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 ...
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 ...
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?
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 ...
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 ...
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 (...
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 ...
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?
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 ...
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
270k views

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

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