# Questions tagged [linearity]

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13 views

### Interpretation of scatter plot - vertical line patter spotted

can I please get quick help on this scatter plot of standardised residuals against predicted values. Does this mean this violated normality, linearity and homogeneity? How should I interpret that ...
33 views

### Relationship between Histogram , Scatter plot , Normality , Linearity

I have the following doubt: suppose you have a categorical variable called 'neighborhood' with 20 categorical levels/values ("vila madalena", "mooca", etc). and I want to check ...
19 views

### Multivariate normal distribution property [duplicate]

The Econonometrics book by Hansen mentions this property of a multivariate normal distribution: If $X∼N(\mu,\Sigma)$ then $AX+b∼N(Aμ+b,AΣA^\prime)$. It goes to say that a simple implication of this ...
31 views

### Assumption logistic regression: linearity of independent variables and log odds?

I checked whether in my logistic regression models the assumption of linearity between the independent variables and the log odds is met. I used R and followed the instructions on this website to do ...
21 views

### Linearity Assumption in Logistic Regression

In test for linearity (Box-Tidwell) both continuous IVs were significant (p<.000). I did the natural log transformation and inverse square root transformation and ran it again including the ...
53 views

### How to Assess Linearity assumption of logit in logistic regression

In Applied Lineare Regression, (Hosmer, Lemeshow, Sturdivant 3rd ed.) Ch. 4, they present "Purposeful Selection." Part of step 5 is to assess the validity of the linearity assumption of the logit vs ...
65 views

### Dealing with violation of OLS assumptions

I am currently writing my Master's thesis in economics. I am analyzing the second home rate in Swiss municipalities in R. The second home rate for municipality $j$ is defined as the share of the ...
29 views

### Mixed Model in R: Test for linearity and inclusion of lagged variable

I have specified a mixed model in R, based on a data set containing advertising awareness as DV and advertising spends as IV. The effect of the advertising spends on awareness is moderated by two ...
19 views

### What is the problem with my Ramsey Test's result?

I run the multiple regression on Stata and now I have to test the linearity of all my independent variables. First, I analyzed the residuals versus predictors and I transformed several variables. ...
26 views

### Prove or disprove the Linearity of Expectiles used in Expectile Regression

For expectation (mean), there are many useful properties such as Linearity of Expectation: $\mathbb{E}[X+Y]=\mathbb{E}[X]+\mathbb{E}[Y]$ $\mathbb{E}[\alpha X]=\alpha\mathbb{E}[X]$ (The 2 equations ...
27 views

### linearity of a measurement device

I like to evaluate the linearity of a measurement system. In order to do so I read ISO 22514-7 as well as Breyfogle's "Implementing six sigma". However, the procedure is still unclear to me. So I'm ...
26 views

### How to test interaction when loglinearity is violated in Cox model?

In a Cox PH regression, I would like to model an interaction between two variables. The problem is that one of the variables breaks the log-linearity assumption. Based on my previous questions (...
36 views

### Why is linearity (as in linearity in BLUE) a desirable property for OLS estimators?

By linearity, I do not mean the linearity of the estimators in the OLS regression equation, what I am trying to ask is why are the beta coefficients a linear function of y(i)'s. Why is linearity a ...
59 views

### Linearity assumption of logistic regression [duplicate]

Do I have to check linearity assumption of logistic regression (Log odds of outcome with continuous variable) using graph of predicted logodds (by logistic regression) and continuous variable Or ...
46 views

### Is there a way to differentiate between linear and non-linear datasets in simulations studies?

I'm trying to find a a measure of "linearity" among different simulated data sets and how I could control for such differences. This idea came from studying Hastie's and Tibshirani's work around ...
164 views

### Should one drop independent variables if they don't have linear relationship with the response variable?

I am building a linear regression model using Ridge regression. Some of the independent variables don't have linear relationships with the dependent variable. I've tried to do data transformations on ...
57 views

### Linear regression, linearity assumption violated?

Below i have attached a scatter plot showing my dependent variable on the Y-axis and my independent variable on the X-axis I am not sure if the linearity assumption is violated? Can anyone explain ...
58 views

### SEM 4 questions - testing linearity, sum score, number of variables, independent variables

For my master thesis I'm making a structural equation model. However, I do not have much experience with this. So here are some different questions. I read that one of the assumptions important for ...
73 views

### How to check the linearity of continuous variable in linear mixed model

I'm doing a linear mixed model using lme. In my adjustement factors, I have a continuous varaible (named X1). And I want to check the linearity of this variable using a spline function or a ...
170 views

### Model assumption of linearity

I am trying to interpret the outcome of a test for assumption of linearity. This is the dataframe: ...
54 views

### Is checking for normality and linearity in this way correct?

Testing normality using a significance test is a little bit useless especially when you have a large sample size So, recently I found a way to test normality by running a fake regression using ...
47 views

### What is relation betwen linearity assumption in OLS and L in BLUE (i.e. OLS is BLUE)

The linearity assumption says that the dependent variable is linear in parameters. When Gauss-Markov assumptions hold, OLS is BLUE, meaning smallest variance amongst Linear Unbiased estimators, where ...
84 views

### How do Component + Residual Plots look like in Polynomial Regression?

Components + resiudal plots or partial residual plots can be used to detect deviations from linearity in multiple linear regression. They work by plotting the variable on the x-axis and the component+...
19 views

### linear relationship [closed]

Could the data points fall on the regression line to assume that the relationship is linear, please check the attached photo what if the scatter plot shows that the relationship is linear but the ...
23 views

### Linear Unconditional X-Y, Non-Linear Conditional X-Y

Intuitively, I can imagine that an unconditional (i.e., unadjusted for any covariates) Y~X relation can present as a linear relation, whereas a conditional Y~X|Z relation can present as a non-linear ...
1k views

### Ways of Testing Linearity Assumption in Multiple Regression apart from Residual Plots

I was going through the assumptions of linear regression and of course one of them was linearity between the dependent and the independent variables - to be precise I should say that the assumption is ...
190 views

### ANCOVA - Non-linearity of covariate

I have a dataset where I calculated genetic distances between populations of some animals (a continuous variable). I want to know if these differences are explained by physical or/and ecological ...
1k views

### Cox PH linearity assumption: reading martingal residual plots

According to a lot of ressources about Cox PH model, continuous numeric variables should be tested for linearity assymption by plotting the Martingale residuals. In R, you can use ...
724 views

### Cox PH model: managing continuous variables and linearity assumption

In an epidemiological study, I'm using martingale plot to assess the linearity of continuous variables. Here are the Martingale Residuals (from Null Model) using R's ...
76 views

### Violation of linearity?

Can anyone tell me if, based on this image, the linearity assumption is violated in my model?
53 views

### Linearity assumption with dependent indicator variable and continuous independent variable?

If i have a regression model with the independent variable as continuous, while my dependent variable is a dummy variable (only one independent variable) then will the linearity assumption hold ...
495 views

### Diagnosing linearity for multiple regression model

I have the following model in R to estimate the change in mosquito abundance each year when controlling for climate variables: ...
2k views

### The best way to check the linearity assumption in ANOVA (except using scatter plots)

I was wondering that ANOVA is based on linearity assumption. If Yes, how can I check the linearity between observations. I know using plot would be useful but it is difficult to find the degree of ...
780 views

### Convexity, linearity and their combination for MLE

I'm going through Murphy's ML a Probabilistic Perspective book and in chapter 9 we have the following excerpt talking about the MLE of exponential family distributions: My question is: How do we ...
2k views

### Interpretation of residual plot for mixed effect linear model

I am trying to do mixed effect regression model with lme4.lmer function. The model has two fixed categorical variables, one random categorical variable and response is continuous variable (distance in ...
3k views

### Does the Box Tidwell test for linearity of the logit require predictors to be in the range [0,1]?

Given a multinomial logistic regression model with 4 independent variables, 4 relevant interactions and a dependent variable with 3 categorical outcomes, I wanted to test for linearity of the logit. ...
284 views

### Problems with zero values when testing for linearity of the logit

From Field's 'Discovering Statistics using SPSS' I read that you should test for linearity of the logit when using a logistic regression. The process explained in the book covers the natural log ...
2k views

### help for interpreting the residuals vs. fitted values plot

I have an ordinal variable (scale of stress) considered as continuous predictor in a multivariate linear regression. I would like to verify the assumption of linearity and this is my residuals vs. ...
157 views

### reconciling Linearity and Multicollinearity assumptions in ANCOVA

For ANCOVA, many textbooks and other resources require, among other assumptions, that covariates be linearly related to the dependent variable, which makes sense. However, many of the same sources ...
17k views

### The linearity of variance

I think the following two formulas are true: $$\mathrm{Var}(aX)=a^2 \mathrm{Var}(X)$$ while a is a constant number $$\mathrm{Var}(X + Y)=\mathrm{Var}(X)+\mathrm{Var}(Y)$$ if $X$, $Y$ are ...
508 views

### When performing a linearizing transformation, do I apply transformation to dummy variables?

Suppose I wanted to transform variables to achieve linearity (e.g.), would I omit the dummy variables from the transformation? ...
317 views

### Non Linear Regression -Regression Trees

For datasets of higher dimensions, how do I decide if a Linear model is sufficient to fit the data or if I have to use non linear models like regression trees to fit the data ? NOTE:I did try both ...
75 views

### Is there a test to verify that data is linear or rather logarithmic?

I've done two small experiments, and if I visualize that data, it seems as there is a linear trend in the first one, and a logarithmic trend in the second. Is there a test to verify that this is ...
299 views

### How to graph continuous independent variable and logit of dichotomous outcome in SPSS

First question: I am using SPSS, and I want to graph the logit of my dependent variable on the y axis and my continuous independent variable on the x-axis. I am interested in visualizing the ...
2k views

### Interpreting linearity in residual vs. fitted plot

I am working on a linear regression model and I am not sure how to interpret the following residual vs fitted values plot. For all I know residuals are supposed to fluctuate randomly around 0 which ...