Nicely done. Very good conceptual explanation of what's going on with the test. Running the test in the software is actually pretty trivial in my mind. Understanding the test and how it works (and what it depends on) is another. I think you did a nice job of capturing that.
In a standard least squares regression model, we assume that individual Y values are normally distributed in relation to their corresponding X values. The z distribution models normally distributed individuals. But remember we are regressing on the of Y (vs X), that is, we are creating a [linear] model that predicts how much of Y we have when we have a certain amount of X. For a normally distributed population of individual values, the sampling distribution of the mean is exactly student's t distributed. We can "prove" this to ourselves using JMP via simulation or using any more ubiquitous statistical programming language like R or Python. For a publication reference, see "Introduction to Probability and Statistics" (Sixth Edition) Alder and Roessier, UC Davis, W.H. Freeman and Company, SF, copyright 1977.
Nicely done. Very good conceptual explanation of what's going on with the test. Running the test in the software is actually pretty trivial in my mind. Understanding the test and how it works (and what it depends on) is another. I think you did a nice job of capturing that.
Thank you...very good explained
Why dont we use z test statistic ?
In a standard least squares regression model, we assume that individual Y values are normally distributed in relation to their corresponding X values. The z distribution models normally distributed individuals. But remember we are regressing on the of Y (vs X), that is, we are creating a [linear] model that predicts how much of Y we have when we have a certain amount of X. For a normally distributed population of individual values, the sampling distribution of the mean is exactly student's t distributed. We can "prove" this to ourselves using JMP via simulation or using any more ubiquitous statistical programming language like R or Python. For a publication reference, see "Introduction to Probability and Statistics" (Sixth Edition) Alder and Roessier, UC Davis, W.H. Freeman and Company, SF, copyright 1977.
bad explanation... Just describe easly how to say tha y intercept in zero, do the t test step by step and explain it !!!!! DO BETTER JOB