Take a look at this multiple choice question from the Open University BSc on psychology. Can you tell what is wrong with it. This is sampled from a set of 15 questions, some of the others aren't this bad, some are guessing the teachers password. One of the questions requires that you know that statistically significant means p<0.05 and can look at a table of p values and say which numbers are less than 0.05.

An educational psychologist believes that an individual's reading speed (in words per minute) and general comprehension abilities (scored out of 10) may be related to how well they do on a timed exam. To study the relative importance of these variables and the association between them, she runs a multiple regression and produces the following predictive model for exam score:

Exam Score =7.78 + (0.05*Reading Speed)+(5.77*Comprehension)

What exam score would you expect students to achieve if they have a reading speed of 120 w.p.m and a comprehension score of 5?
Select one:
o 4726
o 55.67
o 66.44
o 42.63

What level of understanding is necessary to fully understand the question?

From a mathematicians perspective, Multiple linear regression is an algorithm based on variational calculus (Optimizing over a space of functions), to select the function that maximizes the probability density that a model consisting of a linear function from the vector space $R^{3}$ to $R$ plus a Gaussian random variable (with arbitrary standard deviation, that term happens to cancel out) assigns to the observed data. This involves function spaces, matrix inversions, multivariate integrals ect. To understand the mathematical structure that leads up to multivariate regression, you need the idea of jacobians and vector calculus just to integrate your $e^{- \frac{1}{2} x^{2}}$ to find the normalizing constant on your Gaussian random variables. You need continuus probability spaces, but probability isn't defined over arbitrary sets of real numbers, so you need sigma algebras, which brings you to set theory. You need to prove that the integrals exist, that the optimum slope exists and is unique, ect.

In short you need to understand a lot of maths to deeply understand what is going on.

How much understanding do you need to get the answer right. Suppose you have basic English comprehension, but all you know about the symbols "385+*)" is that they are some mysterious code that you can t...

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