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Regression Analysis and Correlation Hypothesis Test

35. A regional commuter airline selected a random sample of 25 flights and found that the correlation between the number of passengers and the total weight, in pounds, of luggage stored in the luggage compartment is 0.94. Using the .05 significance level, can we conclude that there is a positive association between the two variables?

53. The following data show the retails price for 12 randomly selected laptop computers along with their corresponding processor speeds gigaherz.
Computer Speed Price
1 2.0 $ 2,689
2 1.6 1,229
3 1.6 1,419
4 1.8 2,589
5 2.0 2,849
6 1.2 1,349
7 2.0 2,929
8 1.6 1,849
9 2.0 2,819
10 1.6 2,669
11 1.0 1,249
12 1.4 1,159

A. Develop a linear equation that can be used to describe how the price depends on the processor speed.

B. Based on your regression equation is there one machine that seems particularly over-or-underpriced?

C. Compute the correlation coefficient between the two variables. At the .05 significance level conduct a test of hypothesis to determine if the population correlation could be greater than zero

57. Listed below are the movies with the largest world box office sales and their budget (total amount available to spend making the picture)

Movie Budget ($millions) Box office ($millions) Year
1. Star wars 11 1153 1977
2. E.T 54 915 1982
3. Titanic 200 839 1997
4. The Empire strikes back 18 624 1980
5. Return of the jedi 33 599 1983
6. Jurassic park 63 546 1993
7. Star wars: the phantom of menace 110 544 1999
8. Forrest gump 55 500 1994
9. The lion king 97 474 1994
10. Shrek 2 75 451 2004
11. Spider-man 139 446 2002
12. Independence day 75 444 1996
13. Home alone 101 427 1990
14. Pirates of the carribean: dead man's chest 225 423 2006
15. LOTR: return of the king 94 401 2003
16. Spider-man 2 200 385 2004
17. The passion of the Christ 25 382 2004
18. Star wars episode III 115 380 2005
19. Lord of the rings: two towers 94 376 2002
20. The sixth sense 40 370 1999
21. Finding nemo 94 361 2003
22. Harry potter and the socerer's stone 130 360 2001
23. Lord of the ring: fellowship ring 109 355 2001
24. Men in black 90 349 1997
25. Star wars Ep II 120 343 2002
26. Aladdin 28 331 1992
27. Ghost 22 326 1990
28. Pirates of the carribean 125 325 2003
29. The lost world 73 320 1997
30. Terminator 2 judgement day 100 308 1991
31. The matrix reloaded 127 299 1991
32. Chronicles of narania 180 292 2003
33. Harry potter/goblet of fire 140 290 2005
34. Monsters inc 115 290 2005
35. Harry potter/chamber of secrets 100 290 2002
36. Meet the fockers 80 288 2004
37. Armageddon 140 276 1998
38. The incredibles 92 270 2004
39. Harry potter/prisoner of Azkaban 130 257 2004
40. Mission impossible 2 125 256 2000
41. Night at the museum 120 246 2006
42. War of the worlds 128 234 2005
43. King kong 207 218 2005
44. The da vinci code 125 218 2006
45. Ice age the meltdown 80 195 2006
46. Madagascar 124 193 2005
47. Day after tomorrow 125 193 2004
48. Casino royale 150 167 2006
49. Troy 185 138 2004

Find the correlation between the world box office budget and the world box office sales. Comment on the association between the two variables. Can we conclude that there is a significant negative correlation between movies with large budgets and large box office revenues?

Solution Summary

The solution provides step-by-step method of performing a Regression Analysis and Correlation Hypothesis Test. Regression Analysis (Correlation Coefficient, Coefficient of Determination, Covariance, Regression Equation, Least Square Line, Scatter Plot etc.) have been performed in EXCEL. All the steps involved in Correlation Hypothesis Test (formulation of Null and Alternate Hypothesis, Selection of Significance Level, Choosing the appropriate Test-Statistic, Decision Rule, Calculation of Test-Statistic, P-Value and Conclusion) have been explained in details.

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