The data show the chest size and weight of several bears. Find the regression equation, letting chest size be the independent (x) variable. Then find the best-predicted weight of a bear with a chest size of 4848 inches. Is the result close to the actual weight of 298298 pounds? Use a significance level of 0.05. Chest_size_(inches) Weight_ (pounds) 58 355 49 266 58 332 43 177 46 246 57 348
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.
The data show the chest size and weight of several bears. Find the regression equation, letting chest size be the independent (x) variable. Then find the best-predicted weight of a bear with a chest size of 4848 inches. Is the result close to the actual weight of 298298 pounds? Use a significance level of 0.05.
Chest_size_(inches) Weight_ (pounds)
58 355
49 266
58 332
43 177
46 246
57 348
|
n
|
alphaαequals=0.05
|
alphaαequals=0.01
|
NOTE: To test
H0:
rhoρequals=0
against
H1:
rhoρnot equals≠0,
reject
H0
if the absolute value of r is greater than the critical value in the table. |
|---|---|---|---|
|
4
|
0.950
|
0.990
|
|
|
5
|
0.878
|
0.959
|
|
|
6
|
0.811
|
0.917
|
|
|
7
|
0.754
|
0.875
|
|
|
8
|
0.707
|
0.834
|
|
|
9
|
0.666
|
0.798
|
|
|
10
|
0.632
|
0.765
|
|
|
11
|
0.602
|
0.735
|
|
|
12
|
0.576
|
0.708
|
|
|
13
|
0.553
|
0.684
|
|
|
14
|
0.532
|
0.661
|
|
|
15
|
0.514
|
0.641
|
|
|
16
|
0.497
|
0.623
|
|
|
17
|
0.482
|
0.606
|
|
|
18
|
0.468
|
0.590
|
|
|
19
|
0.456
|
0.575
|
|
|
20
|
0.444
|
0.561
|
|
|
25
|
0.396
|
0.505
|
|
|
30
|
0.361
|
0.463
|
|
|
35
|
0.335
|
0.430
|
|
|
40
|
0.312
|
0.402
|
|
|
45
|
0.294
|
0.378
|
|
|
50
|
0.279
|
0.361
|
|
|
60
|
0.254
|
0.330
|
|
|
70
|
0.236
|
0.305
|
|
|
80
|
0.220
|
0.286
|
|
|
90
|
0.207
|
0.269
|
|
|
100
|
0.196
|
0.256
|
|
|
n
|
alphaαequals=0.05
|
alphaαequals=0.01
|
|
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