Two-Way Tables, Scatter Plots and Correlation: Algebra 1 Math Test Answer Key – PDF Download

Question 1: Complete a two-way table (2 points)

1. Totals: \(18+12=30\), \(42+48=90\), \(18+42=60\), \(12+48=60\), and \(30+90=120\).
2. \(\frac{30}{120}=0.25\), or 25%.

Scoring: 1 point for all five totals correct (accept one slip for half credit). 1 point for dividing the Soccer row total by 120 and getting 0.25 or 25%.

Question 2: Compare conditional frequencies (3 points)

1. \(\frac{9}{200}=0.045\), or 4.5%.
2. Bus riders: \(\frac{9}{90}=0.10\). Others: \(\frac{22}{110}=0.20\). 10% and 20%.
3. Yes. Students who do not ride the bus are late twice as often (20% versus 10%), so the two variables appear to be associated.

Scoring: 1 point for 9/200 = 0.045. 1 point for dividing by each row total (90 and 110). 1 point for stating an association with the comparison 10% versus 20%.

Question 3: Describe a scatter plot (2 points)

1. The association is negative (older laptops cost less), strong and linear.
2. r = -0.98: the points fall close to a straight line (calculated \(r\approx -0.98\)).

Scoring: 1 point for naming direction, strength and form (any two correct earn half credit). 1 point for -0.98 with a reason based on the negative direction and tight pattern.

Question 4: Line of fit and prediction (3 points)

1. Slope: \(\frac{48-30}{8-2}=\frac{18}{6}=3\). Then \(30=3(2)+b\) gives \(b=24\). y=3x+24.
2. Each extra hour of weekly practice is associated with a predicted gain of 3 words per minute.
3. \(y=3(10)+24=54\). About 54 words per minute.

Scoring: 1 point for slope 3 and intercept 24 (half credit for a correct slope only). 1 point for a statement with units and the phrase predicted change per hour. 1 point for 54.

Question 5: Compute residuals (3 points)

1. x	Actual	Predicted	Residual
   2	15	13	+2
   4	17	18	-1
   6	26	23	+3
   8	27	28	-1

2. The largest positive residual is +3, so (6, 26) is farthest above the line.

Scoring: 1 point for four correct predicted values (13, 18, 23, 28). 1 point for four correct residuals (actual minus predicted: 2, -1, 3, -1). 1 point for naming (6, 26).

Question 6: Interpret a residual plot (2 points)

1. No. The residuals form a clear arch (negative, then positive, then negative) instead of a random scatter, so the data are curved and a quadratic model is likely better.
2. The residuals would be scattered randomly above and below zero with no pattern.

Scoring: 1 point for answering no and citing the arch or non-random pattern. 1 point for describing random scatter around zero.

Question 7: Interpret the correlation coefficient (2 points)

1. The relationship is negative and strong: students who play more tend to have a lower GPA.
2. The first study. Strength depends on the distance from 0, and \(|-0.84|=0.84\) is greater than \(0.31\).

Scoring: 1 point for negative and strong. 1 point for choosing the first study using absolute values (or distance from 0), not the sign.

Question 8: Correlation and causation (2 points)

1. No. Correlation does not prove causation. Both quantities can increase because of something else.
2. The size of the fire: bigger fires need more trucks and also cause more damage.

Scoring: 1 point for no with the reason that correlation is not causation. 1 point for a reasonable lurking variable such as fire size or severity.

Question 9: Extrapolation (1 point)

\(y=-14(10)+100=-40\). A battery cannot be at -40%, so the prediction is not reasonable: 10 hours is far outside the data (0 to 6 hours), which makes it an extrapolation.

Scoring: 1 point for computing -40 and explaining that it is impossible because 10 hours is an extrapolation. Award no point for a bare calculation.

⬇ Download the Algebra 1 Two-Way Tables, Scatter Plots and Correlation test answer key (PDF, 93 KB)

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