AP Statistics Quiz: Linear Regression Models

What this quiz covers

This quiz focuses on Linear Regression Models, giving you a quick way to practice the rules, question types, and explanations that matter most for AP Statistics.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. For each additional year of age, the predicted weekly streaming time decreases by about 0.15 hours, on average, for users like those sampled. (correct answer)
2. If a user gets 1 year older, that causes their weekly streaming time to drop by exactly 0.15 hours.
3. At age 0, the model predicts 18 hours per week, so newborns would typically stream about 18 hours weekly.
4. A 120-year-old is predicted to stream $18.0-0.15(120)$ hours per week, and this prediction is as reliable as those for ages 13–62.
5. The intercept 18.0 means that 18% of users stream each week.

Question 2

1. For each additional gram of fertilizer, the predicted plant height increases by about 0.48 cm, on average, for plots like those observed. (correct answer)
2. Applying one more gram of fertilizer causes every plant to grow 0.48 cm taller than it otherwise would.
3. If 0 grams of fertilizer are applied, the plant height will be exactly 12.4 cm.
4. At 200 grams of fertilizer, the model can be used to predict plant height accurately because regression lines work for any $x$.
5. The intercept 12.4 means fertilizer explains 12.4% of plant height.

Question 3

1. For each 1°C increase in water temperature, the predicted dissolved oxygen decreases by about 0.18 mg/L, on average, for sites like those measured. (correct answer)
2. Raising the temperature by 1°C causes dissolved oxygen to decrease by exactly 0.18 mg/L at every site.
3. At 0°C, dissolved oxygen will be exactly 12.1 mg/L, so the model is accurate for freezing conditions.
4. Because the slope is negative, higher temperatures and dissolved oxygen are independent.
5. The intercept 12.1 means 12.1% of the sites had 0 dissolved oxygen.

Question 4

1. If a student studies 0 hours, the model guarantees the student will score exactly 58.2 points.
2. For each additional hour studied, the predicted exam score increases by about 4.1 points, on average, for students similar to those in the data. (correct answer)
3. Because the slope is positive, studying an extra hour causes every student's score to increase by 4.1 points.
4. A student who studies 20 hours is predicted to score $58.2+4.1(20)$ points, so the model is accurate for any study time.
5. About 58.2% of the variation in exam scores is explained by study hours.

Question 5

1. A house that is 0 square feet would be predicted to sell for $95{,}000, so the model is unrealistic and cannot be used at all.
2. For each additional 100 square feet of size, the predicted selling price increases by about $8{,}700$, on average, for houses like those observed. (correct answer)
3. Increasing a home's size by 100 square feet causes the selling price to increase by $8{,}700$ for every home.
4. A 3500-square-foot house (x = 35) is predicted to sell for $95+8.7(35)$ thousand dollars, so the model should be used for any home size.
5. The intercept 95 means most houses in the neighborhood are about $95{,}000$.

Question 6

1. Each additional mile from the city center is associated with a decrease of about $42 in the predicted monthly rent, on average, for apartments like those observed. (correct answer)
2. Moving an apartment 1 mile farther from the city center causes the rent to drop by $42.
3. At 0 miles from the city center, every apartment will rent for exactly $1850.
4. An apartment 40 miles away is predicted to rent for $1850-42(40)$, so the model is valid far beyond the observed distances.
5. The intercept 1850 means the average rent of all apartments in the city is $1850.

Question 7

1. Increasing a school's average class size by 1 student will cause the school's average test score to drop by 3.5 points.
2. For each additional student in average class size, the predicted average test score decreases by about 3.5 points, on average, for schools like those studied. (correct answer)
3. Because the intercept is 610, a school with 0 students per class would score 610 points, and this is a reliable prediction.
4. The equation shows that smaller classes are the only reason some schools have higher scores.
5. Since the slope is negative, the correlation must be $r=0$.

Question 8

1. For each additional 1,000 cars per day (within 10–60 thousand), the predicted ozone level increases by about 1.1 ppb, on average. (correct answer)
2. If traffic volume is 0, then the ozone level will be 18 ppb.
3. An increase of 1.1 ppb in ozone causes traffic volume to increase by 1,000 cars per day.
4. Because the slope is positive, increasing traffic causes ozone to increase by 1.1 ppb for every additional 1,000 cars.
5. At 100 thousand cars per day, the model predicts 128 ppb, so it is appropriate to use the model at 100 thousand cars per day.

Question 9

1. For each additional 1,000 pounds of vehicle weight, the predicted highway fuel economy decreases by about 5.2 mpg, on average, for cars like those in the study. (correct answer)
2. Reducing a car's weight by 1,000 pounds will cause its highway mpg to increase by exactly 5.2 for every car.
3. A car that weighs 0 pounds would be predicted to get 46.0 mpg, and that prediction is meaningful because it comes from the model.
4. Because the slope is negative, there is no relationship between weight and mpg.
5. The intercept 46.0 means that 46% of cars get 0 mpg when weight is 0.

Question 10

1. Each additional customer served is associated with an increase of about $0.62 in the predicted total tips for that hour, on average, for shifts like those observed. (correct answer)
2. Serving one more customer causes tips to increase by exactly $0.62 every hour.
3. If 0 customers are served, the server will earn exactly $8.50 in tips.
4. A shift with 120 customers can be predicted accurately using the model since the relationship is linear.
5. The intercept 8.5 means most hours have about 8.5 customers.

Question 11

1. For each additional hour of discharge time, the predicted operating temperature increases by about 2.1°C, on average, for batteries with discharge times 1.5–8.0 hours. (correct answer)
2. Increasing discharge time by 1 hour causes the operating temperature to rise by exactly 2.1°C for every battery.
3. A battery with 0 hours of discharge time will have an operating temperature of exactly 26.5°C, so the model is accurate at $x=0$.
4. Because the intercept is 26.5, the temperature cannot go below 26.5°C.
5. The model predicts the temperature at 20 hours discharge time with the same reliability as within 1.5–8.0 hours.

Question 12

1. For each additional hour studied, the predicted quiz score increases by about 6.5 points, on average, for students with study times similar to those observed. (correct answer)
2. If a student studies 0 hours, the model proves the student will score exactly 52 points on the quiz.
3. Because the slope is positive, studying an extra hour causes quiz scores to increase by 6.5 points for any student.
4. A student who studies 10 hours is predicted to score $52+6.5(10)=117$ points, so the model is accurate for any number of hours.
5. About 6.5% of quiz score is explained by hours studied because the slope is 6.5.

Question 13

1. For each additional page read, the predicted quiz score increases by about 0.35 points, on average, for students with page counts similar to those observed. (correct answer)
2. A student who reads 0 pages will score exactly 58 points on the quiz.
3. Reading 10 more pages causes a student's quiz score to rise by 3.5 points, so increasing reading will always improve scores.
4. If a student reads 200 pages, the model can be trusted to predict the quiz score because the relationship is linear.
5. The slope 0.35 means 35% of the variation in quiz scores is explained by pages read.

Question 14

1. When the temperature is 0°F, the model shows the booth will sell exactly 120 fewer bottles than usual.
2. For each 1°F increase in temperature, the predicted number of bottles sold increases by about 4.1 bottles, on average, for days like those observed. (correct answer)
3. Raising the temperature by 1°F causes bottle sales to increase by 4.1 bottles for any day.
4. Because the intercept is negative, the linear model is invalid and cannot be used for prediction within 60°F to 92°F.
5. At 100°F the booth will sell $-120+4.1(100)=290$ bottles, so the model is reliable for all temperatures.

Question 15

1. Each additional absence is associated with a decrease of about 2.4 percentage points in the predicted final grade, on average, for students like those observed. (correct answer)
2. A student with 0 absences will definitely earn exactly 93% in the course.
3. Reducing absences by 1 causes the final grade to increase by 2.4 percentage points for every student.
4. A student with 30 absences is predicted to earn $93 - 2.4(30) = 21\%$, so the model should be used for any absence count.
5. Because the slope is negative, there is no relationship between absences and final grade.

Question 16

1. For each additional minute on the treadmill, the predicted post-test heart rate increases by about 5.2 beats per minute, on average, for students like those observed. (correct answer)
2. If a student runs 0 minutes, the model proves the heart rate will be exactly 78 bpm after the test.
3. Running one extra minute causes a student's heart rate to increase by 5.2 bpm, so the relationship is causal.
4. The intercept 78 means the average resting heart rate of all students is 78 bpm.
5. A 30-minute treadmill time can be predicted accurately using the model because the regression line is linear.

Question 17

1. Spending an additional $100 on advertising is associated with an increase of about $0.32 thousand in predicted weekly sales, on average, for weeks like those observed. (correct answer)
2. Because the slope is 0.32, increasing advertising by $100 causes weekly sales to rise by exactly $320 for every week.
3. If advertising spending is $0, weekly sales will be exactly $4.6 thousand, and this is a reliable prediction.
4. The model guarantees that sales cannot ever be below $4.6 thousand because the intercept is 4.6.
5. Since the line fits the data, the model is accurate for predicting sales at $x=100$ (i.e., $10,000) hundreds of dollars.

Question 18

1. An additional minute of aerobic exercise per week is associated with about a 0.06 bpm decrease in the predicted resting heart rate, on average, for adults like those sampled. (correct answer)
2. If someone exercises 0 minutes per week, their resting heart rate must be exactly 78 bpm.
3. Exercising 1000 minutes per week would be predicted to produce a negative resting heart rate, so the model proves exercise is harmful.
4. Because the slope is negative, increasing exercise causes resting heart rate to decrease by 0.06 bpm for everyone.
5. The intercept 78.0 means 78% of the variation in resting heart rate is explained by exercise time.

Question 19

1. For each additional minute of weekly aerobic exercise, the predicted resting heart rate decreases by about 0.06 beats per minute, on average, for clients like those in the data. (correct answer)
2. If a client does 0 minutes of exercise per week, the client will have a resting heart rate of exactly 78.4 bpm.
3. Increasing weekly exercise by 10 minutes causes resting heart rate to drop by 0.6 bpm.
4. Because the slope is negative, the relationship must be nonlinear.
5. The model says 78.4% of resting heart rate is explained by exercise time.

Question 20

1. For each additional hour studied per week, the predicted quiz score increases by about 3.2 points, on average, for students with study times like those in the data. (correct answer)
2. If a student studies 0 hours per week, the model proves the student will score exactly 58 points.
3. Studying an extra hour per week causes quiz scores to increase by 3.2 points.
4. A student who studies 20 hours per week will definitely score $58+3.2(20)=122$ points because the line gives the exact score.
5. About 3.2% of the variation in quiz scores is explained by study time.