Chapter 3 AP EXAM

A scatterplot of 13 different flights from Philadelphia on a particular airline suggests that the relationship between x = distance (miles) and y = air fare (dollars) is roughly linear. The computer output summarizes this relationship. Identify and interpret the slope of the least-squares regression line.

• Slope = 0.0298. The predicted air fare increases by $0.0298 for each additional 1 mile increase in the flight distance.

• Slope = 0.0298. For every additional one mile in flight distance, the air fare increases by $0.0298.

• Slope = 101.24. The predicted air fare increases by $101.24 for each additional 1 mile increase in the flight distance.

• Slope = 101.24. For every additional one mile in flight distance, the air fare increases by $101.24.

• Slope = 20.7237. As distance increases by 1 mile, air fare increases by $20.7237.

A scatterplot of 13 different flights from Philadelphia on a particular airline suggests that the relationship between x = distance (miles) and y = air fare (dollars) is roughly linear. The computer output summarizes this relationship. Which of the following best interprets s = 20.7237?

• The air fare typically varies about $20.7237 from the mean air fare.

• Flight distance typically varies about 20.7237 miles from the mean flight distance.

• The air fare is typically about $20.7237 away from the air fare predicted by the least-squares regression line with x = flight distance (in miles).

• The predicted airfare increases by $20.7237 for each additional mile in flight distance.

• The slope of the least-squares regression line typically varies about $20.7237 per mile from the true mean slope.

Mrs. Emerson is studying oak trees and finds that the correlation between x = the ages (measured in years) and y = height (in feet) of a sample of trees is 0.78. Which of the following statements must be true?

• 78% of the variability in tree heights can be explained by variation on the trees’ ages.

• For every year a tree ages, its height increases, on average, by 78%.

• If we let x = height of tree and y = age of tree, then the correlation would be the reciprocal of 0.78.

• If we measure the height in meters instead of feet, the correlation would still be 0.78.

• The unit for correlation in this context is foot-years.

The least squares regression line minimizes which one of the following quantities?

• The sum of the squared differences between the observed values of the response variable and the mean of the response variable.

• The sum of the squared differences between the observed values of the explanatory variable and the mean of the explanatory variable.

• The sum of the squared differences between the observed values of the response variable and the predicted values of the response variable.

• The sum of the squared differences between the observed values of the explanatory variable and the predicted values of the explanatory variable.

• The sum of the squared differences between the predicted values of the explanatory variable and the mean of the explanatory variable.

A study examined the relationship between the sepal length and sepal width for two varieties of an exotic tropical

plant. Varieties X and O are represented by x’s and o’s, respectively, in the following scatterplot. Which of the following statements is true?

• Considering each variety separately, there is a negative correlation between sepal length and width.

• Considering both varieties together, there is a negative correlation between sepal length and width.

• Considering Variety X only, there is a positive correlation between sepal length and width.

• Considering Variety O only, the least-squares regression line for predicting sepal length from sepal width has a

  positive slope.

• Considering both varieties together, the least-squares regression line for predicting sepal length from sepal width

  has a negative slope.

Mr. Beuerle asked the students in his AP® Statistics class to report their overall grade point averages and their SAT

Math scores. The scatterplot below provides information about his students’ data. The dark line is the least-squares

regression line for the data, and its equation is yˆ = 410.54 + 67.3x. Which of the following statements about the circled point is true?

• The standardized score for this student’s GPA is positive.

• If we used the least-squares line to predict this student’s SAT Math score, we would make a prediction that is too

  low.

• This student’s residual is positive.

• Removing this data point would not change the correlation between SAT math score and GPA.

• Removing this student’s data point would decrease the slope of the least-squares line.

A study of the fuel economy for various automobiles plotted the fuel consumption (in liters of gasoline used per 100

kilometers traveled) vs. speed (in kilometers per hour). A least-squares line was fitted to the data. Here is the

residual plot from this least-squares fit. What does the residual plot tell you about the linear model?

• The residual plot confirms the linearity of the relationship between speed and fuel consumption.

• The residual plot does not confirm nor rule out the linearity of the relationship between speed and fuel

  consumption.

• The residual plot suggests that the relationship between speed and fuel consumption may be linear, but more data

  points are needed to confirm this.

• The residual plot clearly indicates that the relationship between speed and fuel consumption is not linear.

• A residual plot is not an appropriate means for evaluating a linear model.

A set of data describes the relationship between the size of annual salary raises and the performance ratings for

employees of a certain company. The least squares regression equation is yˆ = 1400 + 2000x where y is the raise

amount (in dollars) and x is the performance rating. Which of the following statements must be true?

• For each one-point increase in performance rating, the raise will increase on average by $1400.

• The actual relationship between salary raises and performance rating is linear.

• The residuals for half the observations in the dataset will be positive.

• The correlation between salary raise and performance rating is negative.

• If the mean performance rating is 1.2, then the mean raise is $3800.

For children between the ages of 18 - 29 months, there is an approximately linear relationship between height and age. The relationship can be represented by yˆ = 64.93 + 0.63x, where y represents height (in centimeters) and x represents age (in months). Jonathan is 22.5 months old. What is his predicted height?

• 50.80

• 64.96

• 65.96

• 79.11

• 87.40

For children between the ages of 18 - 29 months, there is an approximately linear relationship between height and age. The relationship can be represented by yˆ = 64.93 + 0.63x, where y represents height (in centimeters) and x represents age (in months). Jason is 20 months old and is 80 centimeters tall. What is his residual?

• − 2.47

• 2.47

• –12.60

• 12.60

• 77.53