AP Statistics Least-Squares Regression and Residuals Test with Point Values (PDF)

AP Statistics math test: Least-Squares Regression and Residuals – Maths PDF

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This regression residuals test for AP Statistics covers least-squares regression and residuals (Common Core AP STAT 2.6, AP STAT 2.7, AP STAT 2.8, AP STAT 2.9, HSS-ID.B.6, HSS-ID.C.7), with a free PDF to print.

This 45-minute test covers least-squares lines, residuals, residual plots, r squared, and the cautions about extrapolation and influential points. Show your substitutions and interpret every number in context.

Time and points

About this test

Grade: AP Statistics
Chapter: Least-Squares Regression and Residuals
Standards: AP STAT 2.6, AP STAT 2.7, AP STAT 2.8, AP STAT 2.9, HSS-ID.B.6, HSS-ID.C.7
Time: 45 minutes
Total: 20 points

Regression residuals test: questions

Question 1 – Regression line [3 pts]

Hours studied and score.

The least-squares line for hours studied (x) and score (y) is $\hat{y}=49.1+3.05x$. (a) Predict the score for 7 hours. (1 point) (b) Interpret the slope. (1 point) (c) Find the residual for the point (6, 66). (1 point)

Question 2 – Interpret r squared and s [2 pts]

A regression of tip amount on bill total has r squared = 0.88 and s = $1.20. Interpret both in context.

Question 3 – Residual plot [3 pts]

A residual plot.

(a) Describe the pattern in the residual plot. (1 point) (b) Is a linear model appropriate? (1 point) (c) What does a negative residual mean? (1 point)

Question 4 – Slope from summary [3 pts]

For fuel use (y) against weight (x), r = 0.8, x-bar = 3,000, sx = 400, y-bar = 22, sy = 4. Find the slope and intercept of the regression line. (3 points)

Question 5 – Extrapolation [2 pts]

A line predicts the height of a child from age using data for ages 2 to 12: $\hat{y}=32+2.4x$. Predict the height at age 40 and comment.

Question 6 – Influential point [2 pts]

A point far from the others.

Explain why the point at (12, 4) is likely to be influential.

Question 7 – Interpret the intercept [3 pts]

A line for a gym predicts calories burned from minutes: $\hat{y}=-12+9.5x$. (a) Predict the calories for 30 minutes. (1 point) (b) Interpret the slope. (1 point) (c) The intercept is negative. Explain why it should not be interpreted literally. (1 point)

Question 8 – Compute r [2 pts]

A regression has r squared = 0.49 and negative slope. Find r and describe the association.

Key facts behind this regression residuals test

Key facts

LSRL: y-hat = a + bx, with b = r sy/sx and a = y-bar – b x-bar; it passes through (x-bar, y-bar).
Interpret the slope as the predicted change in y per unit of x, in context.
Residual = actual – predicted; a good linear model has a residual plot with no pattern.
r squared is the percent of variation in y explained by the linear model; s is the typical prediction error.
Avoid extrapolation and check for influential points.

How to use this regression residuals test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All AP Statistics chapters: AP Statistics math.

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