--- title: "AP Statistics Unit 5 Practice Test" description: "A timed AP Statistics Unit 5 (Regression Analysis) practice test in the AP format, drawn from 951 multiple-choice questions and 4 FRQs written for the unit. The standard version takes about 88 minutes." canonical: "https://fiveable.me/ap-stats/unit-test/5" type: "unit-test" subject: "AP Statistics" unit: "Unit 5" --- # AP Statistics Unit 5 Practice Test ## Overview A timed AP Statistics Unit 5 (Regression Analysis) practice test in the AP format, drawn from 951 multiple-choice questions and 4 FRQs written for the unit. The standard version takes about 88 minutes. ## Test Format - 20 Multiple Choice Questions (43 minutes) - 1 FRQ – FRQ 2 – Multi-Focus on Practices 3 and 4 (23 minutes) - 1 FRQ – FRQ 4 – Multi-Focus on Practices 2, 3, and 4 (23 minutes) ## Unit FRQs by Type - [FRQ 2 – Multi-Focus on Practices 3 and 4](/ap-stats/frqs/frq-2?unit=5): 2 questions - [FRQ 4 – Multi-Focus on Practices 2, 3, and 4](/ap-stats/frqs/frq-4?unit=5): 2 questions ## Practice Questions ### Question 1 **Regression Model for Study Time and Assessment Score** > For a sample of 40 students, a least-squares regression model was used to predict assessment score from weekly study time. > > Predicted score = 61.8 + 3.25(study hours) > > | Student | Study hours | Observed score | > |---|---:|---:| > | A | 4 | 78 | > | B | 6 | 79 | > | C | 8 | 91 | > > The correlation is r = 0.72. A residual plot shows a curved pattern: residuals tend to be positive at low and high study times and negative near the middle of the observed range. Source: Fiveable derived practice dataset. Values are synthetic and designed for AP Statistics exam practice. Which of the following correctly identifies the residual for Student B and its meaning in context? - (A) The residual is -2.3, indicating that the linear model overpredicts Student B's assessment score. - (B) The residual is 2.3, indicating that the linear model underpredicts Student B's assessment score. - (C) The residual is -2.3, indicating that the linear model underpredicts Student B's assessment score. - (D) The residual is 2.3, indicating that the linear model overpredicts Student B's assessment score. **Answer: (A)** The residual is the difference between the observed and predicted values (y - y-hat). For Student B, the predicted score is 61.8 + 3.25(6) = 81.3. The residual is 79 - 81.3 = -2.3. Because the observed score is less than the predicted score, the model overpredicts the student's actual performance. ### Question 2 A researcher calculates a correlation of r = 0.85 for a dataset of 20 points showing a positive linear trend. A new point is added to the dataset that has a very high x-value and a very low y-value, placing it far below the original regression line. Which conclusion describes the most likely change to the correlation coefficient? - (A) The correlation coefficient will decrease substantially - (B) The correlation coefficient will increase substantially - (C) The correlation coefficient will remain largely unchanged - (D) The correlation coefficient will become exactly negative **Answer: (A)** Analyzing the influence of outliers on correlation reveals that points deviating from the established pattern weaken the linear association. A point with a high x-value and low y-value opposes the positive trend, acting as a high-leverage outlier that drastically reduces the correlation coefficient. ### Question 3 A study analyzes the relationship between fuel efficiency and speed for a specific vehicle. The data points form a distinct inverted-U shape, perfectly symmetric around the mean speed. Which claim about the correlation coefficient r for this dataset is most appropriate? - (A) The value of r will be close to 0, indicating no linear association - (B) The value of r will be close to 1, indicating a strong linear association - (C) The value of r will be close to -1, indicating a strong linear association - (D) The value of r will be close to 0.5, indicating a moderate linear association **Answer: (A)** Evaluating the definition of the correlation coefficient requires recognizing that r measures only linear strength. For a perfectly symmetric non-linear relationship like a parabola, the positive and negative z-score products cancel out, resulting in a correlation near zero despite the strong curved relationship. ### Question 4 A biologist measures the length (in centimeters) and weight (in grams) of a species, finding a correlation of r = 0.92. If the biologist converts the lengths to meters and weights to kilograms, what conclusion can be drawn about the new correlation? - (A) It remains 0.92, as correlation is independent of the units of measurement - (B) It becomes 0.092, as correlation scales downward with unit conversion factors - (C) It becomes 0.0092, as correlation divides by the product of unit conversions - (D) It becomes -0.92, as correlation inverts when the measurement scale changes **Answer: (A)** Applying the properties of the correlation coefficient confirms that r is a unitless measure calculated from standardized z-scores. Linear transformations of the variables (like unit conversions) do not change the z-scores, so the correlation remains exactly the same. ### Question 5 A dataset of height versus arm span yields a least-squares regression line of ŷ = 5 + 1.0x and a coefficient of determination r² = 0.81. Which conclusion about the correlation coefficient r is supported by this information? - (A) The correlation is 0.9, as the slope is positive and r is the square root of r-squared - (B) The correlation is -0.9, as the slope is positive and r is the negative root of r-squared - (C) The correlation is 0.81, as the correlation equals the coefficient of determination - (D) The correlation is 1.0, as the slope of the line indicates a perfect linear relationship **Answer: (A)** Determining the correlation from regression statistics requires taking the square root of the coefficient of determination (0.81) and assigning the sign of the slope. Since the slope (1.0) is positive, r must be the positive square root of 0.81, which is 0.9. ### Question 6 Study A reports a correlation of r = -0.85 between variable X and Y. Study B reports a correlation of r = 0.65 between variable A and B. Which conclusion correctly compares the strength of the linear relationships in the two studies? - (A) Study A has a stronger relationship, as the absolute value of r is closer to 1 - (B) Study B has a stronger relationship, as the value of r is positive not negative - (C) Study A has a weaker relationship, as negative correlations imply less consistency - (D) Study B has a weaker relationship, as the value of r is further from the origin **Answer: (A)** Comparing the strength of associations requires evaluating the magnitude of r, regardless of its sign. Since |-0.85| is greater than |0.65|, the linear relationship in Study A is stronger, meaning the points lie closer to the regression line. ### Question 7 A researcher calculates the correlation between annual income (x) and savings (y) to be r = 0.75. If the researcher swaps the variables so that savings is the explanatory variable (x) and income is the response variable (y), what is the new correlation? - (A) The correlation remains 0.75, as the calculation of r treats x and y symmetrically - (B) The correlation becomes -0.75, as reversing the roles of variables reverses the sign of the relationship - (C) The correlation becomes 0.5625, as the new correlation equals the square root of the coefficient of determination - (D) The correlation becomes 0.75, but the interpretation changes because income is now the response variable instead of the explanatory variable **Answer: (A)** Analyzing the formula for correlation reveals that it sums the products of z-scores for x and y. Since multiplication is commutative (Zx * Zy = Zy * Zx), swapping the variables has absolutely no effect on the value of r. ### Question 8 For a set of data points, every increase of 3 units in variable x corresponds exactly to a decrease of 4 units in variable y. Which claim about the correlation coefficient r for this dataset is correct? - (A) The correlation is -1.0, as the points lie perfectly on a line with a negative slope - (B) The correlation is 1.0, as the points lie perfectly on a line with a constant slope - (C) The correlation is -0.75, as the value equals the ratio of the change in y to x - (D) The correlation is -1.33, as the value equals the magnitude of the calculated slope **Answer: (A)** Determining the correlation requires assessing the linearity of the data. Since the rate of change is constant ('exactly' 3 units x for -4 units y), all points fall perfectly on a line. The negative relationship ensures r is -1.0. ### Question 9 In a scatterplot of variable x versus variable y, most data points are located in the second and fourth quadrants relative to the point (x̄, ȳ). Based on the formula for the correlation coefficient, which conclusion is most appropriate? - (A) The correlation is negative, as the products of the z-scores for these points are negative - (B) The correlation is positive, as the products of the z-scores for these points are positive - (C) The correlation is zero, as the positive and negative z-score products cancel each other - (D) The correlation is undefined, as z-scores cannot be calculated without standard deviation **Answer: (A)** Analyzing the calculation of r involves the product of z-scores. In the second quadrant (x < x̄, y > ȳ) and fourth quadrant (x > x̄, y < ȳ), the z-scores have opposite signs. Their product is negative, summing to a negative correlation. ### Question 10 A study on vehicle age and resale value yields a correlation coefficient of r = -0.85. Which of the following statements best describes the relationship between these two variables? - (A) Older vehicles are strongly associated with lower resale values in a linear pattern - (B) Older vehicles are weakly associated with lower resale values in a linear pattern - (C) Older vehicles are strongly associated with higher resale values in a linear pattern - (D) Older vehicles are weakly associated with higher resale values in a linear pattern **Answer: (A)** Interpreting the magnitude (0.85) as strong and the sign (-) as negative. A correlation of -0.85 indicates a strong negative linear association, meaning as age increases, resale value tends to decrease. ## Review the Unit - [5.1 Graphical Representations Between Two Quantitative Variables](/ap-stats/unit-5/representing-relationship-between-two-quantitative-variables/study-guide/3rWWsKXcnbYlqY64hQ1j) - [5.2 Correlation](/ap-stats/unit-5/correlation/study-guide/LlS81pC6QricXgIKNuFM) - [5.3 Linear Regression Models](/ap-stats/unit-5/linear-regression-models/study-guide/PSt5cfDuvB5nu60DHulR) - [5.4 Residuals](/ap-stats/unit-5/residuals/study-guide/zdTJQZw0UVGswyK6kkEF) - [5.5 Least-Squares Regression](/ap-stats/unit-5/least-squares-regression/study-guide/cRc4EhpHno3A4KvWrqyj) - [Unit 5 Overview: Regression Analysis](/ap-stats/unit-5/review/study-guide/DTw89sv8RD3Eq3WC58AB) ## Other Unit Tests - [Unit 1: Exploring One–Variable Data and Collecting Data](/ap-stats/unit-test/1) - [Unit 2: Probability, Random Variables, and Probability Distributions](/ap-stats/unit-test/2) - [Unit 3: Inference for Categorical Data: Proportions](/ap-stats/unit-test/3) - [Unit 4: Inference for Quantitative Data: Means](/ap-stats/unit-test/4) ## About This Document Canonical Fiveable pages are available as Markdown at the same path plus `.md`. - [llms.txt](https://fiveable.me/llms.txt): index of Fiveable's sections and URL patterns - [llms-full.txt](https://fiveable.me/llms-full.txt): complete subject and unit listing - [MCP server](https://fiveable.me/mcp): call Fiveable as tools instead of fetching pages (`https://fiveable.me/api/mcp`) - [MCP server for AP teachers](https://fiveable.me/mcp/teachers): a teacher's classes, assignments and AP-rubric grading (`https://fiveable.me/api/mcp/teacher`)