# All Questions

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### Using a subset of parameters in joint confidence region of a linear model

For a standard linear model of the form $y = X\beta + \epsilon$, where $\beta$ is a vector of parameters. we can calculate an individual confidence interval for each parameter (of 1-$\alpha$ quartile)....
55 views

### Bootstrapping with repeated measurements

I am trying to estimate a linear relation between body temperature and body mass, and I have a sample of measurements from subjects, with most subjects having one measurement, but several subjects ...
50 views

### Understanding simplification of constants in derivation of variance of regression coefficient

In looking over TooTone's answer in Derive Variance of regression coefficient in simple linear regression, there's a step in line 3 below where $(\beta_0 + \beta_1x_i + u_i )$ is simplified to $u_i$ ...
98 views

### Interpretation of standardized (z-score rescaled) linear model coefficients

I have analyzed some data on vegetation change as a function of change in soil parameters. I compared a dataset from 2001 with a dataset from 2018 (fully balanced). To investigate the change in ...
43 views

### How to account for incrementation in a log-linear model

I want to perform a mixed regression analysis with random intercept and uncorrelated random slope after multiple imputation. The dependent variable is continuous, namely a duration as number of days ...
56 views

### How can I interpret relative and absolute income of both partners in one regression?

Suppose you want to examine the effect of income on the amount of housework for women. Does it make sense to include both relative income (compared to partners income) and absolute income of BOTH ...
138 views

### R: how is the Pr(>|z|) in the results of glm.fit calculated and why?

I've been searching but I can't find anywhere an explanation of how the Pr(>|z|) column is calculated in the results of R's glm.fit function. I would really appreciate: a) an explanation so I can ...
81 views

### Linear regression very significant βs with multiple variables, not significant alone

Could anyone provide intuition on why for y ~ β1x1 + β2x2 + β3x3, β1 β2 and β3 can be significant in a multiple variable model (p range 7x10-3 to 8x10-4), but the βs are not significant in separate ...
30 views

### Statistical measure for linear regression with two distinct clusters of points

In the following plot, I have a linear regression of 30 points, representing 10 treatments with three replicates each. As you can see, the r-squared value is quite strong (0.83) and the p-value is ...
43 views

### Construct a $95\%$ confidence interval for $5\beta_4$

Construct a $95\%$ confidence interval for $5\beta_4$. If this question were about $\beta_4$ without the $5$, I would absolutely know what to do. But I have to idea how the $5$ comes into play. I can'...
82 views

2k views

### Interpretation of Coefficients in linear regression using 'fitlm'

I require help with regards to the interpretation of linear regression results (I'm using the Matlab 'fitlm' function). My data has 8 features, and when each feature is plotted against the response ...
710 views

### Are sufficient statistics for regression equivalent in the frequentist and Bayesian cases? [duplicate]

If I have a Poisson regression such that $\lambda = \alpha + \beta t$, $\alpha + \beta t \geq 0$ $\forall t, \alpha, \beta$ and $Y_t \sim \textrm{Poisson}(\lambda_t)$ for which I have 10 observations ...
6k views

### Testing a regression coefficient against 1 rather than 0

Brief caveat- I haven't dusted off my stats knowledge since some university courses a few years ago, and I'm struggling with cobwebs. I have a model where a linear 1 to 1 relationship has been ...
1k views

### Prior for the coefficients of a linear regression model

I have a linear regression model $\bf Y=\bf{X}\bf{\beta}+\epsilon$. I want to assign a prior on $\bf\beta$ in order to derive the posterior predictive model $p(y_{predictive}|\bf{y},\bf{X},\beta)$. ...
81 views

### Confidence interval for a multiple of regression coefficient

I am trying to model relationship between length of stay of patients in hospital(Y) vs Age in years(X). The data set I've got doesn't specify the unit of length of stay. So now estimated value of my ...
62 views

### How can I create a linear regression model with some negative coefficients in R? [duplicate]

What I'm trying to do is to construct a linear model in a form like $$Y = \beta_0X_0-\beta_1X_1+\beta_2X_2 + \beta_3$$ where $\beta_0$, $\beta_1$ and $\beta_2$ are coefficient of predictors $X_0$, ...
816 views

### How can I optimize coefficients of an arbitrary model?

This might be terribly easy but I'm probably lacking the keywords to search for. Assume the following (dummy) data: ...
9k views

### Interpreting intercept for the log model in linear regression in R for small predictor

I have a dataset. Assume that y is the dependent variable and x is the independent variable. My goals for this analysis is mainly on the following hypothesis: Expecting x=0 to imply y=0 Expecting ...
1k views

### How to capture & present lm model output from R

After running iterations of lm() in R, I am now stuck with which components of the model's output to present and how to present them. I know that the $R^{2}$ value, ...
295 views

### Coefficient of Determination: For the perimeter and area of a square: Why different?

When calculating the coefficient of determination for a square, why is it that if you use the data set for the side length of as X= (1,2,3,4) and the perimeter as Y=(4,8,12,16) the Coefficient of ...
197 views

### Interpreting regression coefficients of log(y+1) transformed responses

I have measurements $y_1$,...,$y_i$,...,$y_n$ taken from a set of replicates in a factorial designed experiment. In order to use a linear regression I define my response $z_i = log(y_i + 1)$. The ...
1k views

### R: Explanation of a multiple linear regression summary [duplicate]

I am quite new with R and while i am able to perform the basics i am not yet able to understand the output results. For example: summary(lmodel) generates the ...