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AP Stats

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Unit 2

2.11 MC Answers and Review

7 min read•june 18, 2024

AP Statistics 📊

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Answers and Review for Multiple Choice Practice on Exploring Two-Variable Data

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⛔STOP ⛔ Before you look at the answers make sure you gave this practice quiz a try so you can assess your understanding of the concepts covered in Unit 2. Click here for the practice questions: AP Statistics Unit 2 Multiple Choice Questions.

Facts about the test: The AP Statistics exam has 40 multiple choice questions and you will be given 1 hour 30 minutes to complete the section. That means it should take you around 11 minutes to complete 5 questions. The following questions were not written by College Board and although they cover information outlined in the AP Statistics Course and Exam Description the formatting on the exam may be different.

1. After completing a research project on the correlation between AP Stats grade and ACT score, you receive the report that the r value is 1.42. What should you do with this data?

A. Establish that the two variables are strongly correlated

B. Establish that the two variables are not correlated.

C. Establish that the two variables are moderately correlated

D. Find a new statistician

Answer: Since the r value is ALWAYS between -1 and 1, there is no way that the r value could be 1.42. Hence, find a new statistician.

📄 Study AP Stat, Unit 2.5: Correlation

2. What type of chart is best for summarizing two categorical variables?

A. Two way table

B. Scatterplot

C. Dot Plot

D. Stem and Leaf Plot

Answer: When displaying two categorical variables, a two way table or a contingency table is the best option. A scatterplot is used for displaying two quantitative variables and a dot plot or stem and leaf plot is used for displaying one quantitative variable.

📄 Study AP Stat, Unit 2.2: Representing Two Categorical Variables

3. What type of variable will we see along the x-axis of a scatterplot?

A. Response Variable

B. Explanatory Variable

C. Confounding Variable

D. Individualistic Variable

Answer: The x axis (independent variable) is going to display the explanatory variable, while the y axis will show the response variable.

📄 Study AP Stat, Unit 2.4: Representing the Relationship Between Two Quantitative Variables

4. Which of the following is not a part of describing a scatterplot?

A. Form

B. Direction

C. Union

D. Strength

Answer: Form, direction and strength are the major components of describing a scatterplot. Also, unusual features is sometimes necessary when there are apparent outliers.

📄 Study AP Stat, Unit 2.4: Representing the Relationship Between Two Quantitative Variables

5. What value from a computer output will tell us how strongly the points follow a linear correlation?

A. S

B. Slope

C. r-value

D. R^2 Value

Answer: The r value is the number we will use to determine the strength of our correlation. The closer the r value is to 1 or -1, the stronger linear correlation our scatterplot has.

📄 Study AP Stat, Unit 2.5: Correlation

6. In a linear regression model, which variable is predicted?

A. r-value

B. x-value

C. y-value

D. z-value

Answer: The y value is always the predicted part of our linear regression model. To show this in your work, be sure to put a hat over your y to indicate that it is a prediction.

📄 Study AP Stat, Unit 2.6: Linear Regression Models

7. What is the term for when a linear regression model gives us data within a certain range and we use that data to make a prediction for an x value outside of that range?

A. Extrapolation

B. Intrapolation

C. Interpolation

D. Hyperpolation

Answer: Extrapolation is when we take a set of x values and use them to make a prediction outside of that particular domain of x values.

📄 Study AP Stat, Unit 2.6: Linear Regression Models

8. When looking at a residual plot for a linear pattern, what should we see?

A. A parabolic pattern

B. A curved pattern

C. A linear pattern

D. No apparent pattern

Answer: When looking at a residual plot for a linear model, a good linear pattern would show no apparent pattern and an equal scatter of points above and below 0.

📄 Study AP Stat, Unit 2.7: Residuals

9. What does a positive residual value tell us?

A. The actual data value was lower than the prediction from our linear regression model.

B. The actual data value was higher than the prediction from our linear regression model.

C. The actual data value was equal to the prediction from our linear regression model.

D. Our predicted value was a very good prediction based on other points.

Answer: Since the formula for residuals is actual-predicted, a positive residual would tell us that the actual data point is higher than the predicted data point.

📄 Study AP Stat, Unit 2.7: Residuals

10. If the slope of our regression equation is -0.23, what does this tell us about the r value of our model?

A. It is 0.23

B. It is weak

C. It is moderate

D. It is negative

Answer: The signs of our slope always match the sign of our correlation coefficient since both indicate the direction of our model, either positive or negative.

📄 Study AP Stat, Unit 2.5: Correlation

11. Which of the following would be a correct interpretation of a slope of 1.42?

A. As the x value increases by 1, the y value is predicted to increase by 1.42.

B. If our x value is 0, then the predicted y value is 1.42.

C. There is 1.42 x value for every 1 y value.

D. The line increases by 1.42.

Answer: Our slope interpretation is rise over run. As the run increases by 1 (value), our y increases by whatever the slope is. Also, since we are talking about a regression model, this is a prediction.

📄 Study AP Stat, Unit 2.6: Linear Regression Models

12. What is the best way to determine if a point is an outlier from a linear regression model?

A. It has a large residual

B. It has a large x value

C. It has a large y value

D. It doesn't fit

Answer: The best way to show that a point is an outlier is to show that it has a large residual. A point could have a large x or y value but still fall in line with the linear pattern and therefore not really be an outlier.

📄 Study AP Stat, Unit 2.6: Linear Regression Models

13. A study is conducted to determine the effectiveness of different types of fertilizer on grass in the Midwest. Which of the following is the response variable?

A. Fertilizer types

B. Location

C. Rainfall

D. Growth of grass

Answer: The grass growth is our response variable since it responds to the fertilizer (which is our explanatory variable).

📄 Study AP Stat, Unit 2.4: Representing the Relationship Between Two Quantitative Variables

14. Which algebraic process is often used for nonlinear models to transform our data to make it fit a linear pattern?

A. Natural log all x values

B. Natural log all y values

C. Square root all x and y values

D. Scale every value by 10 points

Answer: If we take the natural log of each y value, it often takes nonlinear data and transforms it to a more linear pattern.

📄 Study AP Stat, Unit 2.9: Analyzing Departures from Linearity

15. Which of the following gives a generic interpretation of an R^2 value?

A. There is an R^2% probability that the line contains any given actual data point.

B. R^2% of the points in our data set fall on the linear pattern.

C. R^2% of the variation in (y-value) is explained by its linear relationship with (x-value).

D. For any given sample size, approximately R^2% of the points can be predicted with the linear model calculated.

Answer: The coefficient of variation tells us how much of the variation in our response variable can be explained by our linear model. This is why the R^2 value is often also used to determine how well a model fits a linear relationship and is directly related to the r value.

📄 Study AP Stat, Unit 2.8: Least Squares Regression

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