Questions tagged [linear-model]

Refers to any model where a random variable is related to one or more random variables by a function that is linear in a finite number of parameters.

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What is the difference between linear regression and logistic regression?

What is the difference between linear regression and logistic regression? When would you use each?
107k views

When is it ok to remove the intercept in a linear regression model?

I am running linear regression models and wondering what the conditions are for removing the intercept term. In comparing results from two different regressions where one has the intercept and the ...
47k views

Removal of statistically significant intercept term increases $R^2$ in linear model

In a simple linear model with a single explanatory variable, $\alpha_i = \beta_0 + \beta_1 \delta_i + \epsilon_i$ I find that removing the intercept term improves the fit greatly (value of $R^2$ ...
173k views

What is the difference between linear regression on y with x and x with y?

The Pearson correlation coefficient of x and y is the same, whether you compute pearson(x, y) or pearson(y, x). This suggests that doing a linear regression of y given x or x given y should be the ...
106k views

PCA and proportion of variance explained

In general, what is meant by saying that the fraction $x$ of the variance in an analysis like PCA is explained by the first principal component? Can someone explain this intuitively but also give a ...
25k 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 ...
32k views

Choosing between LM and GLM for a log-transformed response variable

I'm trying to understand the philosophy behind using a Generalized Linear Model (GLM) vs a Linear Model (LM). I've created an example data set below where: $$\log(y) = x + \varepsilon$$ The ...