Two-Variable Data: Models and Scatterplots Flashcards

A scatterplot shows the relationship between hours studied (x) and test score (y). The line of best fit is y = 4.2x + 52. What does the slope 4.2 represent?

Answer: For each additional hour studied, the predicted test score increases by 4.2 points

The slope represents the rate of change: each 1-unit increase in x produces a 4.2-unit increase in predicted y.

The line of best fit for a dataset is y = −3x + 90. Which of the following best describes the relationship between x and y?

Answer: As x increases, y decreases

A negative slope means y decreases as x increases.

A scatterplot has the line of best fit y = 2.5x + 10. Using the model, what is the predicted value of y when x = 8?

Answer: 30

Substitute x = 8: y = 2.5(8) + 10 = 20 + 10 = 30.

A data set about advertising spending (x, in thousands) and sales (y, in thousands) has the line of best fit y = 5x + 20. What does the y-intercept 20 represent in context?

Answer: Predicted sales when advertising spending is $0

The y-intercept is the predicted value of y when x = 0, i.e., sales with no advertising.

A scatterplot of temperature (x, °F) and ice cream sales (y, dollars) shows a strong positive correlation. Which value of r is most consistent with this description?

Answer: 0.87

A strong positive correlation corresponds to r close to +1, so 0.87 is correct.

The table shows values of x and y. Which type of model best fits the data: x: 1, 2, 3, 4; y: 3, 9, 27, 81?

Answer: Exponential

The y values are multiplying by 3 each step (ratio is constant), which is characteristic of an exponential model.

A researcher plots data and finds the residuals are randomly scattered around zero with no pattern. What does this indicate?

Answer: The chosen model is a good fit for the data

Randomly scattered residuals around zero indicate that the model captures the underlying trend well without systematic error.