Linked Questions

0 votes
1 answer
3k views

Negative correlation coefficient but positive regression coefficeint [duplicate]

In one of my research projects, I found a negative correlation between $X$ (a regressor of interest) and $Y$ (an outcome variable). In the regression model, I found that the coefficient of $X$ is ...
Rishik's user avatar
  • 1
2 votes
1 answer
2k views

Why beta sign is different than correlation sign? [duplicate]

I am trying to interpret the sign of my 5 x-variables against y-variable. The sign of some coefficients in the regression output (command: reg) are different than the signs under correlation matrix (...
Asaad's user avatar
  • 23
2 votes
1 answer
2k views

Multiple regression in R results different to simple linear regression? [duplicate]

Hi I am having trouble acquiring the final results for presentation. The results from a multiple regression are different to my results in a simple linear regression. For example, the multiple ...
Nieve K's user avatar
  • 141
0 votes
1 answer
1k views

How to explain change of sign on regression coefficient when another variable is added to OLS model? [duplicate]

I am trying to run an OLS regression, with log of per capita calorie as my dependent variable and age and years of education of household head, log per capita expenditure as my independent variables (...
Monzur's user avatar
  • 21
1 vote
2 answers
632 views

How to interpret multiple regression coefficients [duplicate]

I'm running multiple linear regression with 6 variables. For one of the variables D, the correlation coefficient between D and the response Y is - 0.34. But in the regression output, the coefficient ...
Jane's user avatar
  • 11
0 votes
0 answers
802 views

What does holding other variables fixed in a regression mean? [duplicate]

I am sorry if this sounds redundant but I couldn't find a good explanation on this anywhere else yet. I understand that controlling for a variable in a regression can be imagined by drawing separate ...
Thomas Mankiw's user avatar
0 votes
1 answer
224 views

Cox Regression - IVs have different hazard ratios when modelled alone than all together [duplicate]

I'm currently running a Cox proportional hazards analysis on my data to look at outcomes for cancer survival. I'm looking at variables such as cancer type, martial status, gender etc. For some reason ...
Nome's user avatar
  • 1
1 vote
2 answers
105 views

Simple linear regression vs Multiple Linear regression interpretation [duplicate]

Suppose we have a multiple linear regression model with two predictors, $X_1$ and $X_2$: $$Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + \epsilon.$$ We can interpret $\beta_1$ as the expected increase in $Y$...
user128422's user avatar
1 vote
0 answers
112 views

Non significant main effect after controlling for covariates [duplicate]

After doing a t-test that showed a significant difference, I did an ANCOVA with 3 covariates. The ANCOVA showed no significant effect of the variable that did show a significant difference in the t-...
user1008199's user avatar
2 votes
0 answers
53 views

Coefficient in linear regression changes drastically if additional variables are added. Why? [duplicate]

n <- 100 x2 <- 1 : n x1 <- .01 * x2 + runif(n, -.1, .1) y = -x1 + x2 + rnorm(n, sd = .01) summary(lm(y ~ x1))$coef Coefficients (all significant): (...
Make42's user avatar
  • 565
0 votes
0 answers
36 views

Interpreting coefficients in Linear Regression Y|X1, X2, X3 [duplicate]

I am trying to reconcile an apparent contradiction in the results of my regression against three independent variables $X_1,X_2, X_3 $: 1) For each of the $X_i's$, I regressed $Y|X_i $ and in every ...
MSIS's user avatar
  • 579
149 votes
9 answers
324k views

What is the difference between linear regression on y with x and x with y?

The Pearson correlation coefficient of x and y is the same, whether you compute pearson(x, y) or pearson(y, x). This suggests that doing a linear regression of y given x or x given y should be the ...
user9097's user avatar
  • 3,293
63 votes
3 answers
26k views

What is the intuition behind conditional Gaussian distributions?

Suppose that $\mathbf{X} \sim N_{2}(\mathbf{\mu}, \mathbf{\Sigma})$. Then the conditional distribution of $X_1$ given that $X_2 = x_2$ is multivariate normally distributed with mean: $$ E[P(X_1 | ...
eroeijr's user avatar
  • 631
68 votes
3 answers
134k views

What is the effect of having correlated predictors in a multiple regression model?

I learned in my linear models class that if two predictors are correlated and both are included in a model, one will be insignificant. For example, assume the size of a house and the number of ...
Vivek Subramanian's user avatar
30 votes
3 answers
19k 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 ...
EconStats's user avatar
  • 865

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