Take this Exam: AP Statistics — exploring data | Zestly

Question 1

Which statement about the correlation coefficient $r$ is true?

Accepted Answer

$r$ measures the strength and direction of a LINEAR association, and nothing else

Answer

An $r$ of $0$ shows that the two variables are unrelated

Answer

An $r$ of $0.9$ shows that changes in the explanatory variable cause the changes in the response variable

Answer

Converting both variables from centimetres to inches would change the value of $r$

Question 2

A least-squares line predicting the height of a sapling in centimetres from its age in years is $\hat{y} = 2 + 0.5x$. Which interpretation is correct?

Accepted Answer

Each additional year of age is associated with a predicted increase of $0.5$ centimetres in height

Answer

A sapling is predicted to be $0.5$ centimetres tall when newly planted

Answer

A sapling is predicted to reach a total height of $2.5$ centimetres

Answer

A sapling of any age is predicted to be $2$ centimetres tall

Question 3

A straight line is fitted to a set of paired measurements. Plotting the residuals against the explanatory variable gives a clear U shape: negative in the middle of the range and positive at both ends. What does that indicate?

Accepted Answer

The relationship is not linear, so a straight line is the wrong model even if it fits tolerably well by other measures

Answer

The fit is excellent, since the positive and negative residuals balance out

Answer

The data set contains influential points, which should be removed before refitting

Answer

The residuals are too widely spread, so more observations are needed

Question 4

A least-squares model fitted to a set of paired measurements gives $r^2 = 0.81$. What does that figure report?

Answer

That the correlation between the two variables is $0.81$

Answer

That the slope of the fitted line is $0.81$

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That $81\%$ of the variation in the response variable is accounted for by its linear relationship with the explanatory variable

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That there is an $81\%$ probability the linear model is the correct one

Question 5

Two points are added to a data set on which a least-squares line has been fitted. One sits near the middle of the range of $x$ but far from the line; the other sits far out at the high end of $x$, close to where the line would run. Which is influential, and what makes it so?

Answer

The first, because a point far from the line always has the greater effect on the fitted line

Answer

The second, because an extreme $x$-value gives a point leverage: the line is pulled towards it, and removing it would visibly change the slope

Answer

Neither, since a single point cannot alter a least-squares fit computed from the whole data set

Answer

Both equally, since influence depends only on how far a point lies from the centre of the data in any direction