Statistics · Unit 2 · Paper 3

Exploring Two-Variable Data unit test

A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.

Paper 1 Paper 2 Paper 3

Each paper is built from this unit’s 19 terms and is the same for everyone, so a teacher can assign “Unit 2, Paper 3” and every student sits the identical test. Multiple choice is marked objectively; the written sections you mark yourself against the model answer and rubric.

Suggested time 37 min 34 points0/17 attempted

Coefficient of determination r²

Why r² is not r squared conceptually

Interpreting the slope

Residual

Interpreting the y-intercept

Influential point vs outlier

Transforming to achieve linearity

Choosing a transformation

What r does not tell you

Explanatory vs response variable

Describing a scatterplot

Extrapolation

Short answer 1. Define or explain: Residual plot

3 pts

Short answer 2. Define or explain: Least-squares regression line

3 pts

Short answer 3. Define or explain: Predicting with a regression equation

3 pts

Short answer 4. Define or explain: Effect of removing an influential point

3 pts

Free response

10 pts

A teacher records the number of hours studied (x) and the final exam score (y) for a random sample of 24 students. Least-squares regression gives ŷ = 55 + 4.2x with r = 0.8 and SE(slope) = 0.67.

Interpret the slope in context, and calculate and interpret r² in context.

One student studied 5 hours and scored 80. Calculate and interpret the residual for this student.

State hypotheses and carry out a t-test for the slope at α = 0.05, reporting the test statistic, degrees of freedom, P-value, and a conclusion in context.

Construct a 95% confidence interval for the slope, interpret it in context, and state the conditions required for inference about a regression slope.