AP Stats Regression Analysis 3

Question 1

In the regression model ŷ = b₀ + b₁x, what does b₁ represent?

Accepted Answer

The average change in y for each one-unit increase in x

Answer

b₁ is the slope, representing the estimated average change in the response variable y for each one-unit increase in the explanatory variable x.

Question 2

A researcher finds that the correlation between shoe size and reading ability in children is r = 0.78. The best explanation is:

Accepted Answer

Age is a lurking variable that increases both shoe size and reading ability

Answer

Age is a confounding (lurking) variable — older children have both larger feet and greater reading ability, creating a spurious correlation.

Question 3

In a regression context, an influential observation is best described as a point that:

Accepted Answer

Has high leverage and notably changes the regression line when removed

Answer

An influential observation has high leverage (extreme x-value) and substantially affects the slope and/or intercept when included or excluded.

Question 4

If all points in a scatterplot lie exactly on a straight line with negative slope, what is the value of r?

Accepted Answer

−1

Answer

A perfect negative linear relationship gives r = −1.

Question 5

The standard error of the slope (SE_b₁) in regression is used to:

Accepted Answer

Construct a confidence interval or conduct a t-test for the slope

Answer

SE_b₁ is used to form t-intervals and t-tests to make inferences about the true population slope β₁.

AP Practice Test