- #1
MahaRoho
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- Homework Statement
- I have to find the standard deviation
- Relevant Equations
- There are not any
Standard deviation of response
- Thread starter MahaRoho
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In summary: Sensitivity is a measure of how much a change in one variable affects another. It is defined as:Sensitivity = Var(x) - Covariance(x, y)
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I would think that this is not good enough. What form does the model have? Is the model a linear model? Are there equations for the mean and variance of the model?MahaRoho said:
- #3
MahaRoho
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The model is linear. The nominal values are the means of those parameters.
1. I need to know the standard deviation of a single variable that includes the covariance of that variable.
2. What is the value of correlation co efficient if the variables are fully correlated (I think it is 1), partially (0-1) and anti (0 to -1)?
1. I need to know the standard deviation of a single variable that includes the covariance of that variable.
2. What is the value of correlation co efficient if the variables are fully correlated (I think it is 1), partially (0-1) and anti (0 to -1)?
- #4
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Then you should start by writing down the general form of a linear model and then translate the additional information into statements about that model.MahaRoho said:
A single variable does not have a covariance, it has a variance.MahaRoho said:
CORRECTION: Although the covariance is defined as cov(X,Y)=E[(X-E[X])(Y-E[Y])], there is nothing that says that X and Y have to be different. If they are the same random variable, the covariance is the variance.
Yes.MahaRoho said:
Possibly. Some people would include the negative values (-1,1)MahaRoho said:
Yes. That is also called "negative correlation" and "inverse correlation". I call variables "correlated" even if it is negative and if I want to distinguish positive from negative, I call them "positively correlated" or "negatively correlated". But others might prefer other terminology. In any case, the term "correlation" or "correlation coefficient" includes both the positive and negative cases.MahaRoho said:
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- #5
MahaRoho
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Thanks a lot for the reply. Btw, I think I saw a formula on the internet like Covariance(x)=Standard deviation/ mean... Is that formula correct?
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No, that is not correct. But I have corrected my comment about the covariance in post #4.MahaRoho said:
The definition of covariance of random variables X and Y is cov(X,Y)=E[(X-E[X])(Y-E[Y])].
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Maybe a good starting point is writing down what the definition of sensitivity is.
FAQ: Standard deviation of response
What is the standard deviation of response?
The standard deviation of response is a measure of the spread or variability of data points around the mean or average value. It tells us how much the data points deviate from the mean, and is calculated by taking the square root of the variance.
Why is the standard deviation of response important?
The standard deviation of response is important because it helps us understand the distribution of data and how much the data points vary from the mean. It is commonly used in statistical analysis to assess the reliability of data and to compare different sets of data.
How is the standard deviation of response calculated?
The standard deviation of response is calculated by taking the square root of the variance. The variance is calculated by finding the average of the squared differences between each data point and the mean. This value is then squared to get the standard deviation.
What does a high or low standard deviation of response indicate?
A high standard deviation of response indicates that the data points are spread out over a wider range, while a low standard deviation indicates that the data points are clustered closer to the mean. In other words, a high standard deviation means there is more variability in the data, while a low standard deviation means there is less variability.
How does the standard deviation of response relate to the normal distribution?
The standard deviation of response is a key component of the normal distribution, also known as the bell curve. In a normal distribution, approximately 68% of the data falls within one standard deviation from the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations. This shows how the standard deviation can be used to understand the distribution of data and determine the likelihood of certain values occurring.