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AP Statistics · Unit 2 · Exploring two-variable data · last updated

Exploring two-variable data practice questions (AP Statistics)

Unit 2 covers two-way tables and conditional distributions, scatterplots, correlation, the least-squares regression line, residuals and residual plots, influential points, and transformations to achieve linearity. Below is the one free AP Statistics question on it from our free exams, with its worked answer behind a toggle, then 7 key terms with the formulas typeset, and a door to make an AP Statistics-style paper on this unit from your own notes. The free exams are typeset PDFs with an answer key; the exam downloads without a signup.

Make a practice exam from your notes →Upload your notesAP Statistics style preselected; tick "Unit 2 · Exploring two-variable data" on the next screen. Free to try, no card.

Sample questions

The one free AP Statistics question on this unit, from the free AP Statistics Practice Exam. Each answer is behind its own toggle; the whole paper, its PDF and the full answer key are on the exam page.

  1. Question 12 marks · Regression & r-squared
    A least-squares regression of exam score on hours studied has correlation r=0.8r = 0.8. Which statement is correct?
    • A.
      80 percent of the variation in scores is explained by the regression
    • B.
      64 percent of the variation in scores is explained by the linear relationship with hours studied
    • C.
      Each extra hour of study causes a 0.8-point score increase
    • D.
      The regression predicts scores correctly 80 percent of the time
    • E.
      The residuals have correlation 0.8 with the predictor
    From the free AP Statistics Practice Exam →

Key terms

The definitions and formulas AP Statistics expects for exploring two-variable data, typeset as they appear on the paper.

Describing a scatterplot
Direction (positive or negative), form (linear or curved), strength, and unusual points, all in context. Association is not causation.
Correlation coefficient r
Measures the strength and direction of a linear relationship, between −1-1 and 11. It has no units, is unchanged by swapping xx and yy or rescaling, and is not resistant to outliers.
Least-squares regression line
The line that minimises the sum of squared residuals. Interpret the slope as the predicted change in yy per unit of xx, and the intercept as the predicted yy at x=0x = 0 (only if that makes sense in context).
y^=a+bx,b=r sysx,a=yˉ−bxˉ\hat{y} = a + bx, \qquad b = r\,\frac{s_y}{s_x}, \qquad a = \bar{y} - b\bar{x}
Residual
Actual minus predicted. A residual plot with no pattern supports a linear model; a curved pattern says the model is wrong.
residual=y−y^\text{residual} = y - \hat{y}
Coefficient of determination r-squared
The fraction of the variation in yy explained by the linear relationship with xx. Say it in that sentence, in context, on the exam.
r2=1−∑(y−y^)2∑(y−yˉ)2r^2 = 1 - \frac{\sum (y - \hat{y})^2}{\sum (y - \bar{y})^2}
Influential points and high leverage
A point far from the mean of xx has high leverage; it is influential if removing it changes the slope or correlation substantially. Outliers in yy at a typical xx mainly affect rr.
Transformations to achieve linearity
Taking the log of yy linearises exponential relationships; taking logs of both variables linearises power relationships. Fit the line to the transformed data, then back-transform predictions.
log⁡y^=a+bx  ⇒  y^=10a+bx\log \hat{y} = a + bx \;\Rightarrow\; \hat{y} = 10^{a + bx}

Frequently asked questions

Are there free exploring two-variable data practice questions for AP Statistics?

Yes. 1 question on exploring two-variable data appears in the free AP Statistics Practice Exam, and the sample questions on this page come from it with worked answers. Each exam can be read online or downloaded as a typeset PDF without signing up, and its full answer key is emailed on request.

How do I make an AP Statistics practice paper on exploring two-variable data from my notes?

Open the create page with the AP Statistics style preselected, tick "Unit 2 · Exploring two-variable data" under the units to cover (or upload your notes and slides on it), choose the question mix and time limit, and generate. You get a typeset PDF in the AP format with a separate answer key, in about a minute. It is free to try, no card needed.

What does AP Statistics expect you to know about exploring two-variable data?

Unit 2 covers two-way tables and conditional distributions, scatterplots, correlation, the least-squares regression line, residuals and residual plots, influential points, and transformations to achieve linearity. The terms to have cold: Describing a scatterplot, Correlation coefficient r, Least-squares regression line, Residual, Coefficient of determination r-squared. Each is defined below with its formula typeset where one applies.

What is the AP Statistics exam format?

The AP Statistics guide explains the papers, their timing and mark allocation, with a sample question and mark scheme and the common mistakes, and links to the generator with the AP Statistics style preselected.

Other AP Statistics topics

All AP Statistics topics · AP Statistics exam guide · All free practice exams

Make an AP Statistics paper on exploring two-variable data from your notes

Open "Pick your exam" with the AP Statistics style preselected and tick "Unit 2 · Exploring two-variable data", or upload your notes on it. You get a typeset paper in the AP format with a separate answer key.

Make a practice exam from your notes →Upload your notes