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 ...
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
628 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
vote
1answer
334 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
votes
1answer
202 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
0answers
297 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
55 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
35 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?
1
vote
0answers
35 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 ...
0
votes
0answers
11 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
100
votes
10answers
270k views

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

In particular, I am referring to the Pearson product-moment correlation coefficient.
77
votes
10answers
37k views

What is a complete list of the usual assumptions for linear regression?

What are the usual assumptions for linear regression? Do they include: a linear relationship between the independent and dependent variable independent errors normal distribution of errors ...
77
votes
4answers
217k views

How does the correlation coefficient differ from regression slope?

I would have expected the correlation coefficient to be the same as a regression slope (beta), however having just compared the two, they are different. How do they differ - what different information ...
98
votes
1answer
77k views

Interpreting plot.lm()

I had a question about interpreting the graphs generated by plot(lm) in R. I was wondering if you guys could tell me how to interpret the scale-location and leverage-residual plots? Any comments ...
54
votes
2answers
18k views

Is there a difference between 'controlling for' and 'ignoring' other variables in multiple regression?

The coefficient of an explanatory variable in a multiple regression tells us the relationship of that explanatory variable with the dependent variable. All this, while 'controlling' for the other ...

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