569 views

Confusion regarding “regression by successive orthogonalization” [duplicate]

In trying to answer a question here on Cross Validated, I was re-reading Section 3.2.3, specifically Algorithm 3.1 from Elements of Statistical Learning. What I followed from this is that, given a ...
267 views

Regression anatomy: can a multivariate model with K independent variables be broken down into K bivariate models? [duplicate]

Valerio Filoso (2013) writes: Most econometrics textbooks limit themselves to providing the formula for the $\beta$ vector of the type $$\beta = (X′X)^{-1} X'Y.$$ Although compact and ...
136 views

Hierarchical and sequential regression [duplicate]

I performed a hierarchical multiple regression to study the effect of different variables, above and beyond the apriori selected more important variables. The R script used to perform this regression ...
60 views

Can we solve multiple linear regression using simple linear regression solver? [duplicate]

Suppose I have a blackbox function that solves simple linear regression. Can I use this function to solve "multiple" linear regression? The blackbox computes the slope and intercept in a simple ...
19 views

How to obtain regression coefficients of a multiple linear regression model from simple linear regression models? [duplicate]

Suppose I have a multiple linear regression model $$Y=\beta_0+\beta_1X_1+\cdots+\beta_pX_p+\epsilon$$ How can I obtain the regression coefficients $\hat{\beta_i}$ by fitting just a series of simple ...
5 views

Partailling out approach in multiple linear regression [duplicate]

Assume I run the following regression: $$sales = \beta_{0} + \beta_{1} price + \beta_{2}advert + \beta_{3}advert^2$$ Now I regress sales, price, and advertising separately on advertising_squared ...
73k views

How to derive the least square estimator for multiple linear regression?

In the simple linear regression case $y=\beta_0+\beta_1x$, you can derive the least square estimator $\hat\beta_1=\frac{\sum(x_i-\bar x)(y_i-\bar y)}{\sum(x_i-\bar x)^2}$ such that you don't have to ...
13k views

Line graph has too many lines, is there a better solution?

I'm trying to graph the number of actions by users (in this case, "likes") over time. So I have "Number of actions" as my y-axis, my x-axis is time (weeks), and each line represents one user. My ...
45k views

How to make a time series stationary?

Besides taking differences, what are other techniques for making a non-stationary time series, stationary? Ordinarily one refers to a series as "integrated of order p" if it can be made stationary ...
7k views

Utility of the Frisch-Waugh theorem

I am supposed to teach the Frish Waugh theorem in econometrics, which I have not studied. I have understood the maths behind it and I hope the idea too "the coefficient you get for a particular ...
20k views

Getting a second-order polynomial trend line from a set of data

Alright, so I have about a thousand datapoints that I'm plotting on a chart (scatter plot). Here's a few of the records: ...
2k views

How to understand the correlation coefficient formula?

Can anyone help me understand the Pearson correlation formula? the sample $r$ = the mean of the products of the standard scores of variables $X$ and $Y$. I kind of understand why they need to ...
820 views

How can multiple regression be performed as a sequence of univariate regressions?

Let's say $x$ is correlated to both $y_1$, and $y_2$. Why are the residuals of the nested regression of $x$ against $y_1$ and $y_2$, not equal to the residuals of the simultaneous (multiple) ...