Correlation and Regression Test Answer Key with Scoring – Algebra 1

Question 1 Two-Way Table (3 points)

1. 39 ÷ 120 = 0.325 (32.5%).
2. 54 ÷ 120 = 0.45 (45%).
3. 27 ÷ 60 = 0.45 (45%).

Scoring: 1 point per part.

Question 2 Heart Rate and Workouts (3 points)

1. Negative and strong: more workout time goes with a lower heart rate, and the points hug the line.
2. Each extra hour of workout per week is associated with a resting heart rate about 1.9 beats per minute lower.
3. −1.9(5) + 78.3 = 68.8, about 69 beats per minute.

Scoring: 1 point per part.

Question 3 Find Residuals (2 points)

1. Predicted: 2.5(6) + 10 = 25. Residual: 28 − 25 = +3.
2. Predicted: 2.5(10) + 10 = 35. Residual: 31 − 35 = −4.

Scoring: 1 point per part.

Question 4 Interpret a Correlation Coefficient (2 points)

1. A strong negative linear relationship: as x rises, y tends to fall, and the value is close to −1.
2. Correlation alone does not prove cause. A lurking variable might affect both, so only an experiment could show that x causes the decrease.

Scoring: 1 point per part.

Question 5 Line Through Two Points (3 points)

1. (50 − 14) ÷ (8 − 2) = 6. Each extra guest adds $6.
2. 14 = 6(2) + b, so b = 2: y = 6x + 2.
3. 6(12) + 2 = $74.

Scoring: 1 point per part.

Question 6 Residual Plot (2 points)

1. Yes, a linear model is appropriate.
2. The residuals are scattered above and below 0 with no pattern, and they are small.

Scoring: 1 point per part.

Question 7 Correlation and Causation (3 points)

1. A moderate positive linear relationship: students who eat breakfast tend to have higher scores.
2. No. The study shows association, not cause and effect.
3. For example family income, sleep or study habits could affect both breakfast and scores.

Scoring: 1 point per part.

Question 8 Compare Two Models (2 points)

Sum of squares: A = 16 + 1 + 4 + 9 = 30; B = 1 + 4 + 1 + 4 = 10.

Model B fits better because its sum of squared residuals is smaller.

Scoring: 1 point for both sums, 1 point for the conclusion.