STATISTICS F/BUSINESS+ECONOMICS-TEXT
STATISTICS F/BUSINESS+ECONOMICS-TEXT
13th Edition
ISBN: 9781305881884
Author: Anderson
Publisher: CENGAGE L
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 16, Problem 29SE

A sample containing years to maturity and yield (%) for 40 corporate bonds is contained in the data file named CorporateBonds (Barron’s, April 2, 2012).

  1. a. Develop a scatter diagram of the data using x = years to maturity as the independent variable. Does a simple linear regression model appear to be appropriate?
  2. b. Develop an estimated regression equation with x = years to maturity and x2 as the independent variables.
  3. c. As an alternative to fitting a second-order model, fit a model using the natural logarithm of price as the independent variable; that is, ŷ = b0 + b1ln(x). Does the estimated regression using the natural logarithm of x provide a better fit than the estimated regression developed in part (b)? Explain.

a.

Expert Solution
Check Mark
To determine

Construct a scatter diagram of the data using x=years to maturity as the independent variable.

Decide whether a simple linear regression model appears to be appropriate.

Answer to Problem 29SE

The scatter diagram of the data using x=years to maturity as the independent variable is:

STATISTICS F/BUSINESS+ECONOMICS-TEXT, Chapter 16, Problem 29SE , additional homework tip  1

A simple linear regression model does not appear to be appropriate.

Explanation of Solution

Calculation:

The data gives information on yield (%) of 40 corporate bonds and the respective years to maturity.

Scatterplot:

Software procedure:

Step by step procedure to draw scatter diagram using MINITAB software is given below:

  • Choose Graph > Scatterplot.
  • Choose Simple, and then click OK.
  • In Y–variables, enter the column of Yield.
  • In X–variables enter the column of Years.
  • Click OK.

Observation:

The scatterplot shows a gradual increase in the yield, at a decreasing rate, with increase in years up to 25. After this, there is a reduction in the values of yield. Thus, a simple linear regression model does not appear to be appropriate.

b.

Expert Solution
Check Mark
To determine

Develop an estimated multiple regression equation with x=years to maturity and x2 as the independent variables.

Answer to Problem 29SE

The estimated multiple regression equation with x=years to maturity and x2 as the independent variables is:

Yield=1.01695+0.460636 Years0.0102532 YearsSq_.

Explanation of Solution

Calculation:

Square transformation:

Software procedure:

Step by step procedure to make square transformation using MINITAB software is given as,

  • Choose Calc > Calculator.
  • In Store result in variable, enter YearsSq.
  • In Expression, enter ‘Years’^2.
  • Click OK.

The squared variable is stored in the column of ‘YearsSq’.

Regression:

Software procedure:

Step by step procedure to obtain the regression equation using MINITAB software:

  • Choose Stat > Regression > General Regression.
  • Under Responses, enter the column of Yield.
  • Under Model, enter the columns of Years, YearsSq.
  • Click OK.

Output using MINITAB software is given below:

STATISTICS F/BUSINESS+ECONOMICS-TEXT, Chapter 16, Problem 29SE , additional homework tip  2

From the output, the estimated multiple regression equation with x=years to maturity and x2 as the independent variables is:

Yield=1.01695+0.460636 Years0.0102532 YearsSq_.

c.

Expert Solution
Check Mark
To determine

Develop an estimated multiple regression equation using the natural logarithm of years as the independent variable.

Explain whether the current regression provides a better fit than the estimated regression developed in part b.

Answer to Problem 29SE

The estimated multiple regression equation using the natural logarithm of years as the independent variable is:

Yield=0.827876+1.56261 ln(Years)_.

The estimated regression using the natural logarithm of x provides a better fit than the estimated regression developed in part b.

Explanation of Solution

Calculation:

Logarithmic transformation:

Software procedure:

Step by step procedure to make logarithmic transformation using MINITAB software is given as,

  • Choose Calc > Calculator.
  • In Store result in variable, enter Years.
  • In Expression, enter ln(‘Years’).
  • Click OK.

The logarithm of the variable is stored in the column of ‘ln(‘Years’)’.

Regression:

Software procedure:

Step by step procedure to obtain the regression equation using MINITAB software:

  • Choose Stat > Regression > General Regression.
  • Under Responses, enter the column of Yield.
  • Under Model, enter the columns of ln(Years).
  • Click OK.

Output using MINITAB software is given below:

STATISTICS F/BUSINESS+ECONOMICS-TEXT, Chapter 16, Problem 29SE , additional homework tip  3

From the output, the estimated multiple regression equation using the natural logarithm of years as the independent variable is:

Yield=0.827876+1.56261 ln(Years)_.

Adjusted-R2:

The adjusted R2 is defined as the proportion of variation in the observed values of the response variable that is effectively explained by the regression. The squared correlation gives fraction of variability of response variable (y) accounted for by the linear regression model.

The value of adjusted R2 in the regression equation consisting of ‘Years’ and ‘YearsSq’ is R-Sq(adj)=64.99%.

The value of adjusted R2 in the regression equation consisting of ‘ln(Years)’ is R-Sq(adj)=66.08%.

Evidently, the current regression equation effectively explains more of the variation the response variable, than the second regression equation.

Thus, the estimated regression using the natural logarithm of x provides a better fit than the estimated regression developed in part b.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Microsoft Excel snapshot for random sampling: Also note the formula used for the last column 02 x✓ fx =INDEX(5852:58551, RANK(C2, $C$2:$C$51)) A B 1 No. States 2 1 ALABAMA Rand No. 0.925957526 3 2 ALASKA 0.372999976 4 3 ARIZONA 0.941323044 5 4 ARKANSAS 0.071266381 Random Sample CALIFORNIA NORTH CAROLINA ARKANSAS WASHINGTON G7 Microsoft Excel snapshot for systematic sampling: xfx INDEX(SD52:50551, F7) A B E F G 1 No. States Rand No. Random Sample population 50 2 1 ALABAMA 0.5296685 NEW HAMPSHIRE sample 10 3 2 ALASKA 0.4493186 OKLAHOMA k 5 4 3 ARIZONA 0.707914 KANSAS 5 4 ARKANSAS 0.4831379 NORTH DAKOTA 6 5 CALIFORNIA 0.7277162 INDIANA Random Sample Sample Name 7 6 COLORADO 0.5865002 MISSISSIPPI 8 7:ONNECTICU 0.7640596 ILLINOIS 9 8 DELAWARE 0.5783029 MISSOURI 525 10 15 INDIANA MARYLAND COLORADO
Suppose the Internal Revenue Service reported that the mean tax refund for the year 2022 was $3401. Assume the standard deviation is $82.5 and that the amounts refunded follow a normal probability distribution. Solve the following three parts? (For the answer to question 14, 15, and 16, start with making a bell curve. Identify on the bell curve where is mean, X, and area(s) to be determined. 1.What percent of the refunds are more than $3,500? 2. What percent of the refunds are more than $3500 but less than $3579? 3. What percent of the refunds are more than $3325 but less than $3579?
A normal distribution has a mean of 50 and a standard deviation of 4. Solve the following three parts? 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the answer of the second part.) 2. Compute the probability of a value greater than 55.0. Use the same formula, x=55 and subtract the answer from 1. 3. Compute the probability of a value between 52.0 and 55.0. (The question requires finding probability value between 52 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 52, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…

Chapter 16 Solutions

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Knowledge Booster
Background pattern image
Statistics
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
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
Text book image
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Text book image
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Text book image
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Text book image
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Text book image
College Algebra
Algebra
ISBN:9781938168383
Author:Jay Abramson
Publisher:OpenStax
Correlation Vs Regression: Difference Between them with definition & Comparison Chart; Author: Key Differences;https://www.youtube.com/watch?v=Ou2QGSJVd0U;License: Standard YouTube License, CC-BY
Correlation and Regression: Concepts with Illustrative examples; Author: LEARN & APPLY : Lean and Six Sigma;https://www.youtube.com/watch?v=xTpHD5WLuoA;License: Standard YouTube License, CC-BY