Algebra 1 Scatter Plots, Lines of Fit and Two-Way Tables Test Solutions and Scoring (PDF)

The points rise from left to right and lie close to a line.

Strong positive association

Scoring: 1 point for the direction; 1 point for the strength.

Slope: \(\frac{32 – 12}{6 – 1} = 4\). Then \(12 = 4(1) + b\), so \(b = 8\).

\(y = 4x + 8\)

Scoring: 1 point for the slope; 1 point for the equation.

Slope 4: the model predicts 4 more push-ups for each additional week.

Intercept 8: the predicted number of push-ups before training begins (0 weeks).

4 push-ups per week; 8 at the start

Scoring: 1 point for each interpretation in context.

Predicted: \(4(3) + 8 = 20\). Residual: \(23 – 20 = 3\).

Predicted 20; residual 3

Scoring: 1 point for the prediction; 1 point for the residual.

(a) Close to -1: a strong negative linear relationship.

(b) Close to 0: a weak positive linear relationship.

strong negative; weak positive

Scoring: 1 point for each description.

No. Larger fires lead to more fire trucks being sent, and larger fires cause more damage. The size of the fire is a lurking variable, so the correlation does not show causation.

Scoring: 1 point for answering no; 1 point for a lurking variable explanation.

a) \(\frac{40}{100} = 40\%\).

b) \(\frac{50}{100} = 50\%\).

c) \(\frac{30}{40} = 75\%\).

40%; 50%; 75%

Scoring: 1 point per part.

a) Predicted: \(3, 5, 7\).

b) Residuals: \(4 – 3 = 1\), \(4 – 5 = -1\), \(9 – 7 = 2\).

c) The largest absolute residual is 2, at \((3, 9)\).

3, 5, 7; 1, -1, 2; (3, 9)

Scoring: 1 point per part.

At \(x = 40\): \(0.5(40) + 10 = 30\), which is within the data range, so it is reasonable (interpolation).

At \(x = 200\): this is far outside the data (extrapolation), so the prediction may not be reliable.

x = 40 reasonable (30); x = 200 unreliable

Scoring: 1 point for each correct judgment with a reason.