Linked Questions

2
votes
1answer
3k views

What is the difference between linear regression and polynomial regression? [duplicate]

I'm currently experimenting with different regression techniques on this data set that I have, and I some sources state a method called "polynomial regression". I looked it up and I can't really find ...
0
votes
0answers
64 views

Must the graph of a linear model always be a straight line of the form $y=mx+b$? [duplicate]

Must the graph of a linear model always be a straight line of the form $y=mx+b$? I think that yes, but am checking, whether there might be some exceptions.
2
votes
0answers
57 views

Is a model including a square root of a variable linear in the parameters? [duplicate]

Is the model $$ y = \gamma_0 + \gamma_1 + \sqrt x + \varepsilon $$ linear in parameters? ( $\varepsilon$ is the error term.)
0
votes
1answer
43 views

Regression: Why does using quadratic expressions work with linear estimators? [duplicate]

My questions is, that I see people using R´s lm() (linear regression model) with Y ~ X^2 e.g. here: Simple non-linear regression problem But I dont see how and ...
0
votes
0answers
30 views

how to get polynomial equation for given data in regression analysis? [duplicate]

I have following data and I want apply regression analysis for this data.Based on the data I want derive equation of 2nd or 3rd or 4th order polynomial equation. How can I do that by using math ...
11
votes
4answers
13k views

What does “curvilinear” mean?

As far as I can tell, curvilinear is defined vaguely but means the same as nonlinear. Is that correct? Or does curvilinear have a distinct definition?
6
votes
3answers
2k views

How to interpret coefficients of $x$ and $x^2$ in same regression

If I have the below functional form for an OLS regression, how do I interpret the $x$ and $x^2$? I cannot interpret them separately, correct? Do I interpret them as a summation of the two coefficients,...
8
votes
1answer
12k views

R squared and higher order polynomial regression

The plot below shows the saturation of a road against the impact on journey time (normalized to free flow journey time). The blue (BPR function) curve presents a standardized model used in the field ...
6
votes
2answers
823 views

What can't be expressed as a linear model?

Say I have outcome variable $Y_i$ and predictors $X_{i1}$ and $X_{i2}$ for some data point $i$. Wikipedia says that a model is linear when: the mean of the response variable is a linear combination ...
6
votes
1answer
7k views

Is the decision boundary of a logistic classifier linear?

I'm still a bit confused about the question is the decision boundary of a logistic classifier linear? I followed Andrew Ng's machine learning course on Coursera, and he mentioned the following: It ...
4
votes
3answers
346 views

Linear regression explanations

In explaining simple linear regression, isn't it a bit misleading for many examples to illustrate a straight line going through some scatterplot? This seems to suggest that linear regression only ...
5
votes
1answer
1k views

When is it better to use Multiple Linear Regression instead of Polynomial Regression?

In the course I've just learnt Multiple Linear Regression and Polynomial Regression. Why would you ever use Multiple Linear Regression when Polynomial Regression will always fit the data better?
1
vote
2answers
951 views

How does one perform multiple non-linear regression?

I performed an experiment where I took the heights of plants and measured a number of environmental conditions (air temp, soil temp, lux, air humidity, soil pH, wind) for each of those plants. I want ...
24
votes
1answer
402 views

What is the probability that $n$ random points in $d$ dimensions are linearly separable?

Given $n$ data points, each with $d$ features, $n/2$ are labeled as $0$, the other $n/2$ are labeled as $1$. Each feature takes a value from $[0,1]$ randomly (uniform distribution). What's the ...
1
vote
1answer
1k views

Adding a quadratic term flips the signs of the coefficients

So I have a question of utilizing quadratic (second order) predictors with GLMs in R. Basically I have three predictor variables $(x, y, z)$ and a response variable (let's call it ozone). $x$, $y$, ...

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