Two-Variable Data: Models and Scatterplots Flashcards

Using the model y = −4x + 100, for what value of x does y = 0?

Answer: 25

Set 0 = −4x+100 → 4x=100 → x=25.

A scatterplot shows data points that curve upward steeply, consistent with y growing faster than any linear model. Which model is most appropriate?

Answer: Exponential

Data that curves upward and accelerates beyond linear growth is best described by an exponential model.

A dataset has the best-fit line y = 1.5x + 4. A point at x = 6 has y_actual = 11. What is the residual?

Answer: -2

Predicted: y = 1.5(6)+4 = 9+4 = 13; residual = actual − predicted = 11−13 = −2.

The scatterplot of temperature (x, °C) vs. snowfall (y, cm) shows a strong negative correlation. If x increases by 5°C, and the slope is −3, by how much does y change?

Answer: −15 cm

Change in y = slope × change in x = −3 × 5 = −15 cm.

A linear model y = 0.6x + 12 describes the relationship between monthly rainfall (x, inches) and mushroom count (y). What does 12 represent?

Answer: The predicted mushroom count when rainfall is 0 inches

The y-intercept (12) is the predicted value of y when x = 0, meaning 12 mushrooms are expected even with no rainfall.

A researcher calculates r² = 0.81 for a linear model. What percentage of the variation in y is explained by the model?

Answer: 81%

r² = 0.81 means 81% of the variation in y is explained by the linear relationship with x.

A model y = x² − 6x + 10 is fit to data. What is the minimum value of y according to this model?

Answer: 1

Complete the square: y = (x−3)²+1; minimum is 1 at x = 3.