2 Categorical Variables
A two-way table shows students’ favorite subject (Math, English) by grade level (9th, 10th).
What does a joint relative frequency represent?
A. A total count
B. A proportion within a row
C. A proportion of the entire sample
D. A proportion within a column
C. A proportion of the entire sample
What does the correlation coefficient measure?
A. Slope
B. Strength and direction of a linear relationship
C. Spread of data
D. Mean difference
B. Strength and direction of a linear relationship
What is a residual?
A. Difference between two x-values
B. Observed y − predicted y
C. Predicted y − observed y
D. Slope of a line
B. Observed y − predicted y
What is an explanatory variable?
A. Output variable
B. Response variable
C. Predictor variable
D. Residual
C. Predictor variable
When describing a relationship in an FRQ, which set of components is required for full credit?
A. Direction only
B. Strength and direction only
C. Strength, direction, and form
D. Strength, direction, form, and outliers
D. Strength, direction, form, and outliers
If the conditional distribution of favorite subject is the same across all grade levels, what is true?
A. There is an association
B. There is no association
C. There is causation
D. The sample is biased
B. There is no association
If r=−0.85
A. Weak positive relationship
B. Strong positive relationship
C. Weak negative relationship
D. Strong negative relationship
D. Strong negative relationship
If a residual is negative, what does that mean?
A. Prediction was too high
B. Prediction was too low
C. Data is incorrect
D. No relationship exists
A. Prediction was too high
In a scatterplot, what does a positive association mean?
A. Variables decrease together
B. Variables increase together
C. No relationship
D. One stays constant
B. Variables increase together
A student writes:
“The relationship is strong because r2=0.85"
Why would this lose points?
A. r2 is incorrect
B. Strength cannot be determined numerically
C. Strength should be described from the graph, not justified using r2
D. The statement is correct
C. Strength should be described from the graph, not justified using r2
Which statement best indicates an association between two categorical variables?
A. Row totals are equal
B. Column totals are equal
C. Conditional proportions differ across groups
D. Total sample size is large
C. Conditional proportions differ across group
What happens to correlation if both variables are converted from hours to minutes?
A. It increases
B. It decreases
C. It stays the same
D. It becomes 0
C. It stays the same
What does a residual plot help identify?
A. Mean
B. Standard deviation
C. Linearity and model fit
D. Sample size
C. Linearity and model fit
What is the difference between linear and nonlinear relationships?
A. Strength
B. Direction
C. Shape of the pattern
D. Sample size
C. Shape of the pattern
Which of the following is the correct structure for interpreting the coefficient of determination r2?
A. “85% of x is explained by y”
B. “85% of the variation in y is explained by x”
C. “85% of the data is explained”
D. “85% of the points fit the line”
B. “85% of the variation in y is explained by x”
A study finds that 60% of athletes prefer online classes, while only 30% of non-athletes do. What does this suggest?
A. No association
B. Positive association
C. Negative association
D. Causation
B. Positive association
Which situation would have correlation closest to 0?
A. Strong linear trend
B. Clear curved pattern
C. No pattern
D. Perfect line
C. No pattern
If residuals show a clear pattern, what does this mean?
A. Linear model is appropriate
B. No relationship exists
C. Linear model is not appropriate
D. Correlation is 0
C. Linear model is not appropriate
If points become more spread out as x increases, this indicates:
A. Outliers
B. Nonlinear pattern
C. Changing variability
D. No association
C. Changing variability
Which statement correctly follows FRQ expectations when interpreting a residual?
A. “The residual is 2.94”
B. “The predicted value is 157.06”
C. “The student is 2.94 cm taller than expected based on foot length”
D. “The model is accurate”
C. “The student is 2.94 cm taller than expected based on foot length”
Why can’t we conclude causation from a two-way table?
A. Data is always biased
B. Variables are categorical
C. There may be confounding variables
D. Proportions are used
C. There may be confounding variables
A strong negative correlation means:
A. One variable causes the other to decrease
B. As one variable increases, the other tends to decrease
C. Both variables increase together
D. No relationship exists
B. As one variable increases, the other tends to decrease
An outlier with a large residual but typical x-value is:
A. Influential point
B. High leverage point
C. Vertical outlier
D. Cluster
C. Vertical outlier
Why is it important to distinguish between association and causation?
A. Association proves causation
B. Causation proves association
C. Association does not imply causation
D. They are the same
C. Association does not imply causation
In part (d)-type questions (making a conclusion using previous parts), what is the best strategy?
A. Only answer yes/no
B. Restate the question
C. Use results from earlier parts AND connect to context
D. Give a general explanation
C. Use results from earlier parts AND connect to context