Questions tagged [interpretation]

Refers generally to making substantive conclusions from the results of a statistical analysis.

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259
votes
11answers
156k views

How to understand degrees of freedom?

From Wikipedia, there are three interpretations of the degrees of freedom of a statistic: In statistics, the number of degrees of freedom is the number of values in the final calculation of a ...
250
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16answers
470k views

What is the meaning of p values and t values in statistical tests?

After taking a statistics course and then trying to help fellow students, I noticed one subject that inspires much head-desk banging is interpreting the results of statistical hypothesis tests. It ...
239
votes
2answers
169k views

Interpretation of R's lm() output

The help pages in R assume I know what those numbers mean, but I don't. I'm trying to really intuitively understand every number here. I will just post the output and comment on what I found out. ...
101
votes
2answers
49k views

Removal of statistically significant intercept term increases $R^2$ in linear model

In a simple linear model with a single explanatory variable, $\alpha_i = \beta_0 + \beta_1 \delta_i + \epsilon_i$ I find that removing the intercept term improves the fit greatly (value of $R^2$ ...
83
votes
7answers
44k views

Clustering on the output of t-SNE

I've got an application where it'd be handy to cluster a noisy dataset before looking for subgroup effects within the clusters. I first looked at PCA, but it takes ~30 components to get to 90% of the ...
68
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1answer
70k views

How to interpret coefficients in a Poisson regression?

How can I interpret the main effects (coefficients for dummy-coded factor) in a Poisson regression? Assume the following example: ...
66
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9answers
9k views

Is this chart showing the likelihood of a terrorist attack statistically useful?

I'm seeing this image passed around a lot. I have a gut-feeling that the information provided this way is somehow incomplete or even erroneous, but I'm not well versed enough in statistics to respond....
66
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5answers
52k views

How to interpret an inverse covariance or precision matrix?

I was wondering whether anyone could point me to some references that discuss the interpretation of the elements of the inverse covariance matrix, also known as the concentration matrix or the ...
56
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9answers
20k views

Is it wrong to rephrase “1 in 80 deaths is caused by a car accident” as “1 in 80 people die as a result of a car accident?”

Statement One (S1): "One in 80 deaths is caused by a car accident." Statement Two (S2): "One in 80 people dies as a result of a car accident." Now, I personally don't see very much difference at all ...
54
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2answers
14k views

Real-life examples of moving average processes

Can you give some real-life examples of time series for which a moving average process of order $q$, i.e. $$ y_t = \sum_{i=1}^q \theta_i \varepsilon_{t-i} + \varepsilon_t, \text{ where } \varepsilon_t ...
47
votes
5answers
9k views

Interpreting QQplot - Is there any rule of thumb to decide for non-normality?

I have read enough threads on QQplots here to understand that a QQplot can be more informative than other normality tests. However, I am inexperienced with interpreting QQplots. I googled a lot; I ...
46
votes
3answers
49k views

Interpretation of log transformed predictor and/or response

I'm wondering if it makes a difference in interpretation whether only the dependent, both the dependent and independent, or only the independent variables are log transformed. Consider the case of <...
43
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5answers
51k views

What is the significance of logistic regression coefficients?

I am currently reading a paper concerning voting location and voting preference in the 2000 and 2004 election. In it, there is a chart which displays logistic regression coefficients. From courses ...
40
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3answers
481k views

How to interpret F- and p-value in ANOVA?

I am new to statistics and I currently deal with ANOVA. I carry out an ANOVA test in R using aov(dependendVar ~ IndependendVar) I get – among others – an F-value ...
38
votes
2answers
88k views

Interpretation of R's output for binomial regression

I'm quite new on this with binomial data tests, but needed to do one and now I´m not sure how to interpret the outcome. The y-variable, the response variable, is binomial and the explanatory factors ...
37
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4answers
33k views

How to interpret coefficients from a polynomial model fit?

I'm trying to create a second order polynomial fit to some data I have. Let's say I plot this fit with ggplot(): ...
34
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4answers
42k views

X and Y are not correlated, but X is significant predictor of Y in multiple regression. What does it mean?

X and Y are not correlated (-.01); however, when I place X in a multiple regression predicting Y, alongside three (A, B, C) other (related) variables, X and two other variables (A, B) are significant ...
33
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1answer
38k views

What is the intuitive reason behind doing rotations in Factor Analysis/PCA & how to select appropriate rotation?

My Questions What is the intuitive reason behind doing rotations of factors in factor analysis (or components in PCA)? My understanding is, if variables are almost equally loaded in the top ...
33
votes
2answers
4k views

Understanding p-value

I know that there are lots of materials explaining p-value. However the concept is not easy to grasp firmly without further clarification. Here is the definition of p-value from Wikipedia: The p-...
32
votes
5answers
106k views

What is the difference between “mean value” and “average”?

Wikipedia explains: For a data set, the mean is the sum of the values divided by the number of values. This definition however corresponds to what I call "average" (at least that's what I remember ...
30
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5answers
3k views

Data “exploration” vs data “snooping”/“torturing”?

Many times I have come across informal warnings against "data snooping" (here's one amusing example), and I think I have an intuitive idea of roughly what that means, and why it may be a problem. On ...
30
votes
2answers
78k views

Interpretation of biplots in principal components analysis

I came across this nice tutorial: A Handbook of Statistical Analyses Using R. Chapter 13. Principal Component Analysis: The Olympic Heptathlon on how to do PCA in R language. I don't understand the ...
30
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6answers
3k views

When are confidence intervals useful?

If I understand correctly a confidence interval of a parameter is an interval constructed by a method which yields intervals containing the true value for a specified proportion of samples. So the '...
29
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6answers
163k views

Interpretation of Shapiro-Wilk test

I'm pretty new to statistics and I need your help. I have a small sample, as follows: H4U 0.269 0.357 0.2 0.221 0.275 0.277 0.253 0.127 0.246 ...
29
votes
3answers
24k views

Interpretation of simple predictions to odds ratios in logistic regression

I'm somewhat new to using logistic regression, and a bit confused by a discrepancy between my interpretations of the following values which I thought would be the same: exponentiated beta values ...
29
votes
4answers
37k views

How do you Interpret RMSLE (Root Mean Squared Logarithmic Error)?

I've been doing a machine learning competition where they use RMSLE (Root Mean Squared Logarithmic Error) to evaluate the performance predicting the sale price of a category of equipment. The problem ...
28
votes
1answer
35k views

How to interpret variance and correlation of random effects in a mixed-effects model?

I hope you all don't mind this question, but I need help interpreting output for a linear mixed effects model output I've been trying to learn to do in R. I am new to longitudinal data analysis and ...
27
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3answers
3k views

Can't deep learning models now be said to be interpretable? Are nodes features?

For statistical and machine learning models, there are multiple levels of interpretability: 1) the algorithm as a whole, 2) parts of the algorithm in general 3) parts of the algorithm on particular ...
27
votes
1answer
21k views

What is the difference between generalized estimating equations and GLMM?

I'm running a GEE on 3-level unbalanced data, using a logit link. How does this differ (in terms of the conclusions I can draw and the meaning of the coefficients) from a GLM with mixed effects (GLMM)...
26
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1answer
51k views

How to interpret coefficient standard errors in linear regression?

I'm wondering how to interpret the coefficient standard errors of a regression when using the display function in R. For example in the following output: ...
25
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3answers
84k views

How to interpret the dendrogram of a hierarchical cluster analysis

Consider the R example below: plot( hclust(dist(USArrests), "ave") ) What exactly does the y-axis "Height" mean? Looking at North Carolina and California (...
25
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3answers
43k views

Interpreting interaction terms in logit regression with categorical variables

I have data from a survey experiment in which respondents were randomly assigned to one of four groups: ...
23
votes
1answer
35k views

Mean squared error vs. mean squared prediction error

What is the semantic difference between Mean Squared Error (MSE) and Mean Squared Prediction Error (MSPE)?
23
votes
3answers
32k views

AIC & BIC number interpretation

I am looking for examples of how to interpret AIC (Akaike information criterion) and BIC (Bayesian information criterion) estimates. Can negative difference between BICs be interpreted as the ...
22
votes
3answers
13k views

What does “all else equal” mean in multiple regression?

When we do multiple regressions and say we are looking at the average change in the $y$ variable for a change in an $x$ variable, holding all other variables constant, what values are we holding the ...
22
votes
4answers
2k views

What to say to a client that thinks confidence intervals are too wide to be useful?

Suppose I am a consultant and I want to explain to my client the usefulness of confidence interval. The client says to me that my intervals are too wide to be useful and he would prefer to use ones ...
22
votes
3answers
15k views

interpreting y axis of a partial dependence plots

I have read through other topics on partial dependence plots and most of them are on how you actually plot them with different packages, not how you can accurately interpret them, So: I have been ...
21
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2answers
23k views

Natural interpretation for LDA hyperparameters

Can somebody explain what is the natural interpretation for LDA hyperparameters? ALPHA and BETA are parameters of Dirichlet ...
21
votes
3answers
50k views

How to interpret main effects when the interaction effect is not significant?

I ran a Generalized Linear Mixed Model in R and included an interaction effect between two predictors. The interaction was not significant, but the main effects (the two predictors) both were. Now ...
21
votes
2answers
33k views

How to interpret parameters in GLM with family=Gamma

I have a question regarding parameter interpretation for a GLM with a gamma distributed dependent variable. This is what R returns for my GLM with a log-link: ...
20
votes
2answers
97k views

What happens when I include a squared variable in my regression?

I start with my OLS regression: $$ y = \beta _0 + \beta_1x_1+\beta_2 D + \varepsilon $$ where D is a dummy variable, the estimates become different from zero with a low p-value. I then preform a ...
20
votes
5answers
22k views

What is a block in experimental design?

I have two questions about the notion of block in experimental design : (1) What is the difference between a block and a factor ? (2) I tried to read some books but something is not clear: it seems ...
19
votes
3answers
22k views

ARIMA model interpretation

I have a question about ARIMA models. Let's say I have a time series $Y_t$ that I would like to forecast and an $\text{ARIMA}(2,2)$ model seems like a good way to conduct the forecasting exercise. $$ ...
19
votes
2answers
8k views

Why is regression about variance?

I am reading this note. On page 2, it states: "How much of the variance in the data is explained by a given regression model?" "Regression interpretation is about the mean of the coefficients;...
19
votes
1answer
15k views

Interpreting 2D correspondence analysis plots

I've been searching the internet far and wide... I have yet to find a really good overview of how to interpret 2D correspondence analysis plots. Could someone offer some advice on interpreting the ...
19
votes
2answers
359 views

Can regularization be helpful if we are interested only in modeling, not in forecasting?

Can regularization be helpful if we are interested only in estimating (and interpreting) the model parameters, not in forecasting or prediction? I see how regularization/cross-validation is extremely ...
18
votes
3answers
14k views

Analysis of Kullback-Leibler divergence

Let us consider the following two probability distributions ...
18
votes
4answers
3k views

How is the bayesian framework better in interpretation when we usually use uninformative or subjective priors?

It is often argued that the bayesian framework has a big advantage in interpretation (over frequentist), because it computes the probability of a parameter given the data - $p(\theta|x)$ instead of $p(...
18
votes
2answers
19k views

Interpretation of betas when there are multiple categorical variables

I understand the concept that $\hat\beta_0$ is the mean for when the categorical variable is equal to 0 (or is the reference group), giving the end interpretation that the regression coefficient is ...
18
votes
1answer
7k views

Plot and interpret ordinal logistic regression

I have a ordinal dependendent variable, easiness, that ranges from 1 (not easy) to 5 (very easy). Increases in the values of the independent factors are associated with an increased easiness rating. ...