Essentials of Business Analytics (MindTap Course List)
2nd Edition
ISBN: 9781305627734
Author: Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 8, Problem 17P
Consider the following time series:
- a. Construct a time series plot. What type of pattern exists in the data?
- b. Use simple linear
regression analysis to find the parameters for the line that minimizes MSE for this time series. - c. What is the forecast for t = 6?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Assume that the current date is February 1, 2021. The linear regression model was applied to a monthly time series data based on the last 24 months' sales. (From January 2019 through December 2020). The following partial computer output summarizes the results.
Coefficient
Estimate
t
Intercept
4.3
2.07
Slope
1.6
2.98
Determine the predicted sales for February.
The quarterly sales data (number of copies sold) for a college textbook over the past three years follow.
a) Construct a time series plot. What type of pattern exists in the data?
b) Use a regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. Qtr1=1 if Quarter 1, 0 otherwise; Qtr2=1 if Quarter 2, 0 otherwise; Qtr3=1 if Quarter 3, 0 otherwise.
c) Compute the quarterly forecasts for next year.
d) Let t=1 to refer to the observation in quarter 1 of year 1; t=2 to refer to the observation in quarter 2 of year 1; ...; and t=12 to refer to the observation in quarter 4 of year 3. Using the dummy variables defined in part (b) and also using t, develop an equation to account for seasonal effects and any linear trend in the time series. Based upon the seasonal effects in the data and linear trend, compute the quarterly forecasts for next year.
Consider the following time series:
Quarter
Year 1
Year 2
Year 3
80
74
65
69
61
51
48
50
43
68
71
82
a. Construct a time-series plot. What type of pattern exists in the data? Is there an indication
of a seasonal pattern?
b. Use multiple linear regression model with dummy variables as follows to develop an
equation to account for seasonal effects in the data. Qtrl = 1 if quarter 1,0 else; Qtr2 = 1 if
quarter 2,0 else; Qtr3 = 1 if quarter 3,0 else.
c. Compute the quarterly forecasts for next year.
Chapter 8 Solutions
Essentials of Business Analytics (MindTap Course List)
Ch. 8 - Consider the following time series data:
Using...Ch. 8 - Refer to the time series data in Problem 1. Using...Ch. 8 - Problems 1 and 2 used different forecasting...Ch. 8 - Consider the following time series data:
Compute...Ch. 8 - Consider the following time series...Ch. 8 - Consider the following time series...Ch. 8 - Refer to the gasoline sales time series data in...Ch. 8 - Prob. 8PCh. 8 - Prob. 9PCh. 8 - Prob. 10P
Ch. 8 - For the Hawkins Company, the monthly percentages...Ch. 8 - Corporate triple A bond interest rates for 12...Ch. 8 - The values of Alabama building contracts (in...Ch. 8 - The following time series shows the sales of a...Ch. 8 - Prob. 15PCh. 8 - The following table reports the percentage of...Ch. 8 - Consider the following time series: a. Construct a...Ch. 8 - Consider the following time series:
Construct a...Ch. 8 - Because of high tuition costs at state and private...Ch. 8 - The Seneca Children’s Fund (SCF) is a local...Ch. 8 - The president of a small manufacturing firm is...Ch. 8 - Consider the following time series: a. Construct a...Ch. 8 - Consider the following time series...Ch. 8 - The quarterly sales data (number of copies sold)...Ch. 8 - Prob. 25PCh. 8 - South Shore Construction builds permanent docks...Ch. 8 - Hogs & Dawgs is an ice cream parlor on the border...Ch. 8 - Donna Nickles manages a gasoline station on the...Ch. 8 - The Vintage Restaurant, on Captiva Island near...
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.Similar questions
- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardOlympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forwardTable 6 shows the year and the number ofpeople unemployed in a particular city for several years. Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will the number of unemployed reach 5 people?arrow_forward
- What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forwardLife Expectancy The following table shows the average life expectancy, in years, of a child born in the given year42 Life expectancy 2005 77.6 2007 78.1 2009 78.5 2011 78.7 2013 78.8 a. Find the equation of the regression line, and explain the meaning of its slope. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 2019? e. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 1580?2300arrow_forwardThe US. import of wine (in hectoliters) for several years is given in Table 5. Determine whether the trend appearslinear. Ifso, and assuming the trend continues, in what year will imports exceed 12,000 hectoliters?arrow_forward
- Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?arrow_forwardCable TV The following table shows the number C. in millions, of basic subscribers to cable TV in the indicated year These data are from the Statistical Abstract of the United States. Year 1975 1980 1985 1990 1995 2000 C 9.8 17.5 35.4 50.5 60.6 60.6 a. Use regression to find a logistic model for these data. b. By what annual percentage would you expect the number of cable subscribers to grow in the absence of limiting factors? c. The estimated number of subscribers in 2005 was 65.3million. What light does this shed on the model you found in part a?arrow_forwardTable 2 shows a recent graduate’s credit card balance each month after graduation. a. Use exponential regression to fit a model to these data. b. If spending continues at this rate, what will the graduate’s credit card debt be one year after graduating?arrow_forward
- XYZ Corporation Stock Prices The following table shows the average stock price, in dollars, of XYZ Corporation in the given month. Month Stock price January 2011 43.71 February 2011 44.22 March 2011 44.44 April 2011 45.17 May 2011 45.97 a. Find the equation of the regression line. Round the regression coefficients to three decimal places. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict the stock price to be in January 2012? January 2013?arrow_forwardThe U.S. Census tracks the percentage of persons 25 years or older who are college graduates. That data forseveral years is given in Table 4[14]. Determine whether the trend appears linear. If so, and assuming the trendcontinues. in what year will the percentage exceed 35%?arrow_forwardUse R programming or excel to answer the following. Visualize your answers. Consider the following quarterly time series: Quarter Year 1 Year 2 Year 3 1 923 1112 1243 2 1056 1156 1301 3 1124 1124 1254 4 992 1078 1198 Construct a time series plot. What type of pattern exists in the data? Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. Qtr1 = 1 if quarter 1, 0 otherwise; Qtr2 = 1 if quarter 2, 0 otherwise; Qtr3 = 1 if quarter 3, 0 otherwise. Compute the quarterly forecasts for next year based on the model developed in part b.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Time Series Analysis Theory & Uni-variate Forecasting Techniques; Author: Analytics University;https://www.youtube.com/watch?v=_X5q9FYLGxM;License: Standard YouTube License, CC-BY
Operations management 101: Time-series, forecasting introduction; Author: Brandoz Foltz;https://www.youtube.com/watch?v=EaqZP36ool8;License: Standard YouTube License, CC-BY