AP Statistics: Unit 2 – Lurking and Influential Pointspp.201 – 214

Name: ______Date: ______Period: _____

Practice – Lurking and Influential Points

  1. Abalones are edible sea snails that include over 100 species. Caroline (a marine biologist) is working with a model that uses the number of rings in an Abalone’s shell to predict its age. She finds an observation that she believes has been miscalculated. After removing the outlier, she redoes the calculation. Does it appear that this outlier was exerting very much influence? Explain.
  1. Carolineis happy with her second regression. However, she found a number of shells that have large residuals and is considering removing all of them. Is this a good practice? Explain.
  1. The scatterplot shows five data points. Not surprisingly, the correlation for these points is r = 0. Suppose one additional data point is added at one of the five positions (a – e). Match each point with the correct new correlation from the list.

a)______

b)______

c)______

d)______

e)______

  1. How does the speed at which you drive affect your fuel economy? To find out, researchers drove a compact car for 200 miles at speeds ranging from 35 to 75 mph. From their data, they created the model and created the residual plot below:

a)Interpret the slope of this line in context.

b)Explain why the y-intercept can’t be interpreted in this context.

c)What fuel efficiency does the model predict when the car is driven at 50 mph?

d)Do you think this is an appropriate model for that association? Explain.

AP Stat – Let’s not “regress” and forget how to do these!

  1. Exercise physiologists are investigating the relationship between lean body mass (in kilograms) and the resting metabolic rate (in calories per day) in sedentary males.Based on the computer output above, which of the following is the best interpretation of the value of the slope of the regression line?

(A)For each additional kilogram of lean body mass, the resting metabolic rate increases on average by 22.563 calories per day.

(B)For each additional kilogram of lean body mass, the resting metabolic rate increases on average by 264.0 calories per day.

(C)For each additional kilogram of lean body mass, the resting metabolic rate increases on average by 144.9 calories per day.

(D)For each additional calorie per day for the resting metabolic rate, the lean body mass increases on average by 22.563 kilograms.

(E)For each additional calorie per day for the resting metabolic rate, the lean body mass increases on average by 264.0 kilograms.

  1. In the context ofregression analysis, which of the following statements are true?

I. When the data set includes an influential point, the data set is nonlinear.
II. Influential points always reduce the coefficient of determination.
III. All outliers are influential data points.

(A) I only
(B) II only
(C) III only
(D) All of the above
(E) None of the above

  1. Two variables that are actually not related to each other may nonetheless have a very high correlation, because they both results from some other, possibly hidden, factor. This is an example of…

(A)Leverage

(B)A lurking variable

(C)Extrapolation

(D)Regression

(E)An outlier

  1. All but one of the statements below contain a mistake. Which one could be true?

(A)There is a high correlation between cigarette smoking and gender.

(B)The correlation between age and weight of a newborn baby is r = 0.83 ounces per day.

(C)The correlation between a person’s age and vision (20/20?) is r = -1.04.

(D)The correlation between the species of a tree and its height is r = 0.56.

(E)The correlation between blood alcohol level and reaction time is r = 0.73.

  1. If the point in the upper left corner of the scatterplot is removed, what will happen to the correlation (r) and the slope of the line of best fit?

(A)They will not change.

(B)Both will increase.

(C)Both will decrease.

(D)r will increase and the slope will decrease.

(E)r will decrease and the slope will increase.