6
Check out these threads:
How to tell the difference between linear and non-linear regression models?
Why must linear regressions only generate linear functions that resemble "lines or planes" (*Introduction to Statistical Learning* question)?
"Linear" is talking about the calculation that happens to the unknown coefficients $\beta$. Any ...
2
Let me know if it helps to have graphs of this, but I think the following should be enough to 'visualize' this observation:
Suppose that the variance of $X$ is $\sigma^2 = 1$. Then your equation says that
$$SE(\hat{\beta})^2 = \frac{1}{\sum_{i=1}^n(x_i - \bar{x})^2}$$
Just studying the function $f(t) = 1/t$ for $t$ positive, we can see that if $t < t'$, ...
2
I believe that in the case of linear programming the quantity you are min/maximising is linearly linked with your parameters (decision variables). In linear regression, you are looking for the vector $\beta$ that minimises the squared error: $y^Ty-2\beta^TX^Ty+\beta^TX^TX\beta$ (obviously $\beta$ is not linearly related to it).
Moreover, in case of linear ...
1
I think that the problem is with point 4. The regression is not between $s$ and $p$, but $a$ and $r$, possibly weighted by $s$. In other words, imagine you have short and long races and a horse that likes short races. If today's race is long, it will have a negative residual and a positive residual if today's race is short. The term "residual" of ...
1
In general p-values are not equal to zero, but are just very very tiny, so statistical software tends to report 0 or 0.000 instead of a number like 0.0000000000183 (i.e tend to report such like so: "p <0.001").
Given that your sample size in the in thousands, and that in your specific case you have (fixed effect) coefficients with t test ...
1
You seem to describe a case of linear programming where there is uncertainty in the objective function (and you could generalize this and have uncertainty in the linear boundaries as well).
Could I use my regression as a simulation (aka surrogate model) and find the optimal combination of a the variables this way via linear programming?
No.
Doing this ...
1
I finally found an answer to this in my class notes. The objective function in a linear program can be derived from other analytic models, which includes linear regression, as long as you can identify constraints to demarcate the feasible solution space.
Note that, it seems that everyone who tried to answer this question got it confused with a related, but ...
1
Least squares regression doesn't have a linear objective function, as the name suggests. However, Linear Programming is the standard way to solve Least Absolute Deviation, or more generally, quantile regression problems. The difference is that least squares gives you a forecast of the conditional mean of the response variable, given the data, while LAD/...
1
Could this be because in the language column "Arabic", there isn't any
recorded instance of /v/ so there's a missing segment?
Yes, that would explain it. The interaction parameter is allowing the mean for /v/ in Arabic to be different from what you'd expect based on /v/ vs/f/ generally and on Arabic vs English generally. You don't have any data ...
1
Since your dependent variable is dichotomous, you should do logistic regression. This is what it is designed for.
You don't say what your DV is, but let's suppose it's lived/died. If you treat this as numeric (somehow) then you are saying that there is a continuum between living and dead and also states beyond living and dead. Suppose you make living = 1 ...
1
There seem to be two things going on here.
First, with large data sets normality tests tend to fail. Real data seldom have exactly normal distributions. This page goes into extensive discussion. That doesn't mean normality tests are unimportant, but they have to be interpreted in terms of whether the deviations from normality are sufficiently large to ...
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