AP Stats 5A-5B Day 1 FRQ Practice with Scoring GuideAP Stats 5A-5B Day 1 FRQ Practice with Scoring Guide

FRQ Practice: Scatterplots, Correlation &

Regression Lines

Scatterplots Describing (DFSU) Correlation r Prediction Residuals Slope & intercept

Before you start: every answer needs context (the variable names and who was measured). Slope, intercept and

prediction interpretations need the word predicted. For "describe," cover direction, form, strength and unusual

features.

FRQ 1 · Screens and sleep 5A · scatterplots and correlation

A high school counselor asked 19 randomly chosen students how many hours they spent looking at screens on a

school night, and how many hours they slept that night. The results are shown in Figure 1.

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Screen time on a school night (hours)

Sleep (hours)

Figure 1. Screen time and sleep for 19 students on one school night.

a. Identify the explanatory variable and the response variable.

b. Describe the relationship between screen time and sleep for these students.APS TAT ISTICS · UNIT5 · 5AAND5BD AY 1Five stimulus-based free-response questions, built like the Alternate Examples in the 5A and 5B Day 1 slides. Each has a context, a graph, and several parts. Work them on paper first. The scoring guide starts after FRQ 5.

c. The correlation for all 19 students is r = −0.52. Interpret this value.

d. One student reported 1.0 hour of screen time and 5.2 hours of sleep. If this student is removed, will the correlation get closer to −1, closer to 0, or stay the same? Explain.

e. A parenting blog uses these data to claim that "cutting screen time will make teenagers sleep more." Do the data support this claim? Explain.

FRQ 2 · Hot days, cold drinks 5B Day 1 · prediction, residuals, slope, intercept

The owner of a café recorded the day's high temperature (in °F) and the number of iced coffees sold on 15 randomly selected summer days (temperatures from 58°F to 94°F). The regression line for predicting sales from temperature is ŷ = −59.84 + 1.792x, and the correlation is r = 0.979.

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High temperature (°F)

Iced coffees sold

Figure 2. High temperature and iced coffees sold on 15 summer days, with the regression line ŷ = −59.84 + 1.792x. a. Interpret the correlation.

b. Define the variables ŷ and x in context.

c. Interpret the slope of the regression line.

d. Does the y intercept have meaning in this context? If so, interpret it. If not, explain why. e. On one day the high was 70°F and the café sold 63 iced coffees. Calculate and interpret the residual for this day.

f. The owner wants to use this line to plan for a 40°F day in December. Should she? Explain.

FRQ 3 · Coffee cools down 5A form + 5B Day 1 prediction

A student poured a cup of coffee in a room kept at 72°F and measured its temperature every 5 minutes for an hour. The correlation between time and temperature is r = −0.94. The student fit the line ŷ = 157.41 − 1.546x, where ŷ is the predicted temperature (°F) and x is minutes since pouring.

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Time since poured (minutes)

Temperature (°F)

Figure 3. Temperature of a cup of coffee every 5 minutes, with the regression line ŷ = 157.41 − 1.546x. a. Describe the relationship between time and temperature.

b. The student says, "r = −0.94 is really strong, so the relationship must be linear." Explain why this reasoning is flawed.

c. At 0 minutes the coffee was 180°F. Calculate and interpret the residual.

d. Use the line to predict the temperature 120 minutes after pouring. Explain why this prediction can't be trusted. Give two reasons.

FRQ 4 · One student changes everything 5A outliers & units · 5B Day 1

A keyboarding teacher recorded weekly practice (hours) and typing speed (words per minute) for 13 students. Student M practiced 18 hours per week and types 44 words per minute. For all 13 students, r = 0.409. Without Student M, r = 0.953, and the regression line for the other 12 students is ŷ = 28.40 + 3.816x. 0 5 10 15 20

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Practice (hours per week)

Typing speed (words per minute)

Student M

line for the other 12

Figure 4. Weekly practice and typing speed for 13 students. The line ŷ = 28.40 + 3.816x was fit to the 12 students other than Student M (red).

a. Describe how Student M is unusual compared with the rest of the data.

b. Explain why removing Student M changes the correlation so much.

c. Interpret the slope of the line for the 12 students.

d. A student (not Student M) who practices 5 hours per week types 52 words per minute. Calculate and interpret the residual.

e. Suppose practice had been recorded in minutes per week instead of hours. Would the correlation change? Would the slope change? Explain.

FRQ 5 · Build it yourself 5A–5B Day 1 · construct, describe, predict

Ten students in an AP Statistics class reported how many hours they studied for a test and the score they earned (out of 100).

Hours studied 0.511.522.533.544.5 5

Test score 62 65 64 72 70 78 75 84 85 88

Grid for part (a). Choose your own scales and labels.

a. Construct a scatterplot of the data on the grid above.

b. Describe the relationship between hours studied and test score.

c. Use technology to find the correlation r, then interpret it.

d. The regression line is ŷ = 57.93 + 5.952x. Interpret the slope.

e. Calculate and interpret the residual for the student who studied 3.5 hours.

f. Based on this study, can we conclude that studying an extra hour will cause a student's score to go up? Explain.

Model answers and how each part is scored

FRQ 1 · Screens and sleep

(a) Explanatory: screen time on a school night (hours). Response: hours of sleep that night.

E Both variables named correctly, in context.

P Variables swapped, or only one named.

(b) For most of these 19 students there is a strong, negative, linear relationship between screen time and hours of

sleep. One student is an outlier: about 1 hour of screen time but only 5.2 hours of sleep, far less than the pattern

suggests.

E Direction, form, strength and the outlier, all in context.

P Three of the four, or all four but no context.

I Two or fewer.

(c) r = −0.52 indicates a moderate, negative linear association between screen time and sleep for these 19 students.