AP Statistics Practice Test Unit Three Explring Relatinships Between Variables Name Perid Date True r False: 1. Crrelatin and regressin require explanatry and respnse variables. 1. 2. Every least squares regressin line passes thrugh ( x, y ). 2. Shrt Answer: 3. In a simple, linear regressin mdel, the variable that is being predicted may be called which f the fllwing: (Check all that apply) _ independent variable _ regressin variable _ dependent variable _ respnse variable _ X variable _ Y variable 4. Which f the fllwing crrelatin values represents a perfect linear relatinship between tw quantitative variables? (Check all that apply) _ 0 _ 1 _.9 _.5 _ -1 5. A psitive crrelatin between tw variables X and Y means: If yu increase the X value, this will cause the value f Y t increase. Circle the crrect answer and briefly explain. a. This is always true. b. This is smetimes true. c. This is never true. 6. Describe a situatin in which yu wuld expect a fairly strng assciatin between tw variables that d nt have a cause-and-effect relatinship. 7. Think f a set f bivariate, quantitative data. When the crrelatin cefficient fr these data is clse t 1, must the slpe als be clse t 1? Explain. 8. In the scatterplt f y versus x shwn at the right, circle the pint with the largest residual and place a square arund the pint that wuld be cnsidered an influential bservatin. 1
Multiple-Chice: Circle the best answer. 9. Which f these statements are false? (A) There is a strng linear relatinship between gender and height because we fund a crrelatin f.65. (B) Plant height and leaf height were fund t be negatively crrelated because the crrelatin cefficient is 1.41. (C) Since the crrelatin between X and Y is 0, this means there is n relatinship whatsever between these tw variables. (D) All f the abve. (E) Nne f the abve. 10. Tw measures x and y were taken n 18 subjects. The first f tw regressins, Regressin I, yielded yˆ = 24.5 + 16.1x and had the fllwing residual plt. The secnd regressin, Regressin II, yielded plt. lg( yˆ ) = 1.6 + 0.51 lg( x) and had the fllwing residual Which f the fllwing cnclusins is best supprted by the evidence abve? (A) There is a linear relatinship between x and y, and Regressin I yields a better fit. (B) There is a linear relatinship between x and y, and Regressin II yields a better fit. (C) There is a negative crrelatin between x and y. (D) There is a nnlinear relatinship between x and y, and Regressin I yields a better fit. (E) There is a nnlinear relatinship between x and y, and Regressin II yields a better fit. 11. There is a linear relatinship between the number f chirps made by the striped grund cricket and the air temperature. A least squares fit f sme data cllected by a bilgist gives the mdel yˆ 25.2 + 3. 3x =, 9 < x < 25, where x is the number f chirps per minute and ŷ is the estimated temperature in degrees Fahrenheit. What is the estimated increase in temperature that crrespnds t an increase f 5 chirps per minute? (A) 3.3 F (B) 16.5 F (C) 25.2 F (D) 28.5 F (E) 41.7 F 2
12. The equatin f the least squares regressin line fr the pints n the scatterplt at the right is yˆ = 1.3 +. 73x. What is the residual fr the pint (4, 7)? (A) 2.78 (B) 3.00 (C) 4.00 (D) 4.22 (E) 7.00 y 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 x 13. What des the pattern f the residuals tell yu abut the linear mdel? (A) The evidence is incnclusive. (B) The residual plt clearly cntradicts the linearity f the data. (C) The residual plt cnfirms the linearity f the fuel ecnmy data. (D) Nne f the abve. Free Respnse: Exercises 14-18 relate t the fllwing. Jey read in his bilgy bk that fish activity increases with water temperature, and he decided t investigate this issue by cnducting an experiment. On nine successive days, he measures fish activity and water temperature in his aquarium. Larger values f his measure f fish activity dente mre activity. The figure belw presents the scatterplt f his data. Act i vi t y 450 14. What des the scatterplt reveal? State in plain language as if yu were explaining t a friend wh knws very little statistics. 300 69. 0 72. 0 75. 0 78. 0 81. 0 H2Ot emp 15. What is yur best guess fr the crrelatin cefficient between water temperature and fish activity. 16. If we reversed the variables and made a scatterplt f fish activity vs. water temperature, what wuld the new crrelatin cefficient be? Briefly explain yur reasning. 3
17. Suppse we were t recrd temperature in Celsius degrees instead f Fahrenheit. Hw wuld the crrelatin change? Why? 18. Suppse a new pint at (84, 300), i.e., water temperature = 84 F and fish activity = 300, is added t the plt. Describe the effect, if any, that this new pint will have n the crrelatin cefficient f water temperature vs. fish activity and hw it will affect the slpe f the line. Why des it have this effect? The table shws the number f live births per 1000 wmen aged 15-44 years in the United States starting in 1965. When yu enter the data, enter year as 65, 70, 75, 80, 85, etc.: YEAR 1965 1970 1975 1980 1985 1990 1995 1999 Rate 19.4 18.4 16.3 15.9 15.6 16.4 14.8 14.5 19. Which is the explanatry variable? 20. Make a scatterplt f the data by hand. 21. Determine the equatin f the LSRL fr this data using yur TI-84. Define yur variables: 22. Plt the line n yur scatterplt. Plt it n yur TI-84 and then just cpy it frm the screen. 23. What is the slpe? Define the slpe in the cntext f this prblem. 24. What is the crrelatin between x and y? Interpret this value in the cntext f this prblem. 25. What is the cefficient f determinatin? Interpret this number. 4
26. Predict what the birth rate will be in 2010. Cmment n yur faith in this predictin. 27. Find the residual fr the first pint in the data set. Shw yur wrk belw fr credit. 28. Cnstruct a residual plt in yur calculatr and sketch it belw. 29. Use the residual plt t answer this questin: Is a linear mdel apprpriate fr these tw variables? Explain. A cnsumer rganizatin has reprted test data fr 50 car mdels. We will examine the assciatin between the weight f the car (in thusands f punds) and the fuel efficiency (in miles per galln). Predictr Cef StDev T P Cnstant 48.739 1.976 24.7 0.000 Weight -8.2136 0.6738-12.2 0.000 S = 2.413 R-Sq = 75.6% R-Sq(adj) = 71.2% 30. Using the printut abve, find the LSRL. 30. 31. Find the crrelatin between weight f a car and its gas mileage. 31. 32. What is yur estimate f fuel efficiency (MPG) fr a car that weighs 3000 lbs? Review: 32. 33. The number f new prjects started each mnth at an advertising agency fr the last six mnths is: 2 5 3 3 6 3 The interquartile range fr the abve data is (A) 1.0 (B) 2.0 (C) 3.0 (D) 4.0 (E) 5.0 5 33.
34. The weight f a randmly selected can f a new sft drink is knwn t have a nrmal distributin with a mean f 8.3 unces and a standard deviatin f 0.2 unces. The weight that shuld be stamped n each can s that nly 2% f all cans are underweight is (A) 7.89 unces. (B) 8.13 unces. (C) 8.26 unces. (D) 8.71 unces. (E) 8.02 unces. 34. 35. Birth weights at a lcal hspital have a nrmal distributin with a mean f 110 unces and a standard deviatin f 15 unces. The prprtin f infants with birth weights under 95 unces is (A) 0.341 (B) 0.500 (C) 0.159 (D) 0.682 (E) 0.841 35. 6