SIMPLE LINEAR REGRESSION DERIVATION: THE SLOPE AND INTERCEPT IN 2 WAYS THE LEAST SQUARES CRITERION

SIMPLE LINEAR REGRESSION DERIVATION OF THE SLOPE AND INTERCEPT IN 2 WAYS. THE LEAST SQUARES CRITERION

[drpszn]

Why before you, professors always seem to misinform students on this key step? Iv'e always had trouble with this and your explanation is right on the money. Thank you!

[paritisutaria]

At 4:16, is the calculus approach to find the minimum the only way to find the value? And to show that value(s) is the minimum indeed, why is that often skipped?

[paritisutaria]

Relating this back to our class material on evaluating alternative methods, this method uses MSE (mean squared error) starting off the calculus approach. Can MAD (mean absolute deviation) criterion fit into this simple linear regression analysis? If so, how and what would that method look like?

[alecfisher]

In the means of X and Y for the simple linear regression, as shown in the pre-calculus approach, is this working for the multivariate linear regression as well?

[alecfisher]

When figuring the betas (the coefficient) is there any significant difference in between the variable Y as being a DV and X as being an IV? Or is their weight in determining the coefficient somewhat balanced?

[evanwalker]

21:17 Is it okay to leave beta 0 written as just beta? Or does writing the 0 make it a different variable like how an exponent of 1 is understood to be on the numbers we write, even if we don't write the exponent?
(This is Evan Walker from your Intro to Statistics 2 class)

[marc-steeveslouis-baptiste]

how did the formula ordinary least squares linear regression arrived at?

[kingdevin]

Is it true that the accuracy of each predicted value is measured by its squared residual vertical distance between the point of the data set and the fitted line?

[ANNAARCHUT-vk]

How does this compare with the derivation of the slope and intercept of a nonlinear regression line? Would you have to use partial derivatives to find an answer in the calculus approach?

[jonathandomenech]

Professor,

What if the data set is irregular in terms of negative value or extremely high outlier variables? Would these methods have a limitation on them in a certain situation. For example, in a regression with a very low correlation value would you use the least square method still?

[markweber]

The pre-calculus method was a lot easier for me! Just curious how this is used practically? Is it to compare how two things correlate?

[poisedjoy]

Professor, what is the best way to determine if you should use a linear least-squares method vs. a non-linear least squares method?

[ANNAARCHUT-vk]

You mentioned that y and x are not variables, but rather given values. Would plugging in those values make the derivation easier in either the precalculus or calculus approach or would it complicate it? I assume fewer variables would cause there to be smaller room for error and would still lead to the same answers.

[geoffcolella]

Why is that small part always skipped? Is it not necessary ?

[billyvance]

Hello Professor, I just have a question for the Least Squares Method. When it comes to the dataset that would be provided to us, would there ever be something we could spot or us to figure out whether the Pre Calculus Method or the Calculus Method would work better? Is it just based on personal preference?

[poisedjoy]

Hello Professor, Is it true that the best way to validate your model is to check the residual plot?

[melindatorres]

Can we use simple linear regression for time series analysis?

[alecfisher]

Are both approaches (calculus and pre-calculus approaches) applicable in the same manner for multivariate regression as well? Or just for simple linear regression?