Statistics & Probability Quiz: Fit Linear Models To Scatter Plots

3 questions · exam conditions

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Fit Linear Models To Scatter PlotsQuestion 1 of 3

A school club tracked how many posters they hung and how many students signed up. The scatter plot shows a positive linear association. Two representative points are marked: $(2, 18)$ and $(8, 54)$ , where $x$ is posters and $y$ is sign-ups.

Estimate the slope of a reasonable line of best fit (in sign-ups per poster).

-6

3

9

6

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Statistics & Probability Quiz

Statistics & Probability Quiz: Fit Linear Models To Scatter Plots

Practice Fit Linear Models To Scatter Plots in Statistics & Probability with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Fit Linear Models To Scatter Plots, giving you a quick way to practice the rules, question types, and explanations that matter most for Statistics & Probability.

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All questions

Question 1

Estimate the slope of a reasonable line of best fit (in sign-ups per poster).

$-6$
$3$
$9$
$6$ (correct answer)

Explanation: Fitting a linear model to a scatter plot means drawing a line that best fits the points for posters and sign-ups. The trend is positive and linear, with sign-ups rising as posters increase. Using points (2,18) and (8,54), slope is (54-18)/(8-2)=36/6=6 sign-ups per poster. The intercept would predict sign-ups with zero posters, meaningful for base interest. A slope of 6 matches the trend's steepness and scale. Misconception: negative slope for positive data, but here it's clearly upward. Check direction, calculate slope from points, and assess intercept fit.

Question 2

A car's stopping distance ( $y$ , in feet) was measured at different speeds ( $x$ , in mph). Over this limited range, the relationship appears approximately linear.

Which equation best models the relationship between speed and stopping distance?

$y=x-10$
$y=2x+10$
$y=-2x+110$
$y=2x-10$ (correct answer)

Explanation: When modeling stopping distance versus speed, physics tells us that stopping distance increases with speed, suggesting a positive relationship. If a car traveling at 20 mph has a stopping distance of about 30 feet and at 40 mph it's about 70 feet, the slope is approximately (70-30)/(40-20) = 40/20 = 2 feet per mph. The y-intercept represents stopping distance at 0 mph, which should theoretically be 0, but the model gives -10, suggesting the linear approximation works best within the measured range. The equation y=2x-10 captures the positive trend, though the negative intercept indicates this model shouldn't be extrapolated to very low speeds. A common error is expecting the intercept to always be physically meaningful - linear models sometimes work well only within the data range. Always consider whether extrapolation makes sense for the context.

Question 3

A teacher makes a scatter plot of the number of pages read (x) and the number of points earned on a reading log (y). Two representative points on a reasonable line of best fit are marked at $(10,45)$ and $(30,85)$ . Estimate the slope of a reasonable line of best fit (in points per page).

$0.5$
$2$ (correct answer)
$20$
$-2$

Explanation: Fitting a linear model involves a line through scatter plot points to show trends like earning rates. The plot of pages read (x) and points (y) is positive and linear. Given points (10,45) and (30,85), slope is (85-45)/(30-10) = 40/20 = 2 points per page. Intercept isn't directly needed but would be found by extending to x=0. The slope of 2 matches as it fits the calculated rate and scale. Misconception: inverting rise/run for too-large slopes like 20. Check direction, estimate slope from points, then find intercept if required.