the unknown mean/mew of the normal pdf. How do I prove that or is there proof of that anywhere?

2) And why the arithmetic mean could be a sufficient statistic for the unknown mean and nor do I understand how it's distribution could be that of X(bar)~N(mew, sigma squared/n). Also, if i'm not mistaken, the pdf could be used to show that the arithmetic mean is the MLE of unknown mew, but is there a proof of that? If not, could someone show me how that could be the case?

I have an exam at the beginning of June, so need to get the understanding in there pretty quickly. Also! Hypothesis testing has me confused and how that fits in to all this regression stuff.

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#2

Hi there,

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While you're waiting for an answer, did you know we have 300,000 study resources that could answer your question in TSR's Learn together section?

We have everything from Teacher Marked Essays to Mindmaps and Quizzes to help you with your work. Take a look around.

If you're stuck on how to get started, try creating some resources. It's free to do and can help breakdown tough topics into manageable chunks. Get creating now.

Thanks!

Not sure what all of this is about? Head here to find out more.

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#3

(Original post by

1) The arithmetic mean is the MLE of the unknown mean/mu of the normal pdf. How do I prove that or is there proof of that anywhere?

2) And why the arithmetic mean could be a sufficient statistic for the unknown mean and nor do I understand how it's distribution could be that of X(bar)~N(mu, sigma squared/n). Also, if i'm not mistaken, the pdf could be used to show that the arithmetic mean is the MLE of unknown mu, but is there a proof of that? If not, could someone show me how that could be the case?

**Minni04**)1) The arithmetic mean is the MLE of the unknown mean/mu of the normal pdf. How do I prove that or is there proof of that anywhere?

2) And why the arithmetic mean could be a sufficient statistic for the unknown mean and nor do I understand how it's distribution could be that of X(bar)~N(mu, sigma squared/n). Also, if i'm not mistaken, the pdf could be used to show that the arithmetic mean is the MLE of unknown mu, but is there a proof of that? If not, could someone show me how that could be the case?

Yes. Have you found the MLE of the unknown mean? (by finding the likelihood or log-likelihood, and differentiating to maximise it - this is how the PDF can be used to show that the arithmetic mean is the MLE of unknown mu)

A statistic is sufficient if the PDF factorises into a term with the statistic, and a term without. What is the PDF?

Do you know how to find the distribution of the sum of normal random variables, and how to find the distribution of 1/n times that sum?

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(Original post by

It took me a moment to realise that by "mew" you meant "mu"… it distracted me so much that I amended it in my quotation of you.

Yes. Have you found the MLE of the unknown mean? (by finding the likelihood or log-likelihood, and differentiating to maximise it - this is how the PDF can be used to show that the arithmetic mean is the MLE of unknown mu)

A statistic is sufficient if the PDF factorises into a term with the statistic, and a term without. What is the PDF?

Do you know how to find the distribution of the sum of normal random variables, and how to find the distribution of 1/n times that sum?

**Smaug123**)It took me a moment to realise that by "mew" you meant "mu"… it distracted me so much that I amended it in my quotation of you.

Yes. Have you found the MLE of the unknown mean? (by finding the likelihood or log-likelihood, and differentiating to maximise it - this is how the PDF can be used to show that the arithmetic mean is the MLE of unknown mu)

A statistic is sufficient if the PDF factorises into a term with the statistic, and a term without. What is the PDF?

Do you know how to find the distribution of the sum of normal random variables, and how to find the distribution of 1/n times that sum?

I've managed to find out the MLE of the unknown mean.. At least I think I did. It follows a normal distribution.

Could you just explain the log part again please? How would i find the log likelihood function?

Is the factorization theorem needed for the sufficient statistic then?

"Do you know how to find the distribution of the sum of normal random variables, and how to find the distribution of 1/n times that sum" Unfortunately no, I don't

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#5

(Original post by

I've managed to find out the MLE of the unknown mean.. At least I think I did. It follows a normal distribution.

**Minni04**)I've managed to find out the MLE of the unknown mean.. At least I think I did. It follows a normal distribution.

Could you just explain the log part again please? How would i find the log likelihood function?

Is the factorization theorem needed for the sufficient statistic then?

"Do you know how to find the distribution of the sum of normal random variables, and how to find the distribution of 1/n times that sum" Unfortunately no, I don't

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