Example 4. For the following observations, find the regression coefficients b and b, andhence find correlation coefficient between x and y..{(х, у)} — {(4, 2), (2, 3), (3, 2), (4, 4), (2, 4)}.

Answered: Image /qna-images/answer/54df68be-9d25-40c3-ae83-29c31d2f1522.jpg

Answered: Example 4. For the following…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.6: Regression And Median-fit Lines

Problem 5PPS

See similar textbooks

Similar questions

Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.
Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
If your graphing calculator is capable of computing a least-squares sinusoidal regression model, use it to find a second model for the data. Graph this new equation along with your first model. How do they compare?
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?
In a laboratory experiment on correlation research study the equation of the two regression lines were found to be 2X–Y+1=0 and 3X–2Y+7=0 Find the correlation between the two variables X and Y. Interpret the result as well.
Find the equation of the least-squares regression line y and the linear correlation coefficient r for the given data. Round the constants, a, b, and-r, to-the nearest hundredth. {(1, 3).(5,12),(7,16),(9,20),(11,22)} r=
Find the equation of the least-squares regression line ŷ and the linear correlation coefficient r for the given data. Round the constants, a, b, and r, to the nearest hundredth. {(1, 3), (5, 11), (7, 15), (9, 18), (11, 22)}

Recommended textbooks for you

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:

9781305652224

Author:

Charles P. McKeague, Mark D. Turner

Publisher:

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:

9781305652224

Author:

Charles P. McKeague, Mark D. Turner

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Big Ideas Math A Bridge To Success Algebra 1: Stu…

Algebra

ISBN:

9781680331141

Author:

HOUGHTON MIFFLIN HARCOURT

Publisher:

Houghton Mifflin Harcourt

Calculus For The Life Sciences

Calculus

ISBN:

9780321964038

Author:

GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:

Pearson Addison Wesley,

SEE MORE TEXTBOOKS

Example 4. For the following observations, find the regression coefficients b and xy b аnd hence find correlation coefficient between x and y. {(х, у)} %3D {(4, 2), (2, 3), (3, 2), (4, 4), (2, 4)}.