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Hi, the confidence level when trying to estimate a population mean from a sample mean . Well, a very interesting thing, if I'm interpreting it correctly. The Sampling Distribution of the Mean says roughly that, no matter what the population distribution is - could be just random numbers with what I call a "flat" distribution - the distribution of the sample means goes to normal as the sample size increases. That´s the idea of the Central Limit Theorem Let X1, X2, X3, …, Xn be a sequence of n independent and identically distributed (iid) random variables each having finite values of expectation µ and variance s2 > 0. The central limit theorem states that as the sample size n increases the distribution of the sample average of these random variables approaches the normal distribution with a mean µ and variance s2/n irrespective of the shape of the common distribution of the individual terms Xi. This approximation is exact if X has a normal distribution and it works better with distributions similar to a normal distribution If your sample is large enough (not necessarily very large from what I've read) , you can state that there is a 95% level of confidence that the true mean is within the 1.96 standard deviations of the population mean. Is this correct? Yes, the theorem works well for n>30 then the CI for the population mean is: CI for the mean at (1-)% level is x-bar±z(1-/2)s/vn (standard deviation known) If =0.05 then z(1-0.05/2)=z(0.975)=1.96 CI= x-bar±1.96s/vn there is a 95% level of confidence that the true mean is within the 1.96 times the standard deviation of the sample mean (s/vn) of the sample mean I have two questions about correlations, which are related. How good a fit are the data points to the regression line, and what is the confidence level that this regression line can be used to make predictions for different x variables? The coefficient of determination (R2) it´s a measure of how well fits the regression line to the data points. Formula: R2=r2 where r is tha sample correlation Did you go to the site I sent you? Yes, I see that This gives the user a result, based on a z-score conversion, something like the above, the confidence level that the correlation coefficient is within a certain range of the true r. The pages computes a confidence interval for rho () but if you want to compute an interval for y given a particular value of x you must use the prediction confidence interval (the second one of the above intervals) But what does this tell me about the level of confidence and range for a projection using a regression line? Can I say that, when I project an unknown y from x, I can state there is a 95% chance that the predicted y falls in a certain range? Use the prediction confidence interval Can I get something like this from the F-score? When you use lineEST in excel appears the value of the F-score but if you want to predict an y – value (not only the value, you want a CI) look at the lower and upper limits