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AP Statistics Unit 2: Exploring Two-Variable Data

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Unit 2: Exploring Two-Variable Data

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Question 1

Computer output for a regression of weight ( $y$ , in lbs) on height ( $x$ , in inches) gives: $\overset{y}{^} = - 130 + 4.5 x$ , $r^{2} = 0.71$ . Interpret the slope.

A.For each additional pound, height is predicted to increase by 4.5 inches.B.For each additional inch of height, weight is predicted to increase by 4.5 lbs.C.The average weight is 4.5 lbs.D.71% of the increase in weight is caused by height.

Question 2

A least-squares regression line is fit to data on advertising spending ( $x$ , thousands of dollars) and sales ( $y$ , thousands of units). The residual for one observation is $+ 12$ . What does this mean?

A.The actual sales were 12 thousand units less than predicted.B.The actual sales were 12 thousand units more than predicted.C.Advertising spending was overestimated by 12 thousand dollars.D.The regression line passes 12 units above the data point.

Question 3

A regression of salary ( $y$ , thousands of dollars) on years of experience ( $x$ ) yields $r^{2} = 0.64$ . Which interpretation is correct?

r = 0.64

, indicating a moderately positive linear association.B.64% of the variation in salary is explained by the linear relationship with years of experience.C.64% of employees have salaries predicted correctly by the model.D.Years of experience causes 64% of the increase in salary.

Question 4

A scatterplot of two variables shows a strong curved relationship. A student computes $r = 0.45$ and concludes the association is weak. What is the error in the student's reasoning?

A.The student should use

r^{2}

instead of

r

to assess strength.B.

r

measures only the strength of the linear association; a low

r

with a curved pattern means the relationship is strong but non-linear.C.The student should use Spearman's rank correlation for curved data.D.A value of

r = 0.45

can still indicate a strong relationship.

Question 5

The regression equation for predicting a city's high temperature in July ( $y$ , °F) from its latitude ( $x$ , degrees north) is $\overset{y}{^} = 115 - 1.1 x$ . Interpret the $y$ -intercept in context.

A.At 0° latitude (equator), the predicted July high is 115°F.B.For each degree increase in latitude, temperature decreases by 115°F.C.The average July high temperature across all cities is 115°F.D.The

y

-intercept has no meaningful interpretation because latitude cannot equal zero.

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Question 6

A statistician notes that cities with more churches tend to have more crime. Before concluding that religion causes crime, what is the most important alternative explanation?

A.The correlation between churches and crime is not strong enough to draw any conclusion.B.Population size is a confounding variable — larger cities have both more churches and more crime.C.The data should be analyzed with a

χ^{2}

test, not correlation.D.Crime causes people to build more churches for moral guidance.

Question 7

For a regression of final exam score on midterm score, the regression equation is $\overset{y}{^} = 10 + 0.80 x$ , $r = 0.90$ . A student scored 70 on the midterm. What is the student's predicted final exam score?

A.63B.66C.80D.70

Question 8

Regression output for predicting plant height ( $y$ , cm) from weekly fertilizer dose ( $x$ , grams) is shown below:

Predictor	Coef	SE Coef	T	P
Constant	5.2	1.1	4.73	0.000
Dose	3.8	0.6	6.33	0.000

$r^{2} = 0.77$

A plant received 4 grams of fertilizer per week. What is its predicted height, and what does $r^{2}$ tell us?

A.Predicted height = 20.4 cm; 77% of the variation in height is explained by fertilizer dose.B.Predicted height = 20.4 cm;

r = 0.77

indicates a moderately strong positive association.C.Predicted height = 20.4 cm; 23% of the variation in height is unexplained.D.Predicted height = 17.4 cm; 77% of plants are predicted correctly.

Question 9

The regression of $ln (y)$ on $x$ produces a better fit than the regression of $y$ on $x$ . What does this suggest about the relationship between $x$ and $y$ ?

A.The relationship between

x

and

y

is exponential.B.The relationship between

x

and

y

is linear.C.The relationship between

x

and

y

is a power function.D.

x

must be transformed, not

y

Question 10

A scatterplot of hours studied ( $x$ ) versus exam score ( $y$ ) for 20 students shows a positive linear association with no obvious outliers. The correlation coefficient is $r = 0.83$ . What does this value tell us?

A.83% of the variation in exam scores is explained by hours studied.B.There is a strong positive linear association between hours studied and exam score.C.Studying more hours causes higher exam scores.D.Each additional hour of studying increases the score by 0.83 points.

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Question 11

A researcher removes one influential point from a scatterplot. After removing it, $r$ increases from 0.60 to 0.91. What type of point was removed?

A.A point with a large positive residualB.An outlier in the

y

-direction only (high-leverage point)C.An influential outlier that did not follow the linear pattern of the other pointsD.A data point with

x

-value equal to the mean of

x

Question 12

A residual plot for a linear regression model shows a clear curved (U-shaped) pattern. What does this indicate?

A.The regression line fits the data well.B.There is likely an outlier in the data.C.A linear model is not appropriate; the relationship is non-linear.D.The standard deviation of the residuals is too large.

AP Statistics Unit 2: Exploring Two-Variable Data — Free with Answer Explanations | Test Practice Hub