(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. 1.3 3.5 4.4 7.2 6.9 8.2 9.0 11.2 13.1 y (b) For the (x, y) data set of part (a), compute the equation of the sample least-squares line ŷ = a + bx. (Use 4 decimal places.) a b If the number of hits was 9.3 (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 r2. (Use 4 decimal places.) Test p > 0 at the 1% level of significance. (Use 2 decimal places.) critical t
(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. 1.3 3.5 4.4 7.2 6.9 8.2 9.0 11.2 13.1 y (b) For the (x, y) data set of part (a), compute the equation of the sample least-squares line ŷ = a + bx. (Use 4 decimal places.) a b If the number of hits was 9.3 (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 r2. (Use 4 decimal places.) Test p > 0 at the 1% level of significance. (Use 2 decimal places.) critical t
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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 10° is shown.
Original Time Series
Day
1
2
4
7
8.
9.
10
Hits x 105
1.3
3.5
4.4
7.2
6.9
8.2
9.0
11.2
13.1
14.7
(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.
1.3
3.5
4.4
7.2
6.9
8.2
9.0
11.2
13.1
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 9.3 (× 10°) one day, what do you predict for the number of hits the next day? (Use 1 decimal place.)
(x 10°) hits
(c) Compute the sample correlation coefficient r and the coefficient of determination r. (Use 4 decimal places.)
Test p > 0 at the 1% level of significance. (Use 2 decimal places.)
critical t
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