a) Construct the linear regression equation using the least square method. b) Based on the obtained linear regression line, explain the relationship between the variables X and Y. c) Sketch the scatter plot graph and the linear regression line of the recorded results.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 84RE
Question

QUESTION 4 (LINEAR REGRESSION)
Based on the image attached, shows the results of one data collection. A physiotherapist advises 12 of his patients, all of whom had the same knee surgery done, to regularly perform a set of exercises. He asks them to record how long they practise. He then summarizes the average time they practised (X, time in minutes) and how long it takes them to regain their full range of motion again (Y, time in minutes).

a) Construct the linear regression equation using the least square method.
b) Based on the obtained linear regression line, explain the relationship between the variables X and Y.
c) Sketch the scatter plot graph and the linear regression line of the recorded results.

Xi
Yi
1 2 3
24
64
90
30
35 65
4
5
20 33
60
60
6
27
80
7
42
45
8_4145
8 9
22
10 11 12
50 36
31
50
45
80 35
Transcribed Image Text:Xi Yi 1 2 3 24 64 90 30 35 65 4 5 20 33 60 60 6 27 80 7 42 45 8_4145 8 9 22 10 11 12 50 36 31 50 45 80 35
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