The data given below are the high and low temperatures in January for a random sample of 50 cities. Use the technology of your choice to complet (a) through (d). E Click the icon to view the high and low temperatures. a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b) through (d). For the purposes of this regression, let High be the explanatory variable (x) and let Low be the response variable (y). There is a linear pattern to the data, so it is reasonable to carry out a linear regression. b. Compute the coefficient of determination, r. Select the correct choice below and fill in any answer boxes within your choice. O A. 2 = (Round to three decimal places as needed.) O B. It is not appropriate to carry out a linear regression. c. Determine the percentage of variation in the observed values of the response variable explained by the regression, and interpret your answer. S the correct choice below and fill in any answer boxes within your choice.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
icon
Concept explainers
Question
The data given below are the high and low temperatures in January for a random sample of 50 cities. Use the technology of your choice to complete (a) through (d).

Click the icon to view the high and low temperatures.

a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b) through (d).

For the purposes of this regression, let High be the explanatory variable (x) and let Low be the response variable (y).

There is [a linear pattern] to the data, so it is [reasonable] to carry out a linear regression.

b. Compute the coefficient of determination, \( r^2 \). Select the correct choice below and fill in any answer boxes within your choice.

- \(\circ\) A. \( r^2 = \underline{\hspace{2cm}} \) (Round to three decimal places as needed.)
- \(\circ\) B. It is not appropriate to carry out a linear regression.

c. Determine the percentage of variation in the observed values of the response variable explained by the regression, and interpret your answer. Select the correct choice below and fill in any answer boxes within your choice.

- \(\circ\) A. \(\underline{\hspace{2cm}}\)% (Round to one decimal place as needed.)
- \(\circ\) B. It is not appropriate to carry out a linear regression.
Transcribed Image Text:The data given below are the high and low temperatures in January for a random sample of 50 cities. Use the technology of your choice to complete (a) through (d). Click the icon to view the high and low temperatures. a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b) through (d). For the purposes of this regression, let High be the explanatory variable (x) and let Low be the response variable (y). There is [a linear pattern] to the data, so it is [reasonable] to carry out a linear regression. b. Compute the coefficient of determination, \( r^2 \). Select the correct choice below and fill in any answer boxes within your choice. - \(\circ\) A. \( r^2 = \underline{\hspace{2cm}} \) (Round to three decimal places as needed.) - \(\circ\) B. It is not appropriate to carry out a linear regression. c. Determine the percentage of variation in the observed values of the response variable explained by the regression, and interpret your answer. Select the correct choice below and fill in any answer boxes within your choice. - \(\circ\) A. \(\underline{\hspace{2cm}}\)% (Round to one decimal place as needed.) - \(\circ\) B. It is not appropriate to carry out a linear regression.
The image presents a table with columns labeled "High" and "Low," showing various sets of numerical data:

- The first set of data under "High":
  - 31
  - 30
  - 93
  - 84
  - 64
  - 61
  - 62
  - 58
  - 41
  - 34
  - 26
  - 59
  - 46
  - 42
  - 70
  - 84
  - 81

- The corresponding "Low" values:
  - 22
  - 22
  - 74
  - 71
  - 55
  - 45
  - 45
  - 41
  - 33
  - 21
  - 18
  - 45
  - 36
  - 33
  - 45
  - 73
  - 76

- The second set of data under "High":
  - 35
  - 59
  - 60
  - 63
  - 87
  - 35
  - 85
  - 42
  - 53
  - 66
  - 32
  - 50
  - 62
  - 33
  - 83
  - 30
  - 44

- The corresponding "Low" values:
  - 28
  - 41
  - 46
  - 51
  - 79
  - 23
  - 68
  - 34
  - 41
  - 48
  - 24
  - 42
  - 52
  - 25
  - 78
  - 15
  - 34

This table may represent high and low temperature readings, test scores, or other data points collected over time or across different scenarios. Understanding the context of these "High" and "Low" measures would require additional information.
Transcribed Image Text:The image presents a table with columns labeled "High" and "Low," showing various sets of numerical data: - The first set of data under "High": - 31 - 30 - 93 - 84 - 64 - 61 - 62 - 58 - 41 - 34 - 26 - 59 - 46 - 42 - 70 - 84 - 81 - The corresponding "Low" values: - 22 - 22 - 74 - 71 - 55 - 45 - 45 - 41 - 33 - 21 - 18 - 45 - 36 - 33 - 45 - 73 - 76 - The second set of data under "High": - 35 - 59 - 60 - 63 - 87 - 35 - 85 - 42 - 53 - 66 - 32 - 50 - 62 - 33 - 83 - 30 - 44 - The corresponding "Low" values: - 28 - 41 - 46 - 51 - 79 - 23 - 68 - 34 - 41 - 48 - 24 - 42 - 52 - 25 - 78 - 15 - 34 This table may represent high and low temperature readings, test scores, or other data points collected over time or across different scenarios. Understanding the context of these "High" and "Low" measures would require additional information.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 1 images

Blurred answer
Knowledge Booster
Correlation, Regression, and Association
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
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman