0
votes
1answer
214 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
45 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 ...
0
votes
0answers
48 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
27 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
11 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=\...
87
votes
10answers
246k views

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

In particular, I am referring to the Pearson product-moment correlation coefficient.
68
votes
9answers
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 ...
61
votes
4answers
173k 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 ...
84
votes
1answer
68k 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 ...
44
votes
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 ...
38
votes
4answers
33k views

Effect of switching response and explanatory variable in simple linear regression

Let's say that there exists some "true" relationship between $y$ and $x$ such that $y = ax + b + \epsilon$, where $a$ and $b$ are constants and $\epsilon$ is i.i.d normal noise. When I randomly ...
47
votes
4answers
29k 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 ...
11
votes
4answers
16k 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 ...
20
votes
4answers
938 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 ...
10
votes
4answers
590 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 ...

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