Linear Regression Quiz with Answers

Question 1

A scatter plot shows points that generally go up as $x$ increases, and they cluster fairly close to a straight line. Which statement is most accurate?

Accepted Answer

The correlation is likely positive and relatively strong (close to $+1$).

Answer

You can determine the exact value of $r$ from the picture alone.

Answer

The correlation is likely negative and relatively strong (close to $-1$).

Answer

The correlation is likely close to $0$ because the points are not exactly on a line.

Question 2

Which statement about the least squares regression line is always true?

Accepted Answer

It minimizes the sum of squared vertical residuals $\sum (y-\hat{y})^2$.

Answer

It minimizes the sum of residuals $\sum (y-\hat{y})$.

Answer

It always passes through the origin $(0,0)$.

Answer

It guarantees $r=1$ if the slope is positive.

Question 3

A least squares line is $\hat{y}=20+1.5x$. The mean of $x$ is $\bar{x}=4$. What must the mean of $y$ be (assuming this line was computed from the data)?

Accepted Answer

$\bar{y}=26$

Answer

$\bar{y}=20$

Answer

$\bar{y}=21.5$

Answer

$\bar{y}=14$

Linear Regression Quiz with Answers

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