# 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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### Help factoring matrices out of cross-covariance

I am trying to prove that $\text{Cov}( \boldsymbol{BU}, \boldsymbol B' \boldsymbol W) = \boldsymbol B \text{Cov}(\boldsymbol U, \boldsymbol W) \boldsymbol B'^T$, where $\boldsymbol B$ is $j \times m$...
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### Simple Linear Regression Question Confusion

By using this site I found the two linear regression models that the question asked. The equations came out to be: $$US=60.495+18.550x$$ $$China =-2.08+18.296x$$ A follow-up question asked me to find &...
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### The shape of line differs fom information coming from linear regression? [closed]

The line which represents linear regression (Using scikit-learn library) is totally different from the information that you can get from the library, e.g. ...
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### Effect of increaing number of features on support vector regression with a linear kernel

I am trying to train and optimize a linear kernel support vector regression while analyzing the effect of increasing the number of features used to train the model on the model performance. The number ...
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### How to find regression coefficient from summary table [duplicate]

I'm practicing for an exam ,and I wonder how could I solve this type of questions. Find hgb estimate or this question: Find Sum of squares regression (SSreg)
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### the linear association was different when selecting 3 knots compared to 4 knots in restricted cubic spline based on cox regression model

I applied the restricted cubic spline term of BMI/weight in cox regression to test the linear association between BMI/weight with the outcome. However, the P-value of linear association tested by ...
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### Eigenvalues in PCA [duplicate]

When I carry out Principal Component Analysis, the outputs are the Eigen-values and Eigen-vectors for each PC. Question: are the Eigen-values directly proportional to the Variance explained by the PC? ...
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### The correct tool for testing statistically likely source of endpoint?

Background Whilst I have some experience in statistics, I am not trained in the field and so am at somewhat of a loss with respect to what tool I should employ in the following scenario. I have a ...
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### Residuals in LME models

Good morning everyone! I have implemented the following lme model in r: ...
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### Linear Transformation of a Random Variable with a Laplace Distribution

I have read these two posts ( 1 and 2) about linear transformation of a random variable with a Gaussian distribution. I would like to find the first two moments of a linearly transformed Laplace ...
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### Calculate regression confidence and prediction intervals from the standard errors of the fitted parameters AND the correlation coefficient

In many fields of the natural sciences, it is common practice to report the results of regression analysis as y = a1 + a2 * x. Bad luck, no uncertainties are ...
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### For linear regression, if the theoretical coefficients and the variance of the error is known, is the theoretical R squared value, F statistic known?

For linear regression, suppose we know the true, theoretical coefficients of the predictors (say, for a simulation) and the standard deviation of the error term (sigma). For instance, suppose we know ...
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### How to determine by what percent the target variable will change if we change a variable by some percent in Linear Regression?

I trained a linear regression model on some data. Now I have the intercept and the other coefficients. How to relate that with percent change in target given some percent change in a feature, keeping ...
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### correlation and simple linear regression [duplicate]

what this sentence means"The correlation squared (r2 or R2) has special meaning in simple linear regression. It represents the proportion of variation in Y explained by X".
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### Interpreting log multiple linear regression, backtransformations?

I'm investigating adherence to a special diet (that is scored from 0-18) in relation to C-reactive protein level and am in the process of building multiple linear regression models: To achieve a ...
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### Finding the coefficient of determination from a regression line?

Suppose you are given the following estimated model from a sample of size 1217: $\hat{y} = 1.177663 + 0.0910103x$ and the standard errors of the coefficients are $0.0865446$ and $0.0065643$ ...
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### Establishing relationship between two variables with low sample size(5)

My question is - Is elevation range of plants linked to intraspecific trait variability. I want to explore the relationship between the coefficient of variance (CV) of a certain plant functional ...
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### Full dataset with few repeated measures

I am dealing with a dataset with the majority of entries with one value per individual but, with three cases with 2 repeated measures each. My first approach would be to pursue linear mixed models, to ...
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### Using variance of y variable as weights for weighted linear regression when both x and y variables contain negative values?

I am currently dealing with a weighted linear regression problem in the context of an instrument calibration in analytical chemistry. Let's assume I have a response variable y and a predictor variable ...
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### Do I need to transform this data for linear regression? If yes, what type of transformation is best?

The picture below is the dependent variable on the Y and one of the IVs on the X axis. The Dependent variable is range bound between .5 and 12 while the IVs range from 0-over a million depending on ...
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### How to calculate parameter estimates from the linear predictor with block effect?

I fit the following linear model with block effect in R: M1 <- lm (RV~EV+Block) And estimated the model means like this: M2 <- lm (RV~EV-1+Block) coef(M2) The output: ...