Linked Questions

10
votes
4answers
3k views

Does the variable order matter in linear regression [duplicate]

I'm investigating interplay between two variables ($x_1$ and $x_2$). There is a great deal of linear correlation between these variables with $r>0.9$. From the nature of the problem I cannot say ...
5
votes
2answers
320 views

least square estimator of regression x onto y [duplicate]

I've been reading linear regression and least square estimator. Suppose we have i.i.d data $(x_1, y_q), (x_2, y_2), ..., (x_n,y_n)$ such that we use a linear regression model $y_i = \beta x_i + \...
2
votes
0answers
1k views

For normalized X and Y, how can the slope be equal in lm(Y~X) and lm(X~Y) [duplicate]

Lets consider normalized variables X and Y. Slope of a lm(Y~X) is Cor(Y,X)*sd(Y)/sd(X) and for ...
0
votes
1answer
1k views

Why do we use “Sum of Squared Errors” as loss function in linear regression? [duplicate]

What is a loss function? How can we relate the slope of Linear Regression with Sum of Squared Errors?
-1
votes
1answer
437 views

Are the statistical results of a linear regression affected if I swap IV and DV with each other? [duplicate]

Context: The linear regression Y = mX + c Intuitively, it seems to me that swapping the independent variable and dependent variables won't change the test statistic for the significance of the ...
1
vote
1answer
389 views

standardised random variable least square regression $X$ against $Y$, $Y$ against $X$ [duplicate]

Let $X$ and $Y$ be mean 0 and variance 1 random variables such that we choose $\alpha$ and $\beta$ to minimise $$\mathbb{E}(X-\beta Y)^2$$ and $$\mathbb{E}(Y-\alpha X)^2$$ after not so difficult ...
1
vote
0answers
328 views

Basic Linear Regression in R: Dependent and Independent Variables [duplicate]

This is probably a very basic question but I cannot find the answer after experimenting a lot with it. I am using the Davis dataset from https://vincentarelbundock.github.io/Rdatasets/datasets.html (...
0
votes
0answers
57 views

Inverse linear model doesn't seem exact inverse [duplicate]

I'm dealing with a quantity that diminishes over time from 100% to 0%. I'm trying to plot the values, a lm abline, and large indicative points where the graph intersects ...
1
vote
0answers
42 views

Regression betas of X on Y and Y on X are both less than one? [duplicate]

Intuitively, I can't really wrap my head around this. If I regress y on x and the beta is less that one, shouldn't the beta from a regression of x on y be greater than one. Mathematically, I know the ...
1
vote
1answer
37 views

Coefficient of $Y$ on $X$ and Coefficient of $X$ on $Y$ [duplicate]

Under what circumstances the coefficients from simple linear regression of $Y$ on $X$ is equal to that of $X$ on $Y$? Will it hold when the standard deviations of $X$ and $Y$ are the same? I would ...
1
vote
0answers
36 views

Regression changing of dependent variable [duplicate]

In regression model with random regressors $$y = a + bx + e$$ can I change the equation to $$x = (-a/b) + (1/b)y + (-1/b)e$$ and consistently estimate $(1/b)$ with OLS?
0
votes
0answers
12 views

How can I proot [duplicate]

if R2=0, then the slope estimator of the linear regression of Y to X is equal to the reciprocal of the slope estimator to the linear regression of X to Y
0
votes
0answers
10 views

Effect of interchanging response and predictor in linear regression [duplicate]

I'm trying to run linear regression models using the R data "Auto.csv", which has the data for miles per gallon and the displacement. Now I'm trying to run two different linear regression ...
67
votes
18answers
89k views

Statistics interview questions

I am looking for some statistics (and probability, I guess) interview questions, from the most basic through the more advanced. Answers are not necessary (although links to specific questions on this ...
101
votes
10answers
272k views

What's the difference between correlation and simple linear regression?

In particular, I am referring to the Pearson product-moment correlation coefficient.

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