Scatter Plots - PSAT Math

Based on the scatter plot shown, what is the residual for the data point at $x = 6$ when the line of best fit has equation $y = 2x + 1$ ?
Answer: 1 For $x = 6,$ the line predicts $y = 2(6) + 1 = 13.$ The actual plotted value is 14, so the residual (actual − predicted) is 14 − 13 = 1. B gives the negative of this value, and C and D confuse the difference in location with the residual.
Based on the scatter plot shown, what is the best estimate of the y-intercept of the line of best fit?
Answer: 2 The drawn best-fit line crosses the y-axis at approximately (0,2). Therefore, the y-intercept is about 2. The other numbers do not match the visible intercept point.
The scatterplot above shows data for 10 cities, with average January temperature (°F) on the x-axis and average heating cost per household ($) on the y-axis. A line of best fit is drawn. If the data point (15, 180) is removed from the data set, which of the following is most likely to occur?
Answer: The slope becomes less negative (closer to 0) and the y-intercept decreases. The point (15, 180) lies far to the left and very high, reinforcing the negative slope and pulling the left end of the line upward. Removing it causes the left portion of the line to drop (slope becomes less steep, i.e., less negative) and because the leftmost high point is gone, the y-intercept also decreases. Choice A is the opposite. Choice C mixes directions incorrectly. Choice D ignores that removing an influential point changes slope.
The scatter plot displays plant height over time with a line of best fit given by $y = 4.5x + 32,$ where $x$ is days after planting and $y$ is height in centimeters. What does the slope 4.5 represent in this context?
Answer: The plant's height increases about 4.5 centimeters for each additional day after planting. Slope is rise over run, so 4.5 means the height (centimeters) rises 4.5 for every 1 day. B confuses slope with intercept. C inverts the units, and D confused slope with y-intercept.
The scatterplot shown represents the relationship between outdoor temperature, in °F, and the daily electricity usage, in kilowatt-hours, for a household over 20 days. Which of the following best describes the association?
Answer: Nonlinear (U-shaped) Electricity usage is high at low temperatures (heating) and high at high temperatures (air conditioning), with a minimum in the middle range. This produces a U-shaped (nonlinear) pattern. A purely linear description—positive or negative—misses the minimum at moderate temperatures. There is clearly an association, so choice D is wrong.
Based on the scatter plot above, which of the following points, if added, would most DECREASE the strength of the linear relationship?
Answer: (14, 15) The existing data show a moderate positive trend: as $x$ increases, $y$ roughly increases. Point (14, 15) lies far below the trend line at a large $x$ -value, making it a leveraged outlier that would pull the correlation downward. Points A and B fall near the present trend, while C also extends the trend upward, so they would either maintain or strengthen the correlation.
Using the scatter plot shown, which of the following predicted values is LEAST reliable because it requires the greatest amount of extrapolation beyond the data?
Answer: The value of $y$ when $x = 7$ The plotted data cover $x$ -values from 1 to 6. Predicting at $x = 7$ goes furthest beyond this range, making it the least reliable extrapolation. The prediction at $x = 0$ is also outside the data but is closer than 7. Choices B and C are within the data range and therefore interpolations.
A scientist measured the amount of fertilizer applied to 11 plants and the resulting plant height after 6 weeks. The scatterplot shows fertilizer (grams) on the $x$ -axis and height (centimeters) on the $y$ -axis. A dashed line of best fit is included. What does the slope of the line of best fit represent in this context?
Answer: The predicted increase in plant height (cm) for each additional gram of fertilizer. This question asks about the meaning of the slope in the context of fertilizer and plant height. In a scatterplot with fertilizer (grams) on the x-axis and height (cm) on the y-axis, the slope represents the change in y per unit change in x. Therefore, the slope tells us the predicted increase in plant height (cm) for each additional gram of fertilizer applied. A common error is reversing the interpretation (choice B) - remember that slope is always rise over run, or change in y over change in x. The slope does not represent a specific height value (choice C) or a total (choice D), but rather a rate of change.
The scatterplot above shows the relationship between $x$ and $y$ for 12 points. Curves A, B, C, and D are also shown. Which curve best models the data?
Answer: Curve C: $y = 8\sqrt{x}$ The data points (1, 8), (4, 16), (9, 24), (16, 32) fit $y=8\sqrt{x}$ exactly: $8\sqrt{1}=8, 8\sqrt{4}=16, 8\sqrt{9}=24, 8\sqrt{16}=32$ . Curve A (linear) underpredicts at small x and misses curvature. Curve B (parabolic upward) grows much too fast (at x=16 it predicts 129). Curve D (exponential) grows explosively (at x=16 it predicts about 1,500). Only curve C matches the concave-down, slowly increasing shape of the data.
The scatterplot shows 16 data points together with two lines: line $\ell$ is a line of best fit; line $m$ is another line. Based on the scatterplot, which statement about the sum of squared residuals is most accurate?
Answer: Line $\ell$ has a smaller sum of squared residuals than line $m$ . By definition, the line of best fit (least-squares regression line) minimizes the sum of squared residuals, so any other line — including line $m$ — has a larger sum. Choice A reverses this. Choice C contradicts the uniqueness of the least-squares line when data are not collinear. Choice D incorrectly assumes that passing through two points makes all residuals zero.
A store manager compared the price of a product to the number of units sold in 9 different weeks. The scatterplot (Price vs. Units Sold) shows a negative association. Which claim is supported by the scatterplot, without assuming causation?
Answer: Weeks with higher prices tend to be associated with fewer units sold. This question asks which claim is supported by the scatterplot of price versus units sold, without assuming causation. The plot shows a negative association, with points trending downward, meaning higher prices link to fewer units sold across the weeks. Referencing the data pattern, the supported claim is that weeks with higher prices tend to be associated with fewer units sold, emphasizing correlation over cause. This avoids overreaching into causation like choice A. Common errors include assuming causation or misinterpreting the direction as positive (choice C) or none (choice D). Another mistake is implying constancy in the relationship, ignoring variability. When evaluating scatterplots, prioritize descriptive statements about associations to distinguish them from inferential claims in data literacy.
The scatterplot displays the relationship between the length of a pendulum, $L$ , in meters, and the period, $T$ , in seconds, for 10 pendulums. Which of the following statements is best supported by the scatterplot?
Answer: As length increases, period increases, but at a decreasing rate. The scatter shows period increasing with length but with a clearly concave-down (square-root-like) shape: going from L = 0.25 to 1.0 produces a larger change than from L = 1.5 to 2.25. This indicates an increasing but decelerating relationship, consistent with $T = 2\pi\sqrt{L/g}$ . Choice A (linear) ignores the curvature. Choice C contradicts the positive trend. Choice D ignores the strong association.
The scatterplot above shows the relationship between a car's age, in years, and its resale value, in thousands of dollars, for 14 used cars. The curve of best fit is given by $V(a) = 28(0.85)^a$ . Based on the model, what is the best approximation of the percent decrease in predicted resale value per year?
Answer: $15\%$ For an exponential model $V(a)=V_0 \cdot b^a$ with $0<b<1$ , the annual percent decrease is $(1-b)\times 100\%$ . Here $1-0.85=0.15$ , or $15\%$ . Choice A misplaces the decimal. Choice C is the initial value. Choice D is the retention rate, not the decrease.
Examine the scatter plot. Which equation best models the linear relationship between the two variables?
Answer: $y \approx -3x + 40$ The points fall along a line that decreases about 3 units in $y$ for every 1 unit increase in $x$ and crosses the y-axis near 40, matching choice C. Choice A has too small a slope, B has correct intercept but wrong scale, and D has the wrong sign for the slope.
N
Answer: $28$ The predicted difference is the slope times the difference in x: $3.5(12-4) = 3.5(8) = 28$ . Choice A uses 4 sessions instead of 8. Choice C uses 12. Choice D is the predicted score at x=12 ( $3.5(12)+62=104$ ), not the difference.
Use the scatter plot above to answer the question: According to the line of best fit shown, what is the best estimate of the selling price of a 7-year-old car?
Answer: $10,000 The best-fit line descends roughly $2,000 for every additional year and crosses about $24,000 when the car is new. Substituting 7 years gives $24,000 − $2,000(7) = $10,000. The other values are either too low or too high relative to the plotted trend.
The scatterplot shown displays the number of ice cream cones sold at a beach stand on 15 summer days, with high temperature on the x-axis. The line of best fit is $y = 14x - 600$ . If the actual sales on a day with temperature 80°F was 480 cones, what is the residual for that day?
Answer: $-40$ Predicted sales: $14(80) - 600 = 1120 - 600 = 520$ . Residual = actual − predicted = $480 - 520 = -40$ . Choice B reverses the sign. Choice C is the predicted value. Choice D comes from $14 \times 80 - (-600)$ , a sign error in the intercept.
The scatterplot shows the relationship between the weight, $w$ , in pounds, of 15 adult dogs and their daily food intake, $f$ , in ounces. Based on the line of best fit shown, what is the best interpretation of the slope?
Answer: For every additional pound of body weight, predicted daily food intake increases by approximately $0.25$ ounces. Slope represents the predicted change in the response variable (food, $f$ ) per unit increase in the predictor (weight, $w$ ). The line shown has a slope of about $0.25$ ounces per pound. Choice B reverses the variables. Choice C describes the y-intercept. Choice D misinterprets slope as an average weight.
The scatterplot above shows the population, in thousands, of a bacterial colony at various times, in hours, after the start of an experiment. Which of the following functions best models the data shown?
Answer: $P(t) = 5(1.4)^t$ The data shows values approximately: (0, 5), (2, 10), (4, 19), (6, 38), (8, 75). Ratios between successive points are roughly constant (about 1.96 per 2 hours, i.e., $1.4^2 \approx 1.96$ ), indicating exponential growth with base about 1.4. Choice A describes linear growth, which would not accelerate. Choice C is quadratic: at t=8 it would give 320, far too large. Choice D is decreasing, which contradicts the data.
Based on the scatter plot shown, which statement best characterizes the relationship between daily study time and quiz score for the 12 students?
Answer: There is a strong positive linear association between the two variables. The points rise steadily from left to right, forming an upward-sloping cloud that is roughly straight, indicating a strong positive linear relationship. B is wrong because the pattern is increasing, not decreasing. C is wrong because a clear trend is visible. D is wrong because the pattern does not show noticeable curvature; it is approximately linear.

Start this quiz