3) Now let's assume you wanted to predict weights from heights. In other words, now let's use the same data from problem (1) and do a regression instead. (a) Calculate b0 and b1. (b) Carefully draw your least square regression line on the plot you made in 1(a). (Don't just “sketch”, be a little careful).
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
height 60 67 62 70 66
weight 119 143 131 155 136
3) Now let's assume you wanted to predict weights from heights. In other words, now let's use the same data from problem (1) and do a regression instead.
(a) Calculate b0 and b1.
(b) Carefully draw your least square regression line on the plot you made in 1(a). (Don't just “sketch”, be a little careful).
![S.No.
Y
(x - x)²
(y -7)2
(x -x)(y - y)
1
60
119
25
316.84
89
67
143
4
38.44
12.4
62
131
33.64
17.4
70
155
331.24
91
66
136
1
0.64
-0.8
Total
325
684
64
720.8
209
=x 325
y = - E; yi = = × 684 = 136. 8
= 65
%3D
SS, = E, (x; – x)² = 64
%3D
SSy= E; Vi – )² = 720.8
%3D
%3D
SS-Σ (- 1) (ι - ) - 209
Xi
|
The correlation coefficient is
SScp
VSS,xSS,
E; (xi-X) (y-5)
ср
r =
209
%3D
V64x720.8
= 0.973
25
2.
3.
4)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F89c0aec8-fa87-403f-a89a-bd303d48e75d%2Fe5fc8780-88bc-4552-85fe-1c2a8b99481e%2Fodrfrgn_processed.jpeg&w=3840&q=75)
![180
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60
40
20
58
60
62
64
66
70
72
Height
Weight
68](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F89c0aec8-fa87-403f-a89a-bd303d48e75d%2Fe5fc8780-88bc-4552-85fe-1c2a8b99481e%2Fo27qs5p_processed.jpeg&w=3840&q=75)
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