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 bes predicted weight of a bear with a chest size of 63 inches. Is the result close to the actual weight of 442 pounds? Use a significance level of 0.05. Chest size (inches) 58 50 65 59 59 48 Weight (pounds) 414 312 499 450 456 260 Click the icon to view the critical values of the Pearson correlation coefficient r. What is the regression equation? Critical Values of the Pearson Correlation Coefficient r y =+x (Round to one decimal place as ne Critical Values of the Pearson Correlation Coefficient r NOTE: To test Ho: p=0 against H,: p+0, reject Ho if the absolute value of r is greater than the critical value in the table a = 0.05 a = 0.01 4 0.950 0.990 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 0.497 0.623 0.606 0.590 16 17 0.482 18 0.468 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 0.286 0.269 80 0.220 90 0.207 100 0.196 0.256 ¤ = 0.05 a = 0.01
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 63 inches. Is the result close to the actual weight of 442 pounds? Use a significance level of 0.05.
Chest size (inches)
58
50
65
59
59
48
Weight (pounds)
414
312
499
450
456
260
Click the icon to view the critical values of the Pearson correlation coefficient r.
What is the regression equation?
Critical Values of the Pearson Correlation Coefficient r
y=D+x (Round to one decimal place as ne
Critical Values of the Pearson Correlation Coefficient r
NOTE: To test Ho: p=0
against H,: p+0, reject Ho
if the absolute value of r is
greater than the critical
value in the table.
a = 0.05
a = 0.01
4
0.950
0.990
0.878
0.811
0.754
5
0.959
6
0.917
7
0.875
8
0.707
0.834
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
0.468
0.456
18
0.590
19
0.575
20
0.444
0.561
25
0.396
0.505
30
0.361
0.463
0.430
0.402
35
0.335
40
0.312
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
a = 0.05
a = 0.01
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