Unit 5: Regression Analysis
Statistics · Unit 5 · Paper 1

Regression Analysis 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 1Paper 2Paper 3
Each paper is built from this unit’s 45 terms and is the same for everyone, so a teacher can assign “Unit 5, Paper 1” 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 33 min 30 points0/17 attempted
1

Lurking variable

2

Extrapolation warning in slope inference

3

Residual

4

Conditions for slope inference (LINER)

5

Sum of the residuals

6

Interpreting the slope

7

Coefficient of determination r²

8

Predicting with a regression equation

9

Influential point vs outlier

10

Least-squares regression line

11

Why df = n − 2

12

Residual for a specific point

Short answer 1. Define or explain: Effect of removing an influential point

3 pts

Short answer 2. Define or explain: r is unitless and bounded

3 pts

Short answer 3. Define or explain: What r does not tell you

3 pts

Short answer 4. Define or explain: Direction, form, strength

3 pts

Free response

6 pts

A microbiology class measures the number of bacteria in a culture at the end of each of six consecutive hours. A least-squares line fit to the raw counts versus time gives r² = 0.85, but the residual plot shows a clear U-shaped pattern. The class then takes the natural logarithm of each count and refits, obtaining predicted ln(count) = 3.20 + 0.45t where t is time in hours. For the transformed data, r² = 0.996 and the residual plot shows no pattern.

A. Explain what the U-shaped residual plot for the original fit indicates, and why a high r² of 0.85 does not by itself justify the linear model.

B. Using the transformed model, predict the number of bacteria at t = 6 hours.

C. Interpret the slope of the transformed model in terms of the number of bacteria.

D. Write the transformed model as an exponential equation predicting count directly from t, and interpret the value of the constant factor.

E. Explain why the class should be cautious about using this model to predict the bacterial count at t = 48 hours.