Questions tagged [linear]

For statistical topics which involve the assumption of linearity, for example, linear regression or linear mixed models, or for the discussion of linear algebra as applied to statistics.

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How to show $\rho(\beta_0, \beta_1) \leq 0$ when $x_i \geq 0$?

Consider a simple linear regression modelled by $Y_i = \beta_0 + \beta_1x_i + \epsilon_i$ where each $\epsilon_i$ is independent and follows a normal distribution with mean $0$ and variance $\sigma^2$....
37 views

Determining if linear regression is appropriate

I am designing an experiment, and I want to know if using a hypothesis test on the linear regression model to analyze my data is appropriate. The experiment will have five independent variable values ...
52 views

Linear model with both additive and multiplicative effects

In linear regression, the independent variables have an additive effect on the response (level-level regression): $y=\beta_0+\beta_1x+\epsilon$ In a log-level regression, the independent variables ...
23 views

Multiple linear regression approach: difference in set-up and dataset split

Firstly, I am new to modelling linear regression models. I want to build a linear regression model to predict building energy use based on building parameters. I'm having a dataset of 100000 buildings ...
135 views

Linear and Nonlinear Components of a Time Series

I am starting to develop a hybrid ARIMA-ANN model for forecasting. Most of the journals I read mention mostly a linear component for ARIMA and a nonlinear for ANN. How can you know which components ...
46 views

Why is $Y=\beta_0 x^{\beta_1} e$ a linear model?

Why is $Y=\beta_0 x^{\beta_1} e$ a linear model? When we apply the transform, it becomes $lnY = ln\beta_0+\beta_1 lnx +lne$, and why is it still linear when the $\beta_0$ part is under ln?
27 views