PRACTICE OF STATISTICS F/AP EXAM
PRACTICE OF STATISTICS F/AP EXAM
6th Edition
ISBN: 9781319113339
Author: Starnes
Publisher: MAC HIGHER
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 3.2, Problem 59E

(a)

To determine

To explain is a line an appropriate model to use for these data.

(a)

Expert Solution
Check Mark

Answer to Problem 59E

Yes, a line appears to be appropriate for these data.

Explanation of Solution

The relationship of the number of Mentos and the amount of coke expelled is given in the question. The scatterplot and the residual plot for the same is given. Thus, a line appears to be appropriate for these data because there is no strong curvature present in the scatterplot and there is no strong curvature in the residual plot either.

(b)

To determine

To find the correlation.

(b)

Expert Solution
Check Mark

Answer to Problem 59E

  r=0.7760

Explanation of Solution

The relationship of the number of Mentos and the amount of coke expelled is given in the question. The scatterplot and the residual plot for the same is given. Thus, the coefficient of determination r2 is given in the computer output after “R-Sq” as:

  r2=60.21%=0.6021

Thus, the linear correlation coefficient r is the positive or negative square root of the coefficient of determination r2 . Thus, we note that the pattern in the scatterplot slopes upwards, which indicates that there is a positive association between the variables and thus the linear correlation coefficient r is positive. This then implies that,

  r=+r2=+0.6021=0.7760

(c)

To determine

To find out what is the equation of least square regression line.

(c)

Expert Solution
Check Mark

Answer to Problem 59E

  y^=1.0021+0.0708x .

Explanation of Solution

The relationship of the number of Mentos and the amount of coke expelled is given in the question. The scatterplot and the residual plot for the same is given. The general equation of the least square regression line is:

  y^=b0+b1x

Thus, the estimate of the constant b0 is given in the row “Constant” and in the column “Coef” of the computer output as:

  b0=1.0021

And the estimate of the slope b1 is given in the row “Mentos” and in the column “Coef” of the computer output as:

  b1=0.0708

Thus, putting the values in the general equation we will get,

  y^=b0+b1xy^=1.0021+0.0708x

(d)

To determine

To interpret the value of s and r2 .

(d)

Expert Solution
Check Mark

Explanation of Solution

The relationship of the number of Mentos and the amount of coke expelled is given in the question. The scatterplot and the residual plot for the same is given. Thus, the standard error of the estimate s is given after “S=” in the computer output as:

  s=0.6724

As we know that the standard error of the estimate s represents the average error of predictions thus the average deviation between actual and the predicted values. Thus the predicted amount expelled using the equation of least square regression line deviated on average by 0.6724 cups from the actual amount expelled.

Now, the coefficient of determination is given after “R-Sq” in the computer output as:

  r2=60.21%=0.6021

As we know that the coefficient of determination measures the proportion of variation in the responses y variable that is explained by the least square regression model using the explanatory x variable. Thus, we can say that 60.21% of the variation in the amount expelled is explained by the least square regression line using the number of Mentos as explanatory variable.

Chapter 3 Solutions

PRACTICE OF STATISTICS F/AP EXAM

Ch. 3.1 - Prob. 11ECh. 3.1 - Prob. 12ECh. 3.1 - Prob. 13ECh. 3.1 - Prob. 14ECh. 3.1 - Prob. 15ECh. 3.1 - Prob. 16ECh. 3.1 - Prob. 17ECh. 3.1 - Prob. 18ECh. 3.1 - Prob. 19ECh. 3.1 - Prob. 20ECh. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - Prob. 23ECh. 3.1 - Prob. 24ECh. 3.1 - Prob. 25ECh. 3.1 - Prob. 26ECh. 3.1 - Prob. 27ECh. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - Prob. 30ECh. 3.1 - Prob. 31ECh. 3.1 - Prob. 32ECh. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.1 - Prob. 35ECh. 3.1 - Prob. 36ECh. 3.2 - Prob. 37ECh. 3.2 - Prob. 38ECh. 3.2 - Prob. 39ECh. 3.2 - Prob. 40ECh. 3.2 - Prob. 41ECh. 3.2 - Prob. 42ECh. 3.2 - Prob. 43ECh. 3.2 - Prob. 44ECh. 3.2 - Prob. 45ECh. 3.2 - Prob. 46ECh. 3.2 - Prob. 47ECh. 3.2 - Prob. 48ECh. 3.2 - Prob. 49ECh. 3.2 - Prob. 50ECh. 3.2 - Prob. 51ECh. 3.2 - Prob. 52ECh. 3.2 - Prob. 53ECh. 3.2 - Prob. 54ECh. 3.2 - Prob. 55ECh. 3.2 - Prob. 56ECh. 3.2 - Prob. 57ECh. 3.2 - Prob. 58ECh. 3.2 - Prob. 59ECh. 3.2 - Prob. 60ECh. 3.2 - Prob. 61ECh. 3.2 - Prob. 62ECh. 3.2 - Prob. 63ECh. 3.2 - Prob. 64ECh. 3.2 - Prob. 65ECh. 3.2 - Prob. 66ECh. 3.2 - Prob. 67ECh. 3.2 - Prob. 68ECh. 3.2 - Prob. 69ECh. 3.2 - Prob. 70ECh. 3.2 - Prob. 71ECh. 3.2 - Prob. 72ECh. 3.2 - Prob. 73ECh. 3.2 - Prob. 74ECh. 3.2 - Prob. 75ECh. 3.2 - Prob. 76ECh. 3.2 - Prob. 77ECh. 3.2 - Prob. 78ECh. 3.2 - Prob. 79ECh. 3.2 - Prob. 80ECh. 3 - Prob. R3.1RECh. 3 - Prob. R3.2RECh. 3 - Prob. R3.3RECh. 3 - Prob. R3.4RECh. 3 - Prob. R3.5RECh. 3 - Prob. R3.6RECh. 3 - Prob. T3.1SPTCh. 3 - Prob. T3.2SPTCh. 3 - Prob. T3.3SPTCh. 3 - Prob. T3.4SPTCh. 3 - Prob. T3.5SPTCh. 3 - Prob. T3.6SPTCh. 3 - Prob. T3.7SPTCh. 3 - Prob. T3.8SPTCh. 3 - Prob. T3.9SPTCh. 3 - Prob. T3.10SPTCh. 3 - Prob. T3.11SPTCh. 3 - Prob. T3.12SPTCh. 3 - Prob. T3.13SPT
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.
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
Mod-01 Lec-01 Discrete probability distributions (Part 1); Author: nptelhrd;https://www.youtube.com/watch?v=6x1pL9Yov1k;License: Standard YouTube License, CC-BY
Discrete Probability Distributions; Author: Learn Something;https://www.youtube.com/watch?v=m9U4UelWLFs;License: Standard YouTube License, CC-BY
Probability Distribution Functions (PMF, PDF, CDF); Author: zedstatistics;https://www.youtube.com/watch?v=YXLVjCKVP7U;License: Standard YouTube License, CC-BY
Discrete Distributions: Binomial, Poisson and Hypergeometric | Statistics for Data Science; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=lHhyy4JMigg;License: Standard Youtube License