Statistics for Business and Economics (13th Edition)
13th Edition
ISBN: 9780134506593
Author: James T. McClave, P. George Benson, Terry Sincich
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 14.9, Problem 14.54ACI
Mortgage interest rates. Refer to the data on annual mortgage interest rate (Yt), Exercise 14.41 (p. 14-37). You fit the simple linear regression model, E (Yt) =β0 + β1t, to the data for the years 1990-2015 (t = 0, 1, 2, ... , 25).
a. Find and plot the regression residuals against I. Does the plot suggest the presence of autocorrelation? Explain.
b. Conduct the Durbin-Watson test (at α = .05 ) to test formally for the presence of positively autocorrelated regression errors.
c. Comment on the validity of the inference concerning model adequacy in light of the result of part b.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
The data shown below are the initial weights and gains in weight (in grams) of female rats on a high protein diet from 24 to 84 days of age. The point of interest in these data is whether the gain in weight is related to (dependent on) the initial weight. If so, then feeding experiments on female rats can be made more precise by adjusting for differences in initial weights of the rats. Statistically test this with a regression analysis.
Rat Number
Initial Weight (gms)
Weight Gain (gms)
1
50
128
2
64
159
3
76
158
4
64
119
5
74
133
6
60
112
7
69
96
8
68
126
9
56
132
10
48
118
11
57
107
12
59
106
13
46
82
14
45
103
15
65
104
I used excel's regression took pak and got the following:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.489416452
R Square
0.239528464
Adjusted R Square
0.181030653
Standard Error
8.869929833
Observations
15…
Calculate two lines of regression and calculate a linear regression equation to model the data given below:
years (1980,1985,1990,1995,2000)
Enrolment ( 21,25,29,39,47)
We want to predict the percentage weight loss for 2011 participants, based on 2010 data. If we construct a simple linear regression model, predicting percentage weight loss as a function of starting weight, what are the values of y-intercept ("a") and regression coefficient ("b"), rounded to one and two decimal places?0.4 and 0.110.3 and 0.010.4 and 0.020.3 and 0.07According to the regression model calculated above, what is the value of "r", rounded to one decimal place?00.200.300.400.500.1
In the above question, what does "r" represent?Spearman's correlation coefficientPearson's correlation coefficientThe variability of the dependent variable explained by the independent variableThe variability of the independent variable explained by the dependent variable
If we were to add "age" as an additional independent variable to the calculated regression model, we'd have a multiple linear regression equation. For such a model, would the calculated "R" be :- equal to or greater than the "r"…
Chapter 14 Solutions
Statistics for Business and Economics (13th Edition)
Ch. 14.1 - Explain in words how to construct a simple index.Ch. 14.1 - Explain in words how to calculate the following...Ch. 14.1 - Explain in words the difference between Laspeyres...Ch. 14.1 - The table below gives the prices for three...Ch. 14.1 - Refer to Exercise 14.4. The next table gives the...Ch. 14.1 - Annual median family income. The table below lists...Ch. 14.1 - Annual U.S. craft beer production. While overall...Ch. 14.1 - Quarterly single-family housing starts. The...Ch. 14.1 - Spot price of natural gas. The table shown in the...Ch. 14.1 - Employment in farm and nonfarm categories....
Ch. 14.1 - GOP personal consumption expenditures. The gross...Ch. 14.1 - GDP personal consumption expenditures (contd)....Ch. 14.1 - Weekly earnings for workers. The table in the next...Ch. 14.1 - Production and price of metals. The level or price...Ch. 14.2 - Describe the effect of selecting an exponential...Ch. 14.2 - A monthly time series is shown in the table to the...Ch. 14.2 - Annual U.S. craft beer production. Refer to the...Ch. 14.2 - Foreign fish production. Overfishing and pollution...Ch. 14.2 - Yearly price of gold. The price of gold is used by...Ch. 14.2 - Personal consumption in transportation. There has...Ch. 14.2 - OPEC crude oil imports. The data in the table...Ch. 14.2 - SP 500 Stock Index. Standard Poors 500 Composite...Ch. 14.5 - How does the choice of the smoothing constant w...Ch. 14.5 - Refer to Exercise 14.4 (p. 14-9). The table with...Ch. 14.5 - Annual U.S. craft beer production. Refer to...Ch. 14.5 - Quarterly single-family housing starts. Refer to...Ch. 14.5 - Consumer Price Index. The CPI measures the...Ch. 14.5 - OPEC crude oil imports. Refer to the annual OPEC...Ch. 14.5 - SP 500 Stock Index. Refer to the quarterly...Ch. 14.5 - SP 500 Stock Index (contd). Refer to Exercise...Ch. 14.5 - Monthly gold prices. The fluctuation of gold...Ch. 14.6 - Annual U.S. craft beer production. Refer to the...Ch. 14.6 - Annual U.S. craft beer production (contd). Refer...Ch. 14.6 - SP 500 Stock Index. Refer to your exponential...Ch. 14.6 - SP 500 Stock Index (contd). Refer to your Holt...Ch. 14.6 - Monthly gold prices. Refer to the monthly gold...Ch. 14.6 - US school enrollments. The next table reports...Ch. 14.8 - The annual price of a finished product (in cents...Ch. 14.8 - Retail sales in Quarters 14 over a 10-year period...Ch. 14.8 - What advantage do regression forecasts have over...Ch. 14.8 - Mortgage interest rates. The level at which...Ch. 14.8 - Price of natural gas. Refer to Exercise 14.9 (p....Ch. 14.8 - A gasoline tax on carbon emissions. In an effort...Ch. 14.8 - Predicting presidential elections. Researchers at...Ch. 14.8 - Life insurance policies in force. The table below...Ch. 14.8 - Graphing calculator sales. The next table presents...Ch. 14.8 - Prob. 14.47ACICh. 14.9 - Define autocorrelation. Explain why it is...Ch. 14.9 - For each case, indicate the decision regarding the...Ch. 14.9 - What do the following Durbin-Watson statistics...Ch. 14.9 - Company donations to charity. Refer to the Journal...Ch. 14.9 - Forecasting monthly car and truck sales. Forecasts...Ch. 14.9 - Predicting presidential elections. Refer to the...Ch. 14.9 - Mortgage interest rates. Refer to the data on...Ch. 14.9 - Price of natural gas. Refer to the annual data on...Ch. 14.9 - Life insurance policies in force. Refer to the...Ch. 14.9 - Modeling the deposit share of a retail bank....Ch. 14 - Insured Social Security workers. Workers insured...Ch. 14 - Insured Social Security workers (contd). Refer to...Ch. 14 - Retail prices of food items. In 1990, the average...Ch. 14 - Demand for emergency room services. With the...Ch. 14 - Mortgage interest rates. Refer to the annual...Ch. 14 - Price of Abbott Labs stock. The yearly closing...Ch. 14 - Price o f Abbott Labs stock (contd). Refer to...Ch. 14 - Prob. 14.65ACICh. 14 - Prob. 14.66ACICh. 14 - Quarterly GOP values (contd). Refer to Exercise...Ch. 14 - Prob. 14.68ACICh. 14 - Prob. 14.69ACICh. 14 - Prob. 14.70ACICh. 14 - IBM stock prices. Refer to Example 14.1 (p. 14-5)...Ch. 14 - Prob. 14.72ACI
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
- Olympic 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_forwardXYZ 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_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_forward
- What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forwardTable 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_forwardFind the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forward
- Table 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_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_forwardWhat is regression analysis? Describe the process of performing regression analysis on a graphing utility.arrow_forward
- A Dubious Model of Oil Prices The following table shows the prices of oil in U.S. dollars per barrel, t years since 1990, One analysis involving additional data used a cubic equation to model this data. t Years since 1990 0 2 5 7 10 12 15 17 20 21 P Price, dollars per barrel 18.91 16.22 16.63 18.20 27.04 23.47 49.63 69.04 77.46 106.92 a. Use cubic regression to model these data. Round the regression parameters to four decimal places. b. Plot the data along with the cubic model. c. In the analysis mentioned above, the graph is expanded through 2020. Expand the viewing window to show the model from 1990 to 2020. d. What estimate does the model give for oil prices in 2015? e. The actual price of oil in December of 2015 was about 35 per barrel. What basic principle in the use of models would be violated in relying on the estimate in part d?arrow_forwardThe least-squares regression equation is y = 602.1x + 17,023 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.6748. Complete parts (a) through (d). C Median Income 55000- 25000 ● (c) Interpret the slope. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal. Do not round.) A. For 0% of adults having a bachelor's degree, the median income is predicted to be $ B. For a median income of $0, the percent of adults with a bachelor's degree is %. O C. For every dollar increase in median income, the percent of adults having at least a bachelor's degree is %, on average. OD. For every percent increase in adults having at least a bachelor's degree, the median income increases by $, on average. 15 20 25 30 35 40 45 50 55 60 Bachelor's % U (a) Predict the…arrow_forwardUsing the unemployment data provided, investigate the association between the male unemployment rate in 2007 and 2010 for a sample of 52 countries. Complete parts (a) through (d). cessible Res Click the icon to view the data table. 車 urchase Opti a) Find a regression model predicting the 2010 rate from the 2007 rate for the sample of 52 countries. 2010 Index = + x 2007 Index (Round to three decimal places as needed.) Communicatiarrow_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 LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher: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
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
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