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 serialcorrelation 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 aboutserial 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'sblood 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 weekafter the vaccination for 8 weeks. Results are shown in the following time series.Original Time Series4 5Week178Buildup Factor2.34.66.27.58.09.410.612.1To 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 areshifting 1 week ahead, we now have 7 data pairs (not 8).Data for Serial Correlation2.34.66.27.58.09.410.6y4.66.27.58.09.410.612.1For convenience, we are given the following sums.Ex = 48.6, Ey = 58.4, Ex2 = 385.86, Ey² = 526.98, Exy = 448.7(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. (Round your answers to four decimal places.)a =b =If the buildup factor was x = 5.7 one week, what would you predict the buildup factor to be the next week? (Round your answer to two decimal places.)

Answered: Image /qna-images/answer/6b2d8eb2-7d60-4914-b755-30f728d76d7b.jpgIf, x=5.7, the predicted value of y is y5.7=2.1457+(0.8926×5.7)=2.1457+5.0878=7.2335≈7.23.

Math

Statistics

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 For convenience, we are given the following sums. Ex = 48.6, Ey = 58.4, Ex? = 385.86, Ey? = 526.98, Exy = 448.7 (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. (Round your answers to four decimal places.) a = b = If the buildup factor was x = 5.7 one week, what would you predict the buildup factor to be the next week? (Round your answer to two decimal places.)

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 For convenience, we are given the following sums. Ex = 48.6, Ey = 58.4, Ex? = 385.86, Ey? = 526.98, Exy = 448.7 (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. (Round your answers to four decimal places.) a = b = If the buildup factor was x = 5.7 one week, what would you predict the buildup factor to be the next week? (Round your answer to two decimal places.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: O a.r = -0.2548 O b.r = -0.9382 O c.r= 0.9963 O d.r= 0.0767

A: We have given that, Which of the following linear correlation Coefficients suggests a weak negative…

Q: The following data are the morning and evening high tide levels for Charleston, SC from January…

A: Given, data on the morning and evening high tide levels for Charleston. The steps to obtain the…

Q: A sociologist hypothesizes that the number of gun shops in a city will be related to its violent…

Q: Use the given data set to complete parts (a) through (c) below. (Use a= 0.05.) 10 13 9 11 14 6 4…

A: (a) Use EXCEL to construct the scatter plot. EXCEL procedure: Go to EXCEL Go to Insert menu…

Q: 1, Zoom Add Page Insert Table Chart Text Shape Media Comment The table below gives the list price…

Q: riance and correlation matric

A: s no X1 X2 X3 X4 1 48 7.2 4.9 495 2 40 7.4 5 524 3 41 7.7 5.3 461 4 52 7.1 4.8 552 5 41…

Q: ) Which of the following represents the closest relationship between two variables? Or= -0.50…

Q: Develop a formal paper on the following topic. The paper should be verbally and visually…

A: A linear correlation between two variables occurs if the change in one variable affects the change…

Q: Given the information find the equation for the least square lones as well as the correlation…

Q: Name the two variables of interest(1 measured variable on an interval/ratio, and another is…

A: First of all Interval scale where order and the difference between two values are meaningful for…

Q: A researcher wants to know how the number of drinks consumed on a night out affects decision-making…

A: 1] Null Hypothesis HO: p = 02] Alternative hypothesis H1: p is not equal to 03]df = n-2 = 34]…

Q: a pearson correlation value (r) indicates the exact degree of accuracy in which a researcher can…

A: Pearson Correlation Coefficient r is a measure which indicates the strength of a linear association…

Q: For these data, find the SSx, SSy, SP, and Pearson correlation coefficient, r.

A: Given: XY16025835545710230

Q: 2- Listed below are # of inches of snow in the storm and # of the kids absent from the school next…

A: The linear correlation between the two variable are tested using the t test. It is calculated using…

Q: A biologist was interested in the relationship between the ve- locity at which a beluga whale swims…

A: We have to check what changes happen in correlation cofficient on changing unit of one variable.

Q: Which variable has the strongest linear relationship with salary? Which two variables have the…

A: The extent of linear relation between two variables is known as correlation. It is denoted by r.…

Q: A researcher measures IQ and weight for a group of college What kind of correlation is likely to be…

A: The likely correlation between IQ and weight for a group of college students.The correct option is…

Q: Fill in the following table and calculate the correlation coefficient.

A: Given data table in the question is,

Q: We have obtain the following x-y-pairs of data: x 1.8 10 4.2 7 -8.3 y 6.3 9.6 7.4 -1.3 -1.6 Compute…

Q: The relationship between two variables partialling out the effect that a third variable has on one…

A: The correct answer is a. Partial correlation.

Q: 1. A pork producer is interested in figuring out if weaning weight is associated with a pig's weight…

A: Introduction: It is required to obtain the correlation coefficient between the two variables,…

Q: Every morning, Naomi jogs the same 2-mile route around her neighborhood. She selects a random sample…

A: The relationship between the time to complete a jogging route and the pulse rate is measured.A…

Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

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
4 5
Week
1
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
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
For convenience, we are given the following sums.
Ex = 48.6, Ey = 58.4, Ex2 = 385.86, Ey² = 526.98, Exy = 448.7
(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. (Round your answers to four decimal places.)
a =
b =
If the buildup factor was x = 5.7 one week, what would you predict the buildup factor to be the next week? (Round your answer to two decimal places.)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Correlation, Regression, and Association$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions

A survey was taken in 2018 that asked people about their saving habits. Researchers wanted to know if people who saved more also spent less. The scatterplot below shows their results when comparing two variables: the amount people reported that they put into savings each month, and the amount they reported that they spent on clothes. The researchers found the correlation coefficient for this data to be -0.239. Which of the following is true about these variables? a. There is no relationship between savings and money spent on clothes each month.b. There is a weak, positive linear relationship between savings and money spent on clothes each month.c. There is a perfect, negative linear relationship between savings and money spent on clothes each month.d. There is a weak, negative linear relationship between savings and money spent on clothes each month.
Below is data for two variables, X and Y. Answer the questions that follow. X Y X-MX Y-MY (X-MX)2 (Y-MY)2 (X-MX)(Y-MY) 3 3 -2 -1 4 1 2 4 3 -1 -1 1 1 ___ 6 4 1 ___ 1 0 0 7 6 2 2 ___ 4 4 Positive or negative correlation?
A Pearson correlation of r = -0.90 indicates that the data points are clustered close to a line that slopes down to the right. Question 3 options: True False
A history instructor has given the same pretest and the same final examination each semester. he is interested in determining if there is a relationship between the scores of the two tests. he computes the linear correlation coefficient and notes that it is 1.15. what does the correlation coefficient value tells the instructor? a. there is a strong positive correlation between the test b. there is a strong negative correlation between the test c. the history instructor has made a computational error d. the correlation is something other than linear
A random sample of college students was surveyed about how they spend their time each week. The scatterplot below displays the relationship between the number of hours each student typically works per week at a part- or full-time job and the number of hours of television each student typically watches per week. The correlation between these variables is r = –0.63, and the equation we would use to predict hours spent watching TV based on hours spent working is as follows: Predicted hours spent watching TV = 17.21 – 0.23(hours spent working) Since we are using hours spent working to help us predict hours spent watching TV, we’d call hours spent working a(n) __________________ variable and hours spent watching TV a(n) __________________ variable. The correlation coefficient, along with what we see in the scatterplot, tells us that the relationship between the variables has a direction that is _________________ and a strength that is ______________________. According to the…
Which of the following sets of data represent valid functions? OR = {(– 5,0), (2, 3), (6, 4), (8, 9), (15, 14)} OG = {(– 5, – 3), (2, 1), (2, 4), (8, 7), (15, 13)} OS = {(– 5, – 4), (2, 3), (6, 5), (7, 9), (11, 16)} OF = {(– 4, – 1), (3, 2), (5, 4), ( – 4, – 1), (10, 15)} - - Question Help: DVideo
Pls help ASAP
e. Compute the covariance and correlation coefficient r between the right tire pressure. f. How do you know the relationship between pressure in the left and right tires is positive. g. What value would a correlation coefficient (r) be close to if there was no (linear) relationship between the 2 tire pressures?
As temperature decreases, rates of crime also seem to decrease. Which of the following Pearsons R values represents the strongest possible correlation between these two variables?" -0.5 -1 0.5 1
At question c it reads - competitor number 14(row12)
After gathering data about the number of starfish and measuring the pollution in areas of the ocean you find a negative linear correlation between pollution levels and number of starfish. What can you conclude based on this information? a. There is a confounding variable that is affecting both pollution and starfish. b. As pollution rises the number of starfish falls c. That pollution is causing starfish to die, leading to the negative correlation d. That pollution is supporting starfish, leading to the negative correlation
This is a continuation of the last question I posted: f. The value of linear correlation coefficient r is i. 0.948 ii. 0.974 iii. -0.948 iv. -0.974 g.Based on your answer in part (f), the linear dependance between weekly exercise time and change in cholesterol level is strong negative i. True ii. False H. When weekly exercise time is 460 minutes (approximately 66 minutes per day), the 95 percent confidence interval for change in cholesterol level is (197.3, 225.4). This means that: i. If one person exercises 460 minutes per week, his/hers change in cholesterol level will be between 197.3 and 225.4 with 95 percent certainty.ii. If several people exercise 460 minutes per week, their average change in choles- terol level will be between 197.3 and 225.4 with 95 percent certainty. I. When weekly exercise time is 460 minutes (approximately 66 minutes per day), the 95 percent prediction interval for change in cholesterol level is (155.1, 267.6). This means that i. If one person…