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 Buildup Factor 1 2 3 4 6. 7 8. 2.1 4.7 6.2 7.5 8.0 9.3 10.7 12.4 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 | 2.1 4.7 y | 4.7 For convenience, we are given the following sums. 6.2 7.5 8.0 9.3 10.7 6.2 7.5 8.0 9.3 10.7 12.4 Ex = 48.5, Ey = 58.8, Ex² = 386.17, Ey² = 535.52, Exy = 452.1 (a) Use the sums provided (or a calculator with least-squares regression) to compute the equation of the sample least-squares line, ŷ = a + bx. (Use 4 decimal places.) a If the buildup factor was x = 5.4 one week, what would you predict the buildup factor to be the next week? (Use 2 decimal places.) (b) Compute the sample correlation coefficient r and the coefficient of determination 2. (Use 4 decimal places.) Test p> 0 at the 1% level of significance. (Use 2 decimal places.) critical t Conclusion O Reject the null hypothesis, there is sufficient evidence that p > 0. O Reject the null hypothesis, there is insufficient evidence that p > 0. O Fail to reject the null hypothesis, there is insufficient evidence that p > 0. O Fail to reject the null hypothesis, there is sufficient evidence that p > 0.
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 Buildup Factor 1 2 3 4 6. 7 8. 2.1 4.7 6.2 7.5 8.0 9.3 10.7 12.4 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 | 2.1 4.7 y | 4.7 For convenience, we are given the following sums. 6.2 7.5 8.0 9.3 10.7 6.2 7.5 8.0 9.3 10.7 12.4 Ex = 48.5, Ey = 58.8, Ex² = 386.17, Ey² = 535.52, Exy = 452.1 (a) Use the sums provided (or a calculator with least-squares regression) to compute the equation of the sample least-squares line, ŷ = a + bx. (Use 4 decimal places.) a If the buildup factor was x = 5.4 one week, what would you predict the buildup factor to be the next week? (Use 2 decimal places.) (b) Compute the sample correlation coefficient r and the coefficient of determination 2. (Use 4 decimal places.) Test p> 0 at the 1% level of significance. (Use 2 decimal places.) critical t Conclusion O Reject the null hypothesis, there is sufficient evidence that p > 0. O Reject the null hypothesis, there is insufficient evidence that p > 0. O Fail to reject the null hypothesis, there is insufficient evidence that p > 0. O Fail to reject the null hypothesis, there is sufficient evidence that p > 0.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 15PPS
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