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. An Internet advertising agency is studying the number of "hits" on a certain web site during an advertising campaign. It is hoped that as the campaign progresses, the number of hits on the web site will also increase in a predictable way from one day to the next. For 10 days of the campaign, the number of hits x 105 is shown. Original Time Series 2 3 1.2 3.5 4 10 Day Hits x 105 4.4 7.3 6.9 8.3 9.0 11.2 13.2 14.9 (a) To construct a serial correlation, we use data pairs (x, y) where x = original data and y = original data shifted ahead by one time period. Construct the data set (x, y) for serial correlation by filling in the following table. 1.2 3.5 4.4 7.3 6.9 11.2 13.2 8.3 9.0 (b) For the (x, y) data set of part (a), compute the equation of the sample least-squares line ý = a + bx. (Use 4 decimal places.) a If the number of hits was 9.6 (x 105) one day, what do you predict for the number of hits the next day? (Use 1 decimal place.) ](x 105) hits (c) 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. Would you say the time series of website hits is relatively predictable from one day to the next? Explain.
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. An Internet advertising agency is studying the number of "hits" on a certain web site during an advertising campaign. It is hoped that as the campaign progresses, the number of hits on the web site will also increase in a predictable way from one day to the next. For 10 days of the campaign, the number of hits x 105 is shown. Original Time Series 2 3 1.2 3.5 4 10 Day Hits x 105 4.4 7.3 6.9 8.3 9.0 11.2 13.2 14.9 (a) To construct a serial correlation, we use data pairs (x, y) where x = original data and y = original data shifted ahead by one time period. Construct the data set (x, y) for serial correlation by filling in the following table. 1.2 3.5 4.4 7.3 6.9 11.2 13.2 8.3 9.0 (b) For the (x, y) data set of part (a), compute the equation of the sample least-squares line ý = a + bx. (Use 4 decimal places.) a If the number of hits was 9.6 (x 105) one day, what do you predict for the number of hits the next day? (Use 1 decimal place.) ](x 105) hits (c) 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. Would you say the time series of website hits is relatively predictable from one day to the next? Explain.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
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
Transcribed Image Text: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.
An Internet advertising agency is studying the number of "hits" on a certain web site during an advertising campaign. It is hoped that as the
campaign progresses, the number of hits on the web site will also increase in a predictable way from one day to the next. For 10 days of the
campaign, the number of hits x 105 is shown.
Original Time Series
Day
Hits x 105
2
3
4
6
7
8.
10
1.2
3.5
4.4
7.3
6.9
8.3
9.0
11.2
13.2
14.9
(a) To construct a serial correlation, we use data pairs (x, y) where x = original data and y = original data shifted ahead by one time
period. Construct the data set (x, y) for serial correlation by filling in the following table.
1.2
3.5
4.4
7.3
6.9
8.3
9.0
11.2
13.2
y
(b) For the (x, y) data set of part (a), compute the equation of the sample least-squares line ý = a + bx. (Use 4 decimal places.)
a
b
If the number of hits was 9.6 (x 105) one day, what do you predict for the number of hits the next day? (Use 1 decimal place.)
|(× 105) hits
(c) 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.
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.
Would you say the time series of website hits is relatively predictable from one day to the next? Explain.
O No, the data do not support a high serial correlation and do not indicate a predictable original time series from one day to the
next.
O Yes, the data support a high positive serial correlation and indicate a predictable original time series from one day to the next.
Yes, the data support a high negative serial correlation and indicate a predictable original time series from one day to the next.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Knowledge Booster
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.Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman