Test #2 (Chapter 3)Honor Pledge ______

AP StatisticsName ______

9/23/08Wood/MyersPeriod ______

Test #2 (Chapter 3)Honor Pledge ______

Part I - Multiple Choice (Questions 1-10) – Bubble the answer of your choice on the scantron form.

1. There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. A least squares fit of data collected by a biologist gives the model

Where x is the number of chirps per minute and is the estimated temperature in degrees Fahrenheit. What is the estimated increase in temperature that corresponds to an increase of 5 chirps per minute?

(a) (b) (c) (d) (e)

2. The equation of the least-squares regression line for the points on the scatterplot is

What is the residual for the point (4,7)?

(a) 2.78(b) 3.00(c) 4.00(d) 4.22(e) 7.00

3. Which of the following is false about the correlation coefficient?

(a)

(b) If r is negative, a negatively-associated relationship is indicated.

(d) A value of r = 0.2 indicates a weak linear relationship.

(e) r measures the percent of variability in the y-variable.

4. Moving times (in minutes) and weights (in pounds) were recorded for a random sample of 20 moving jobs requiring three-man crews, and the results of the regression analysis are shown below.

Predictor / Coeff / StDev / T / P
Constant / 21.84 / 25.54 / 0.86 / 0.404
Weight / 0.036538 / 0.002977 / 12.27 / 0.000
S = 30.32 / R-Sq = 89.3% / R-Sq (adj) = 88.7%
Analysis of Variance
Source / DF / SS / MS / F / P
Regression / 1 / 138434 / 138434 / 150.60 / 0.000
Residual Error / 18 / 16546 / 919
Total / 19 / 154980

The equation for the least-squares regression line is

(a)

(b)

(c)

(d)

(e)

5. Which of the following values is most likely to represent the correlation coefficient for the data shown in this scatterplot?

(a)r = -0.67 (b) r = -0.10 (c) r = 0.71 (d) r = 0.93 (e) r = 0.96

6. Suppose we fit the least squares regression line to a set of data. What is true if a plot of the residuals shows a curved pattern?

(a)A straight line is not a good model for the data.

(b)The correlation must be 0.

(c)The correlation must be positive.

(d)Outliers must be present.

(e)The LSRL might or might not be a good model for the data, depending on the extent of the curve.

7. Mr. Nerdly 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 . Which of the following statements about the highlighted point is FALSE?

(a) This student has a grade point average of 2.9 and an SAT Math score of 670.

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

(d) Removing this data point would cause the correlation coefficient to increase.

(e) Removing this student’s data point would increase the slope of the least-squares line.

8. A copy machine dealer has data on the number x of copy machines at each of 89 customer locations and the number y of service calls in a month at each location.

Summary calculations give = 8.4, = 2.1, = 14.2, = 3.8, and r = 0.86.

What is the slope of the least-squares regression line of number of service calls on number of copiers?

(a) 0.86(b) 1.56(c) 0.48(d) None of these(e) Not enough information

9. A set of two-variable data (x,y) has been transformed such that and . The correlation of the original data was 0.75. The correlation of the transformed data will:

(a) increase(b) decrease(c) stay the same(d) be undefined(e) 0

10. All four scatterplots show 1990 vehicle-related deaths per 100,000 residents on the y-axis for 16 southern states(open circles) and the District of Columbia (x). Each plot shows a different predictor on the x-axis.

One of the predictors is the minimum age required for obtaining a driver’s license. DC is an influential point – by removing it, the correlation changes from -.66 to -.17. Which plot corresponds to this situation?

(a) A(b) B(c) C(d) D(e) none of the scatterplots is appropriate

Part II – Free Response (Questions 11-12) – Show your work and explain your results clearly.

11. [4 points] A simple random sample of 9 students was selected from a large university. Each of these students reported the number of hours he or she allocated to studying and the number of hours allocated to work each week. A least squares regression was performed and part of the resulting computer output and the scatterplot of the data are shown below.

(a) After point P, labeled on the graph, was removed from the data, a second linear regression was performed and the computer output is shown.

Does point P exercise a large influence on the regression line? Explain.

(b) The researcher who conducted the study discovered that the number of hours spent studying reported by the student represented by P was recorded incorrectly. The corrected data point for this student is represented by the letter Q in the scatterplot.

Explain how the least squares regression line for the corrected data (in this part) would differ from the least squares regression line for the original data.

12. [6 points] David was comparing the number of vocabulary words children know about transportation at various ages. He fit a least-squares regression line to the data. The residual plot and part of the computer printout for the regression are given below.

/ Predictor / Coef / StDev / t ratio / P
Constant / 3.371 / 1.337 / 2.52 / .065
Age / 2.1143 / 0.2321 / 9.11 / .001
s = 0.9710 / R-sq = 95.4% / R-sq (adj) = 94.3%

(a) Is a line an appropriate model for these data? Explain.

(b) What is the equation of the least-squares regression line for predicting the number of words from age?

(d) Interpret the slope of the regression line in the context of the problem.

(e) Interpret the value of r2 in the context of the problem.

(f) Interpret the value of s in the context of the problem.