# Questions tagged [regression]

Techniques for analyzing the relationship between one (or more) "dependent" variables and "independent" variables.

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### Why does the Lasso provide Variable Selection?

I've been reading Elements of Statistical Learning, and I would like to know why the Lasso provides variable selection and ridge regression doesn't. Both methods minimize the residual sum of squares ...
10answers
273k views

### What's the difference between correlation and simple linear regression?

In particular, I am referring to the Pearson product-moment correlation coefficient.
5answers
98k views

### What does a “closed-form solution” mean?

I have come across the term "closed-form solution" quite often. What does a closed-form solution mean? How does one determine if a close-form solution exists for a given problem? Searching online, I ...
3answers
97k views

### Does an unbalanced sample matter when doing logistic regression?

Okay, so I think I have a decent enough sample, taking into account the 20:1 rule of thumb: a fairly large sample (N=374) for a total of 7 candidate predictor variables. My problem is the following: ...
7answers
59k views

### Why use gradient descent for linear regression, when a closed-form math solution is available?

I am taking the Machine Learning courses online and learnt about Gradient Descent for calculating the optimal values in the hypothesis. h(x) = B0 + B1X why we ...
18answers
84k views

### Including the interaction but not the main effects in a model

Is it ever valid to include a two-way interaction in a model without including the main effects? What if your hypothesis is only about the interaction, do you still need to include the main effects?
9answers
41k views

### Is there an intuitive explanation why multicollinearity is a problem in linear regression?

The wiki discusses the problems that arise when multicollinearity is an issue in linear regression. The basic problem is multicollinearity results in unstable parameter estimates which makes it very ...
1answer
79k views

### Interpreting plot.lm()

I had a question about interpreting the graphs generated by plot(lm) in R. I was wondering if you guys could tell me how to interpret the scale-location and leverage-residual plots? Any comments ...
8answers
38k views

### What is the benefit of breaking up a continuous predictor variable?

I'm wondering what the value is in taking a continuous predictor variable and breaking it up (e.g., into quintiles), before using it in a model. It seems to me that by binning the variable we lose ...
5answers
14k views

### Why is ANOVA taught / used as if it is a different research methodology compared to linear regression?

ANOVA is equivalent to linear regression with the use of suitable dummy variables. The conclusions remain the same irrespective of whether you use ANOVA or linear regression. In light of their ...
5answers
132k views

### How to calculate Area Under the Curve (AUC), or the c-statistic, by hand

I am interested in calculating area under the curve (AUC), or the c-statistic, by hand for a binary logistic regression model. For example, in the validation dataset, I have the true value for the ...
4answers
30k views

### Why isn't Logistic Regression called Logistic Classification?

Since Logistic Regression is a statistical classification model dealing with categorical dependent variables, why isn't it called Logistic Classification? Shouldn't the "Regression" name be reserved ...
2answers
41k views

### When to use regularization methods for regression?

In what circumstances should one consider using regularization methods (ridge, lasso or least angles regression) instead of OLS? In case this helps steer the discussion, my main interest is improving ...
2answers
59k views

### Solving for regression parameters in closed-form vs gradient descent

In Andrew Ng's machine learning course, he introduces linear regression and logistic regression, and shows how to fit the model parameters using gradient descent and Newton's method. I know gradient ...
3answers
84k views

### What is the lasso in regression analysis?

I'm looking for a non-technical definition of the lasso and what it is used for.
8answers
15k views

### Line of best fit does not look like a good fit. Why?

Have a look at this Excel graph: The 'common sense' line-of-best-fit would appear be an almost vertical line straight through the center of the points (edited by hand in red). However the linear ...
4answers
230k views

### How does the correlation coefficient differ from regression slope?

I would have expected the correlation coefficient to be the same as a regression slope (beta), however having just compared the two, they are different. How do they differ - what different information ...
5answers
21k views

### What are modern, easily used alternatives to stepwise regression?

I have a dataset with around 30 independent variables and would like to construct a generalized linear model (GLM) to explore the relationship between them and the dependent variable. I am aware that ...
10answers
38k views

### What is a complete list of the usual assumptions for linear regression?

What are the usual assumptions for linear regression? Do they include: a linear relationship between the independent and dependent variable independent errors normal distribution of errors ...
7answers
83k views

### Is it necessary to scale the target value in addition to scaling features for regression analysis?

I'm building regression models. As a preprocessing step, I scale my feature values to have mean 0 and standard deviation 1. Is it necessary to normalize the target values also?
10answers
172k views

### How should outliers be dealt with in linear regression analysis?

Often times a statistical analyst is handed a set dataset and asked to fit a model using a technique such as linear regression. Very frequently the dataset is accompanied with a disclaimer similar to ...
9answers
62k views

### Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests?

In a multiple linear regression, why is it possible to have a highly significant F statistic (p<.001) but have very high p-values on all the regressor's t tests? In my model, there are 10 ...
6answers
25k views

### Principled way of collapsing categorical variables with many levels?

What techniques are available for collapsing (or pooling) many categories to a few, for the purpose of using them as an input (predictor) in a statistical model? Consider a variable like college ...
0answers
64k views

### How can a regression be significant yet all predictors be non-significant? [duplicate]

My multiple regression analysis model has a statistically significant F value however all beta values are statistically non-significant. All the regression assumptions are met. No multicollinearity ...
1answer
86k views

### What correlation makes a matrix singular and what are implications of singularity or near-singularity?

I am doing some calculations on different matrices (mainly in logistic regression) and I commonly get the error "Matrix is singular", where I have to go back and remove the correlated variables. My ...
4answers
25k views

### How to visualize what canonical correlation analysis does (in comparison to what principal component analysis does)?

Canonical correlation analysis (CCA) is a technique related to principal component analysis (PCA). While it is easy to teach PCA or linear regression using a scatter plot (see a few thousand examples ...
6answers
45k views

### Why is the L2 regularization equivalent to Gaussian prior?

I keep reading this and intuitively I can see this but how does one go from L2 regularization to saying that this is a Gaussian Prior analytically? Same goes for saying L1 is equivalent to a Laplacean ...
5answers
140k views

### Explain the difference between multiple regression and multivariate regression, with minimal use of symbols/math

Are multiple and multivariate regression really different? What is a variate anyways?
10answers
64k views

### What is wrong with extrapolation?

I remember sitting in stats courses as an undergrad hearing about why extrapolation was a bad idea. Furthermore, there are a variety of sources online which comment on this. There's also a mention of ...
2answers
35k views

### Shape of confidence interval for predicted values in linear regression

I have noticed that the confidence interval for predicted values in an linear regression tends to be narrow around the mean of the predictor and fat around the minimum and maximum values of the ...