Sample Size Calculator: Simple Linear Regression
Hypothesis: Two-Sided Equality
Data Input: (Help) (Example)
Input
Results
α
£m
£]
£l
£m_{x}
N
£m_{y}
£f_{1}
Variables
Descriptions
£\
Probability of type I error
Probability of type II error
The standard deviation of the independent variable
The standard deviation of the dependent variable
Slope of the linear regression line
Standard deviation of the regression errors
Correlation
Sample size
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Application: This section illistrates how to determine the minimum sample size for simple linear regression.
Procedure:
a) Value of £\, the two-sided confidence level
b) Value of £], the type II error (1-power)
c) Standard deviations of independent and dependent variables
d) Slope of the linear regression line
a) The standard deviation of the regression errors, correlation and sample size.
Formulae:
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Example
A dieting program encourages patients to follow a specific diet and to exercise regularly. We want to determine whether the actual average time per day spent exercising is related to BMI after 6 months on this program. Previous study suggests that exercise time of female participants has a standard deviation of £m_{x}=7.5 minutes; the reported standard deviation of the female subjects is £m_{y}=4.0kg/m^{2}. We want to determine the sample size with which we can detect a true drop of BMI of £f_{1}=-0.0667 kg/m^{2} per minute of exercise. Assume £\=0.05 and £]=0.2.
N = [(1.960+0.842)*3.9686/(-0.1251*7.5)]^{2}= 494
Therefore, 494 female participant is required.