![]() ![]() The cognitive factor comprised the rating items “succinctness” and “familiarity,” whereas the affective factor reflected the ratings for “beauty” and “liking.” A higher cognitive factor predicted shorter dwelling time. Using factor analysis, we extracted two key factors of the aesthetic appeal of the texts: an affective and a cognitive factor. The results showed that the rating scores were interactively modulated by both familiarity-driven and meter-driven fluency. Aesthetic ratings of all sentences were collected afterwards, and the relationships between the ratings, levels of familiarity, meter, and eye-tracking datasets were tested. During reading, pupil sizes and eye movements were recorded. Across all four groups, the sentences moreover varied with regard to featuring or not featuring meter. Participants read four groups of short sentences in which a key predictor of aesthetic liking, i.e., familiarity, was systematically modified to four degrees. The present study investigated whether similar effects can be found in visual text processing. That unless the outcome, $y$, and predictor, $x$, variables are perfectly correlated, the fitted values, $\hat| / s_y 1.Eye-tracking parameters (fixation and pupillary responses) have been shown to be modulated by the aesthetic perception and evaluation of visual and auditory artworks (e.g., paintings, music). Sometimes, this kind of difference might be traced to charismatic and idiosyncratic teachers who you have imitated ever since you sat at their feet.ġ) The term regression comes from the fact that in the usual simple linear regression model: Nevertheless people with considerable experience and expertise have it the other way round. I was brought up to say "plot $y$ against (or versus) $x$ " and the reverse sounds singularly odd to me. Consider a related issue, the meaning of "versus". There may be no logic here, just memes passed on along in textbooks, teaching and discussions. I don't hear "regressed against" or "regressed with". I don't have a story for "on" rather than any other word that would fit. How are you going to do it? Use some or all of these variables. What are you trying to do? Predict whatever. Even if it is clear, it makes sense to mention the important things first. What often perhaps drives the sequence we use in statistical discussions is that scientifically or practically we usually have a clear idea of what we are trying to predict - it is mortality, or income, or wheat yield, or votes in an election, or whatever - while the pool of potential or actual predictors may not be so clear. Setting aside the equally interesting (or uninteresting!) question of what we call different kinds of variables.īut it seems equally valid mathematically and statistically to mention the predictors first, just as many mathematicians write mappings or functions with arguments first. I'd guess that the sequence mentioning the outcome or response before the predictors follows from conventions in writing, using words or using notation or mixing the two, all the way up to I've often used and heard this way of speaking. Ideally I'm hoping that a proper explanation of why this terminology exists will help students remember it, and stop them from saying it the wrong way around.Īs I said, I doubt that this is an explanation of why this terminology exists (perhaps only of why it persists?), but I am sure it can help students remember it. From this point of view, it would make less sense to say that $X$ is regressed on $y$ or that $y$ is regressed "against" or "with" $X$. Since $y$ is being projected on $X$, that is what I think when I hear that $y$ is "regressed on" $X$. This is a very useful interpretation of linear regression. In its core, linear regression amounts to orthogonal projection of $\mathbf y$ on (onto) $\mathbf X$, where $\mathbf y$ is the $n$-dimensional vector of observations of the dependent variable and $\mathbf X$ is the subspace spanned by the predictor vectors. Consider the following figure from The Elements of Statistical Learning by Hastie et al.: I do not know what the etymology of "is regressed on" is but here is the interpretation that I have in mind when I am saying or hearing this expression. ![]()
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