Refers to any model where the a random variable is related to one or more random variables by a function that is linear in a finite number of parameters.
0
votes
0answers
45 views
R linear model summaries, why is one model “better” than the other?
I am attempting to get my head around the summaries of linear models given within R. In other words i am trying to identify when the summary of a model is good or bad. Consider the following two ...
0
votes
1answer
50 views
Var(AZ)=A Var(Z) A^T?
I am learning linear models, and I do not understand the following:
$\text{Var}(AZ)=A \text{Var}(Z) A^T$ where $A$ is a constant matrix. I want to know the variance $\widehat{\beta}$ in a linear ...
0
votes
1answer
37 views
Alternatives to least-Chi-square to fit a straight line,
as stated in the title I am looking for alternative ways to fit my data to a straight line. My current approach is a least Chi-Square Fitting, but the predicted relative errors for the slope exceed ...
3
votes
0answers
34 views
How to build a model where variance depends on covariate?
I have what I believe is a very simple problem for anyone used to modelling with unequal variances (which I am unfortunately not). I have a dependent variable "totrich" which I want to model as a ...
0
votes
1answer
40 views
Basic questions concerning the interpretation of results from summary(lm(…~…)) in R [duplicate]
set.seed(11)
a = runif (12)
b = rep(c(1,2,3),4)
summary(lm(a~b))$coeff
summary(lm(a~b-1))$coeff
What does a p.value for the intercept means ?
What differences ...
0
votes
1answer
29 views
ncvTest from R and interpretation
I have done a ncvTest, but I am not really sure how to interpret this properly. I look documentation and examples online but was not able to find anything that clearly explains about ncvTest.
Here ...
1
vote
0answers
9 views
Dummy variable as side constraint in DEA
What do you think these dummy variables do to the resulting weight values in a BCC/VRS data envelopment analysis? It appears the 1 and -1 relations drive the program to make the weights for the ...
-3
votes
1answer
65 views
Calculating the linear model with R
I need to calculate the linear model in R, i did the following:
summary(model)
But what if I wanted to calculate only the first point? A bit stuck with this one... Many thanks!
Here is the code ...
1
vote
0answers
19 views
Reference Group for dummy coding [migrated]
Is there any way to explicitly specify which group to take as reference group for dummy coding when modeling with lm function in R using categorical variables??
1
vote
1answer
35 views
Interpreting regression coefficents when the variables are in proportions
I have the following cross-sectional regression.
per capita car ownership = 0.025*per capita college degrees + 0.012*availability of underground(dummy variable) - 0.287
I am having difficulty with ...
7
votes
1answer
149 views
Conditional expectation of R-squared
Consider the simple linear model:
$$\pmb{y}=X'\pmb{\beta}+\epsilon$$
where $\epsilon_i\sim\mathrm{i.i.d.}\;\mathcal{N}(0,\sigma^2)$ and
$X\in\mathbb{R}^{n\times p}$, $p\geq2$ and $X$ contains a ...
2
votes
1answer
69 views
Prediction on mixed effect models: what to do with random effects?
Let's consider this hypothetical dataset:
...
1
vote
2answers
60 views
Line of best fit (Linear regression) over vertical line
I want to get a line of the best fit which is a line that passes as close as possible to a set of points defined by coordinates point_i = (X_i, Y_i).
When I apply linear regression, I have a special ...
-1
votes
0answers
31 views
interaction effect of two variables is much higher than each variables' main effect !!! is this justifiable? [duplicate]
I need to do statistical analysis for my thesis. I'm not familiar with statistics, I would be thankful if you help.
Is it possible to have high interaction effect, while main effect of each variable ...
1
vote
0answers
18 views
Calculating error bars for Excel Linear Regression [duplicate]
I've ben sent a forecast of sales from a consultancy. It uses Excel's LINEST function, taking 4 factors that seem to have affected sales in the past, and used them to make a prediction.
How do I go ...
0
votes
0answers
70 views
Correct structuring of random effects?
I have produced a mixed effects model as follows;
lmer(TotalPayoff~Type+Game+PgvnD*Asym+(1|Subject)+(1|Pairing),REML=FALSE,data=table)-
each pairing contains 2 subjects and each Subject is ...
3
votes
1answer
68 views
Statistic For The Curvature or Non-Linearity Of Data Set
I'm trying to estimate the curvature/structural complexity of datasets, or the amount by which it is non-linear. The datasets are mostly very linear but with instances of very arbitrarily structured ...
3
votes
2answers
77 views
Noisy linear relationship: Can the functional form be known?
Let's say I know the relation between x and y is linear yet noisy. Given a noisy (x,y) ...
1
vote
1answer
147 views
Zero conditional mean assumption
How can I check the zero conditional mean assumption for a multiple linear regression? I read that when the assumption is violated, your model is misspecified. And your estimators are biased. So we ...
4
votes
1answer
173 views
R, Differences between lm and aov
What does explain the differences in p.values in the following aov and lm ?
Is the difference only due to different types of Sum of square calculations ?
...
1
vote
1answer
107 views
How do I set up a single continuous independent variable for a repeated measures linear model?
I'm doing an education study and I'm trying to see the effect of website usage on quiz scores in a class of college students. There were 30 students in the class and they took 10 weekly quizzes over ...
1
vote
0answers
55 views
Strange linearity test for ANCOVA
There is an easy way to test the linearity hypothesis for a simple regression model $y \sim {\cal N}(\alpha+\beta x,\sigma^2)$: calling $H_0$ this model, perform a test against the ANOVA model $H_1$ ...
1
vote
1answer
103 views
Solved Assumptions of Linear Regression [duplicate]
I am a bit confused with this.
Independence - The response variables are independent. I only have a single response variable so OK? Or observations are independent of each other? E.g Auto Correlated ...
8
votes
2answers
294 views
Where do the assumptions for linear regression come from?
I'v already known that there are several assumpations when using linear regression model. But I cannot understand why some of them exists. They are:
independent errors
normal distribution of errors
...
0
votes
1answer
88 views
Dropping a variable from a multiple linear regression model, causes another to become non-significant [duplicate]
Suppose we have a regression model that measures college Grade Point Averages. The variables that we are using are hsize (the size of the graduating class in ...
0
votes
1answer
103 views
Regression on means of log-transformed variables
Suppose that I want to study the relationship between two variables $Y$ and $X$ using the linear model $Y \sim X$. Unfortunately, both $Y$ and $X$ are not normally distributed, say they are both ...
2
votes
1answer
78 views
How to extract/compute leverage and Cook's distances for linear mixed effects models
Does anyone know how to compute (or extract) leverage and Cook's distances for a mer class object (obtained through lme4 ...
0
votes
2answers
228 views
How to interpret a positive beta coefficient in linear regression?
Could someone provide a sample interpretation for the following:
...
0
votes
1answer
37 views
Fitting models in R with time restriction on coefficients
How should I define a model formula in "R", when one (or more) exact linear restrictions binding the coefficients is available.
Equation: y = b1*x1 + b2*x1
where y = b1*x1 for t < t1 and y = ...
4
votes
1answer
114 views
Two simple or one complex model, BIC and likelihood
I have a set of data points with a total number of Nt. I know a priori that the data comes from two distinct processes (distributions). I am trying to find the optimal model parameters together with ...
0
votes
1answer
62 views
Trend in data - determining according to angle between regression line and vertical line?
This question is a little bit referring to this question How to determine trend strength from linear regression slope? but I found a another solution so I am creating new question to confirm my idea. ...
1
vote
0answers
104 views
Repeated measures ANOVA: Mauchly's test undefined
I'm doing a two-way between-within ANOVA in SPSS. I have two groups with 9 subjects each (so total = 18), and 24 levels of one repeated measure.
I understand why Mauchly's test of Sphericity has no ...
0
votes
0answers
75 views
Details of Bayesian linear regression
In Bayesian Linear Regression, we have a data set with {$x_{i}$, $t_{i}$} where $x_{i}$ are input vectors and $t_{i}$ are their resulting observations. We want to find a vector $\bf{w}$ in order to ...
0
votes
0answers
13 views
Y v level for different additives; how to handle zero level
I want to model the effect of Level (continuous) of different Additives (categorical) on Y (continuous) by fitting a linear model, so my data is going to look like this:
...
0
votes
1answer
168 views
additive and non-additive(multiplicative) interactions - soft question -
we use models with multiplicative interaction effects when relationship between independent variable and dependent variable are non-additive.
My question is, Are all models with multiplicative ...
3
votes
1answer
110 views
What does intercept actually mean in a simple linear model?
Given y = a + b*x, does "a" represent simply an intercept or mean y?
For y = a + b*ln(x), is there a need to interpret the intercept "a?"
0
votes
0answers
36 views
Linear mixed model estimated means
I am trying to determine how to get SPSS (19.0) to give out estimated means for my interaction. To preface, my analysis has 3 groups (group a, b and c) and each group was measured at 5 time points. We ...
1
vote
1answer
147 views
To find significant differences between means using repeated measures GLM
I am new in using SPSS and stuck with General Linear Model [which is just linear model] procedure.
I have 8 cognition variables like latency, thigmotaxis, spatial, quadrant, nt quadrant, proximity, ...
0
votes
2answers
82 views
Do we need Overlap/Common Support in case of a parametric regression?
If I want to make a causal statement based on selection on observables. One typically assumes "Common Support" (/"Overlap") - which means that for any value of the confounding variables X a unit i can ...
5
votes
3answers
291 views
Perform linear regression, but force solution to go through some particular data points
I know how to perform a linear regression on a set of points. That is, I know how to fit a polynomial of my choice, to a given data set, (in the LSE sense). However, what I do not know, is how to ...
2
votes
0answers
73 views
What insights can be found by using leverage plots?
I'm trying to figure out whether leverage plots can provide valuable information. See example in http://www.jmp.com/support/help/Leverage_Plot_Details.shtml
3
votes
1answer
127 views
Why does the rank of the design matrix X equal the rank of X'X?
Why does the rank of the design matrix $\boldsymbol X$ equal the rank of $\boldsymbol{X'X}$? Is this true in all circumstances?
If X is not linearly independent, what would the rank of X'X be?
0
votes
0answers
32 views
Estimable function of OLS parameters can be shown by inner product with Null space?
I am in a advanced linear models class, and we are currently covering estimable functions. The criterion that we have for an estimable function is that for any $a^T\beta$ there exists an unbiased ...
2
votes
1answer
103 views
Trend line does not seem to fit data
I'm trying to do a simple scatterplot and trend line in R, but it doesn't look right. Have I messed up something blatantly obvious? Any ideas as to why the line doesn't fit the data?
Here is the ...
0
votes
0answers
47 views
Which models should be compared when using the regression formulation of multi-way ANOVA?
I dithered about whether to post this on Stack Overflow or here, but I think the question is more ideological than practical, so please forgive if there's too much technical detail!
I'm trying to ...
2
votes
1answer
108 views
Should I include an interaction term for a covariate if I expect it to be correlated with one or more of the variables?
I'm fitting a linear model where the response variable is a measure of physical performance-- running speed for example-- and the predictor variables are sex and drug treatment, with an interaction ...
1
vote
1answer
44 views
Is there a general rule about max nr of variables to use in (generalized) linear model?
I am running a generalized linear model on a dataset with 19 individuals and have 4 variables of interest. There are furthermore a number of interactions that might be interesting to look at. I was ...
2
votes
1answer
69 views
Reference needed - Who first introduced linear models, fixed and random effects models?
I am writing an essay which briefly discusses linear models as well as models with fixed and random effects. I am googling since ages to find a reference which says who first introduced linear models ...
5
votes
2answers
229 views
lm() - model specification
If have multivariate data of 3 response variables and 2 factors (f1 and f2). I can specify an linear model in different ways for this data, however I don't know what the difference between the models ...
3
votes
2answers
158 views
Troublesome residual plot from linear mixed model
I have fitted the following linear mixed model based on the results of an economic game:
lmer(TotalScore~perOOgivenP+Game+(1|Subject),REML=T,data=mdl1table)->m1
...
