webassign.net/web/Student/Assignment-Responses/last?dep=33455659#Q19 Career C School = U Relaunch to update : Anyone who has been outdoors on a summer evening has probably heard crickets. Did you know that it is possible to use the cricket as a thermometer? Crickets tend to chirp more frequently as temperatures increase. In the following data, x is a random variable representing chirps per second and y is a random variable representing temperature (F). X 20.3 16.4 20.3 18.2 16.2 15.5 14.7 17.1 y 88.2 70.8 91.9 84.7 79.6 75.2 69.7 82.0 X 15.4 16.2 15.0 17.2 16.0 17.0 14.4 y $9.4 83.3 79.6 82.6 80.6 83.5 76.3 USE SALT Complete parts (a) through (e) after verifying that x = 249.9, y = 1,197.4, x = 4,208.37, y = 96,189.34, xy = 20,081.36, and r = 0.8038. (a) Draw a scatter diagram displaying the data. 9 y (temperature (in degrees Fahrenheit)) 70 70 75 80 80 85 85 90 F1 15 16 17 18 19 20 y(chirns per second APR 1 19 tv F2 80 F3 DOD 000 F4 P5 20 19 18 y (temperature (in degrees Fahrenheit)) 17 17 > 16 15 70 75 80 y(chirns per second ZOOM A G 34 DI FO F7 F8 & 85 90 A F9 P W NEW 610 24 t F12 C Career Cengage Learning X Math 1025 Wk 16: Prac HW C webassign.net/web/Student/Assignment-Responses/last?dep=33455659#Q19 School y (temperature (in degrees Fahrenheit)) 20 20 19 18 17 16- 15 15 16 70 75 17 + 18 19 20 70 75 x (chirps per second) 80 x (chirps per second) 85 90 (b) Find x (in chirps per second). (Round your answer to four decimal places.) x = 16.66 chirps per second Find y (in F). (Round your answer to four decimal places.) y = F y (temperature (in degrees Fahrenheit)) 70 70 75 75 80 80 85 85 90 90 80 x (chirps per second) 85 90 15 16 17 18 19 20 20 x(chirps per second) Find the equation of the least-squares line = a + bx. (Round your numerical values to four decimal places.) y= 30.7463 + 2.9460x APR 19 -> Career C File Edit View History Bookmarks Profiles Tab Window Help Math 1025 Wk 15: Practice Qu X Cengage Learning webassign.net/web/Student/Assignment-Responses/last?dep=33455659#Q22 9 School Math 1025 Wk 16: Prac HW C x + 20 Fri Apr 19 6:38 PM G U Relaunch to update : Serial correlation, also known as autocorrelation, describes the extent to which the result in one period of a time series is related to the result in the next period. A time series with high serial correlation is said to be very predictable from one period to the next. If the serial correlation is low (or near zero), the time series is considered to be much less predictable. For more information about serial correlation, see the book Ibbotson SBBI published by Morningstar. A research veterinarian at a major university has developed a new vaccine to protect horses from West Nile virus. An important question is: How predictable is the buildup of antibodies in the horse's blood after the vaccination is given? A large random sample of horses were given the vaccination. The average antibody buildup factor (as determined from blood samples) was measured each week after the vaccination for 8 weeks. Results are shown in the following time series. Original Time Series Week 1 23 4 5 6. 7 8 Buildup Factor 2.3 4.6 6.2 7.5 8.0 9.4 10.6 12.1 To construct a serial correlation, we simply use data pairs (x, y) where x = original buildup factor data and y = original data shifted ahead by 1 week. This gives us the following data set. Since we are shifting 1 week ahead, we now have 7 data pairs (not 8). Data for Serial Correlation X 2.3 4.6 6.2 7.5 8.0 9.4 10.6 y 4.6 6.2 7.5 8.0 9.4 10.6 12.1 USE SALT For convenience, we are given the following sums. x = 48.6, y = 58.4, Ex = 385.86, y = 526.98, xy = 448.7 (a) Use the sums provided (or a calculator with least-squares regression) to compute the equation of the sample least-squares line, = a + bx. (Round your answers to four decimal places.) a = 2.1454 100 b = 0.8926 If the buildup factor was x = 5.4 one week, what would you predict the buildup factor to be the next week? (Round your answer to two decimal places.) 6.97 O APR 1 19 tv S ! ZOOM A G X W NEW Chrome File Edit View History Bookmarks Profiles Tab Window Help Math 1025 Wk 15: Practice Qu x Cengage Learning X Math 1025 Wk 16: Prac HW CI X C webassign.net/web/Student/Assignment-Responses/last?dep=33455659#Q22 Career School Buildup Factor 2.3 4.6 6.2 7.5 8.0 9.4 10.6 12.1 + QO Fri Apr 19 6:39 PM G U Relaunch to update : To construct a serial correlation, we simply use data pairs (x, y) where x = original buildup factor data and y = original data shifted ahead by 1 week. This gives us the following data set. Since we are shifting 1 week ahead, we now have 7 data pairs (not 8). Data for Serial Correlation X 2.3 4.6 6.2 7.5 8.0 9.4 10.6 y 4.6 6.2 7.5 8.0 9.4 10.6 12.1 I USE SALT For convenience, we are given the following sums. x = 48.6, y = 58.4, x = 385.86, Zy2 = 526.98, xy = 448.7 (a) Use the sums provided (or a calculator with least-squares regression) to compute the equation of the sample least-squares line, = a + bx. (Round your answers to four decimal places.) a = 2.1454 b = 0.8926 If the buildup factor was x = 5.4 one week, what would you predict the buildup factor to be the next week? (Round your answer to two decimal places.) 6.97 (b) Compute the sample correlation coefficient r and the coefficient of determination 2. (Round your answers to four decimal places.) 100 = 0.9853 2 = 0.9708 Test p > 0 at the 1% level of significance. (Round your answers to three decimal places.) t = critical t = 3.365 nclusion APR 1 19 tv d CC ZOOM A G X P W NEW 80 F3 000 000 FA FG F7 F5 DIL F8 F9 FTO 4