AP Statistics- Chapter 3

36. The equation of the least squares regression line for a set of points in a scatterplot is given by ŷ=1.3+0.27x. The point (3,2) is one point on this scatterplot. Which of the following is the residual for the point (3,2)?

A) -0.11

38. A linear model was constructed for a set of bivariate data using least squares regression techniques. Given the residual plot shown, what conclusion should be drawn?

A) A linear model was not a good fit for the data.

30. Which of the following statements about correlation r are true?

A) I only

1. For the years 1950-1980, the number of heart disease deaths per 100,000 people in the United States were recorded. The regression line below was computed using a statistical software package. Which statement is the correct interpretation of the slope? The regression equation is Number of deaths=7387-3.63 year

A) The number of heart disease deaths per 100,00 people has been dropping by an estimated 3.63 deaths per year on the average

7. The correlation coefficient is

A) a number between -1 and +1 that measures the strength and direction of the linear relationship between two variables

31. The regression line for a set of data is ŷ=2x+b. This line passes through the point (3,4). If x̅ and ȳ are the sample means of the x and y values respectively, then ȳ=

D) ŷ=2x̅+b

28. Which of the following best describes the correlation between two variables if r=0.978?

D) positive and strong

18. The equation of the least squares regression line for a set of points in a scatterplot is given by ŷ=2.2+0.81x. The point (5,7) is one point on this scatterplot. Which of the following is the residual for the point (5,7)?

B) 0.75

7. In a statistics course, a linear regression equation was computed to predict the final exam score based on the score on the first test of the term. The equation was: y=25+0.7x where y is the final exam score and x is the score on the first test. George scored 80 on the first test. On the final exam George scored 85. What is the value of his residual?

B) 4

2. A regression line includes the point (2,14) and has the equation ŷ=mx+4. If x̅ and ȳ are the sample means of the x and y values, then ȳ=

B) 5x̅+4

2. Which of the following statements about a linear regression model is true? I. The sum of the residuals is always zero. II. If r²=0, the regression line is a horizontal line. III. No pattern in the residual plot is an indication that a nonlinear model will show a better fit to the data than a straight line regression model.

B) I and II only

32. The correlation r between the magnitude of an earthquake and the depth below the surface of the earth at which the quake occurs has been determined experimentally to be about 0.51. Suppose we use the magnitude of the earthquake (x) to predict the depth below the surface (y) at which the quake occurs. We can infer that

B) the fraction of the variation in depths explained by the least squares regression line of y on x is 0.26.

27. A straight line of the form ŷ=a+bx is fitted to the 5 data points (1,0), (0,3), (3,1), (2,-3), and (4,2) by the method of least squares. What is the value of b?

C) -1/10

2. There is a linear relationship between the duration x (in seconds) of an eruption of a geyser and the interval of time y (in minutes) until the next eruption. A least-squares regression line of data collected by a geologist is represented by, ŷ=41.9+0.18x, 100<x<300. What is the estimated increase in the interval of time until the next eruption that corresponds to an increase of 60 seconds in the duration?

C) 10.8 minutes

29. Data are obtained for a group of computer technicians examining the relationship between years of experience (x) and salary (y), in thousands of dollars. The resulting regression equation is ŷ=20.17+0.82x with r=0.597. What percent of the variation in salary can be explained by the least squares regression of salary on years of experience?

C) 35.6%

29. Data are obtained from a group of high school seniors comparing age and the number of hours spent on the telephone. The resulting regression equation is Predicted number of hours= 0.123 (age) + 2.57 with r=0.866 What percentage of the variation in the number of hours spent on the telephone can be explained by this least-squares regression model?

C) 75%

26. The regression line of a set of data is ŷ=2x+b which passes through the point (3,6). If x̅ and ȳ are the sample means of the x and y values, respectively, then

C) ȳ=2x

12. Consider the following three scatterplots: What is the relationship between r1, r2 and r3, the correlations coefficients of each scatterplot?

D) r2<r1<r3

22. The correlation between height and weight among men between the ages of 18 and 70 in the United States is approximately 0.42. Which of the following conclusions does NOT follow from the data?

D) If a man in this group changes his diet and gains 10 pounds, he is likely to get taller.

40. A student was interested in the relationship between weight of a car and gas consumption measured in mpg. He selected sixteen different automobiles and recorded their weights along with their advertised mpg. The regression equation and regression plot are shown below. What affect would the addition of the point (4,300 lbs., 15.63 mpg) have on the value of r²?

D) It will increase r² because it is an influential point which lies on the least squares line.

9. What is the effect on the correlation between two variables (x,y) if each x-value is cut in half and 0.04 is subtracted from each y-value?

D) The correlation is unchanged.

31. The residual plot below came from data which plotted grade at midterm grade against grade on final exam. A linear regression line was calculated. Which conclusion could be reached by analyzing the residual plot?

D) There exists unequal variance throughout the model.

9. The 'least-squares' method of determining a regression equation of the form ŷ=a+bx where the u=values are represented on the vertical axis and the x-values are represented on the horizontal axis

D) minimizes the sum of the squares of the vertical distances between the regression line and the data points

11. A teacher raised each student's grade by 10 points on an algebra exam. Which of the following describes the correlation between students' original grades and their adjusted grades?

E) 1

8. Suppose the regression line for a set of data, y=3x+b, passes through point (2,5). If x̅ and ȳ are the sample means of the x and y values respectively, then ȳ=

E) 3x̅-1

31. Which of the following statements are true?

E) All of the above

11. Imagine a least squares regression model is generated that predicts y based on x of the form ŷ=b0+b1x. Which of the following statements about the residuals from this regression model are true?

E) I, II, and III

23. Which of the following statements related to residuals are true? I. The mean of the least-squares residuals is always zero. II. If one tries to fit a linear model to bivariate data, a curved pattern in residual plot shows that the relationship between two variables is not linear. III. A residual plot can be a scatter plot of the regression residuals against the explanatory variable.

E) I, II, and III

6. Which of the following statements is true?

E) The correlation can be strongly affected by a few outlying observations.

12. What is the following associations between the two given variables is likely to have a negative correlation?

E) The time and speed required to travel a given distance

8. A researcher wishes to examine the relationship between years of schooling completed and the number of pregnancies in young women. Her research discovers a linear relationship, and a least squares fit of her data results in the model ŷ=6.4-0.12x where x is the number of years completed in school and y is the number of pregnancies that corresponds to the completion of an additional 10 years of school?

E) a decrease of 1.2

30. The points (x,y) on a scatterplot form an ellipse. As the ellipse becomes thinner, what can be concluded about the correlation r between the variables x and y?

E) no conclusion can be drawn