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Analyse statistique avancée

Analyse statistique avancée

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[one answer] When looking at the residual plot, what are we looking for?

Residuals as large as possible, showing the model is learning.

Residuals that are all positive, showing the model does not underestimate.

A horizontal band of constant width, with no particular shape.

Residuals lined up along a rising line.

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[one answer] To judge whether a regression model is good, what is the procedure?

Add variables until the R² stops rising.

Compute the R²: if it is high the model is good, nothing else is needed.

Draw the cloud, fit the line, read the R², test the slope, then look at the residuals.

Check that the p-value is small, which guarantees the predictions will be right.

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[one answer] Two variables rise together very regularly. What can we conclude?

That there is no real link, since it has not been proven.

That the second causes the first.

That they are linked, without knowing why: a third variable may pull both.

That the first causes the second.

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[one answer] When may we use the line to predict?

Anywhere, provided the R² is above ninety per cent.

Inside the range of the observed values; beyond it, it is a guess.

Only at values that appear exactly in the data.

Anywhere: that is the whole point of having an equation.

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[one answer] What have you understood about R²?

The share of the variation of the explained variable that the line accounts for.

The proportion of points that fall exactly on the line.

The probability that the model gives the right answer.

The strength of the cause-and-effect link between the two variables.

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[one answer] What have you understood about the slope of a regression line?

The amount of error the model makes.

The average value of the explained variable.

How much the explained variable changes on average when the explanatory variable goes up by one unit.

The steepness of the cloud, with no unit, always between minus one and one.

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[one answer] What have you understood about the intercept?

It must always be positive, otherwise the model is wrong.

It is always the best prediction when the explanatory variable is zero.

It is the average value of the residuals.

It anchors the line; it only means something concrete if the value zero exists in the data.

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[one answer] Why draw the scatter plot when we already have the indicators?

To see the shape of the link: indicators cannot tell a line from a curve or from an outlier.

To compute the slope faster than with the formula.

To make the report nicer to read.

To check that there are enough observations.

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[one answer] A variable looks very important on its own, then its effect vanishes when another variable joins the model. Why?

Both models are wrong and the data must be collected again.

On its own it was speaking for the second variable, to which it is strongly linked.

The second model is less reliable because it has more variables.

There must be a computation error in one of the two models.

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[one answer] What have you understood about the p-value of the slope test?

The probability that the model gets its predictions wrong.

The size of the measured effect.

The probability of seeing a result at least this marked if there were in fact no link at all.

The probability that the starting hypothesis is true.

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