Source | MS FI 1, 23) = Nunber of oba = 25 24.23 Nodel Reeidual 8395.74904 7970.25096 1 8395.74904 23 346.53265 R-squared Prob > P 0.0001 0.5130 Total | 16366.00 24 681.916667 Adj R-aquared = 0.4918 - 18.615 Root MEE nort | Coat. Std. Err. [95% Conf. Interval] smoking cona 1.087532 -2.885319 4.922 -0.125 P>|t| 0.000 0.901 .5304724 -50.5342 1.544592 44. 76356 23.03372 2209452
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.
Below is a sample output you might see from STATA statistical software for a simple linear regression of mortality versus smoking rates. Does an increase in the smoking rate significantly increase the mortality rate according to these results?
a. Yes since the coefficient is 1.08 (i.e., greater than 0) and the p- value is 0.000
b. No since the estimate of the constant is 2.88 and is not significant.
c. Yes, since R-squared = 0.5130
d. No, an increase in the smoking rate was associated with a decreased in the mortality rate in this study.
![Source |
MS
FI 1, 23) =
Nunber of oba =
25
24.23
Nodel
Reeidual
8395.74904
7970.25096
1 8395.74904
23
346.53265
R-squared
Prob > P
0.0001
0.5130
Total |
16366.00
24 681.916667
Adj R-aquared = 0.4918
- 18.615
Root MEE
nort |
Coat.
Std. Err.
[95% Conf. Interval]
smoking
cona
1.087532
-2.885319
4.922
-0.125
P>|t|
0.000
0.901
.5304724
-50.5342
1.544592
44. 76356
23.03372
2209452](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7f7a3cdb-acd6-406d-905b-9a4ffd3722ac%2F20aab551-f6bf-4a19-92e7-d554f3b69607%2Fvse1qpb.png&w=3840&q=75)
The output is provided for a simple linear regression of mortality versus smoking rates. To test the null hypothesis: Whether an increase in the smoking rate significantly increase the mortality rate.
The p-value is mentioned as 0.001 and 95% confidence interval is used, that is, the level of significance is 5% or 0.05.
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