# Linked Questions

1answer
229 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 ...
1answer
47 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 ...
0answers
51 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 ...
0answers
29 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 (...
0answers
12 views

### Question regarding the R-squared of regressors in a multiple regression [duplicate]

What is the R-squared of the regression of $X_2$ on $X_1$ if the R-squared of the regression of $X_1$ on $X_2$ is $R^2_1=0.5$? (where $X_1$ and $X_2$ are the two regressors in the regression \$Y=\...
10answers
250k views

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

In particular, I am referring to the Pearson product-moment correlation coefficient.
11answers
33k 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 ...
4answers
180k 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 ...
1answer
70k 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 ...
2answers
12k 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 ...
4answers
30k views

### Choosing between LM and GLM for a log-transformed response variable

I'm trying to understand the philosophy behind using a Generalized Linear Model (GLM) vs a Linear Model (LM). I've created an example data set below where: $$\log(y) = x + \varepsilon$$ The ...
4answers
17k views

### Why do we say the outcome variable “is regressed on” the predictor(s)?

Is there some intuitive explanation for this terminology? Why is it this way, and not the predictor(s) being regressed on the outcome? Ideally I'm hoping that a proper explanation of why this ...
4answers
1k views

### Difference between the assumptions underlying a correlation and a regression slope tests of significance

My question grew out of a discussion with @whuber in the comments of a different question. Specifically, @whuber 's comment was as follows: One reason it might surprise you is that the assumptions ...
4answers
609 views

### Is regression of x on y clearly better than y on x in this case?

An instrument used to measure the levels of glucose in a person's blood is monitored on a random sample of 10 people. The levels are also measured using a very accurate laboratory procedure. The ...
2answers
11k views

### Relationship between regressing Y on X, and X on Y in logistic regression

Correlation and linear regression are sometimes distinguished in statistics books by saying that the former is symmetric and the latter is asymmetric in the following sense: in the case of correlation,...

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