PRACT STAT W/ ACCESS 6MO LOOSELEAF
PRACT STAT W/ ACCESS 6MO LOOSELEAF
4th Edition
ISBN: 9781319215361
Author: BALDI
Publisher: Macmillan Higher Education
Question
Book Icon
Chapter 28, Problem 28.41E

(a)

To determine

To use the Minitab output to estimate each parameter in this multiple regression model for predicting calories burned with the Cybex machine and estimate σ .

(a)

Expert Solution
Check Mark

Answer to Problem 28.41E

  Calories=64.75+145.841MPH50.01 Ind_slow145.06 NoIncline72.83 2%Incline .

Explanation of Solution

In the question, it is given that,

  Ind_slow=1 for MPH3Ind_slow=0 for MPH>3NonIncline=1 for 0%inclineNonIncline=0 for other inclines2%Incline=1 for 0%incline2%Incline=0 for other inclines

And a Minitab output is shown fitting a multiple regression model to predict calories form MPH, Ind_slow, NoIncline and 2% Incline for a man.

Thus, the parameter in this multiple regression model for predicting calories burned with the Cybex machine can be modeled as, from the output Minitab:

  Calories=64.75+145.841MPH50.01 Ind_slow145.06 NoIncline72.83 2%Incline

And the estimated σ is from the Minitab as:

  s=34.2865 .

(b)

To determine

To find out how many separate lines are fitted with this model and explain do the lines all have the same slope and identify each fitted line.

(b)

Expert Solution
Check Mark

Answer to Problem 28.41E

There are eight separate lines that are fitted with this model and no, all the lines do not have the same slope.

Explanation of Solution

In the question, it is given that,

  Ind_slow=1 for MPH3Ind_slow=0 for MPH>3NonIncline=1 for 0%inclineNonIncline=0 for other inclines2%Incline=1 for 0%incline2%Incline=0 for other inclines

And a Minitab output is shown fitting a multiple regression model to predict calories form MPH, Ind_slow, NoIncline and 2% Incline for a man.Thus, the parameter in this multiple regression model for predicting calories burned with the Cybex machine can be modeled as, from the output Minitab:

  Calories=64.75+145.841MPH50.01 Ind_slow145.06 NoIncline72.83 2%Incline

Now, there are eightseparate lines that are fitted with this model and no,all the lines do not have the same slope because as we see in the Minitab output for this model and all the slopes are different. The lines that are fitted with this model are as follows:

  Calories=64.75+145.841MPH50.01 Ind_slow145.06 NoIncline72.83 2%Incline=64.75+145.841MPH50.01(0)145.06(1)72.83(1)=153.14+145.841MPH

  Calories=64.75+145.841MPH50.01 Ind_slow145.06 NoIncline72.83 2%Incline=64.75+145.841MPH50.01(0)145.06(0)72.83(1)=8.08+145.841MPH

  Calories=64.75+145.841MPH50.01 Ind_slow145.06 NoIncline72.83 2%Incline=64.75+145.841MPH50.01(0)145.06(0)72.83(0)=64.75+145.841MPH

  Calories=64.75+145.841MPH50.01 Ind_slow145.06 NoIncline72.83 2%Incline=64.75+145.841MPH50.01(0)145.06(1)72.83(0)=80.31+145.841MPH

  Calories=64.75+145.841MPH50.01 Ind_slow145.06 NoIncline72.83 2%Incline=64.75+145.841MPH50.01(1)145.06(1)72.83(1)=203.15+145.841MPH

  Calories=64.75+145.841MPH50.01 Ind_slow145.06 NoIncline72.83 2%Incline=64.75+145.841MPH50.01(1)145.06(0)72.83(1)=58.09+145.841MPH

  Calories=64.75+145.841MPH50.01 Ind_slow145.06 NoIncline72.83 2%Incline=64.75+145.841MPH50.01(1)145.06(0)72.83(0)=14.74+145.841MPH

  Calories=64.75+145.841MPH50.01 Ind_slow145.06 NoIncline72.83 2%Incline=64.75+145.841MPH50.01(1)145.06(1)72.83(0)=130.32+145.841MPH

(c)

To determine

To explain do you think that this model provides a good fit for these data.

(c)

Expert Solution
Check Mark

Answer to Problem 28.41E

Yes, this model provides a good fit for these data.

Explanation of Solution

In the question, it is given that,

  Ind_slow=1 for MPH3Ind_slow=0 for MPH>3NonIncline=1 for 0%inclineNonIncline=0 for other inclines2%Incline=1 for 0%incline2%Incline=0 for other inclines

And a Minitab output is shown fitting a multiple regression model to predict calories form MPH, Ind_slow, NoIncline and 2% Incline for a man. Thus, the parameter in this multiple regression model for predicting calories burned with the Cybex machine can be modeled as, from the output Minitab:

  Calories=64.75+145.841MPH50.01 Ind_slow145.06 NoIncline72.83 2%Incline

Since the R2=99.3% that means 99.3% of the variation is explained by the MPH in the model and that is why this model provides a good fit for these data.

(d)

To determine

To explain is there significant that more calories are burned for higher speeds and state the hypotheses and identify the test statistics and P-value and provide a conclusion.

(d)

Expert Solution
Check Mark

Answer to Problem 28.41E

Yes, there is significant that more calories are burned for higher speeds and P-value is zero and F=1819.18 .

Explanation of Solution

In the question, it is given that,

  Ind_slow=1 for MPH3Ind_slow=0 for MPH>3NonIncline=1 for 0%inclineNonIncline=0 for other inclines2%Incline=1 for 0%incline2%Incline=0 for other inclines

And a Minitab output is shown fitting a multiple regression model to predict calories form MPH, Ind_slow, NoIncline and 2% Incline for a man. Thus, the parameter in this multiple regression model for predicting calories burned with the Cybex machine can be modeled as, from the output Minitab:

  Calories=64.75+145.841MPH50.01 Ind_slow145.06 NoIncline72.83 2%Incline

The hypothesis will be defined as:

Null hypothesis: There is no significant difference between them.

Alternative hypothesis: There is significant evidence that more calories are burned for higher speeds.

Since we can see that the P-value is zero i.e. P<0.05Reject H0 . Thus, we can conclude that we have sufficient evidence to show that there is significant that more calories are burned for higher speeds. The test statistics value is F=1819.18 .

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
3. A bag of Skittles contains five colors: red, orange, green, yellow, and purple. The probabilities of choosing each color are shown in the chart below. What is the probability of choosing first a red, then a purple, and then a green Skittle, replacing the candies in between picks? Color Probability Red 0.2299 Green 0.1908 Orange 0.2168 Yellow 0.1889 Purple 0.1736
Name: Quiz A 5.3-5.4 Sex Female Male Total Happy 90 46 136 Healthy 20 13 33 Rich 10 31 41 Famous 0 8 8 Total 120 98 218 Use the following scenario for questions 1 & 2. One question on the Census at School survey asks students if they would prefer to be happy, healthy, rich, or famous. Students may only choose one of these responses. The two-way table summarizes the responses of 218 high school students from the United States by sex. Preferred status 1. Define event F as a female student and event R as rich. a. Find b. Find or c. Find and 2. Define event F as a female student and event R as rich. a. Find b. Find c. Using your results from a and b, are these events (female student and rich) independent? Use the following scenario for questions 3 & 4. At the end of a 5k race, runners are offered a donut or a banana. The event planner examined each runner's race bib and noted whether Age Less than 30 years old At least 30 years old Total Choice Donut Banana 52 54 106 5 72 77 Total 57 126…
I need help with this problem and an explanation of the solution for the image described below. (Statistics: Engineering Probabilities)
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Text book image
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Text book image
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Text book image
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
Text book image
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Text book image
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman