1. ## confidence interval/f-tests

Basically Fe (iron) is the x variable/predictor, and MDD loss is the y variable/response in minitab.

1. I generated some data (regressoin analysis). How do i find a standard error for the estimated regression coefficient? (with or without minitab, either is fine)

2. I generated the anova table (see below), but how do i find the estimate of sigma^2?

3. How do i do an F-test and t-test in minitab or outside minitab (by hand)?

4. I calculated the 95% confidence interval using the formula given in my notes (see below), but how do i do it for the 4th value of the explanatory variable?

Many thanks.

2. The standard error for each of your terms in the simple linear regression model is given in the ANOVA table. SE coef of your beta_0 term is 1.403, and the value under that would be the standard error for the Fe coefficient (which would be your beta_1).

Well, I am not sure about sigma^2. Your table gives you the standard deviation of the data set you worked with. If you square that then you would get the sample variance of the data set you provided.

Well, I am going to assume that your alpha critical value is .05. Remember, to do an F test, if your F-stat is larger than your f critical value (the one you obtain from the F distribution table), then you reject H_0. If you are doing a two sided T test, then you reject the null hypothesis if |T| is greater than your t critical value. You have to obtain your F and T critical values from computer software or a table. However, your stats are in the ANOVA table.

4? I'm not really sure. I'll get back to you. I am assuming you do the same thing as in the previous confidence interval formula, but you would change one of the variables.