Connect and share knowledge within a single location that is structured and easy to search. What did I do? With hope of simpler proof, just like proving unbiased estimator of sample variance as shown here , I attempted as below, but stuck after few steps. I am stuck after this step. Is it a duplicate Q? The books are "Introductory". The expectation of the square of a standard normal equals its variance, which is 1.
Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Why error sum of squares has n-2 df possibly not duplicate, please read on? Asked 2 years, 11 months ago. Active 9 months ago. Viewed 3k times. Question: 1. Why n-2?
In another one here , in hat-matrix. Previous Question. Improve this question. Parthiban Rajendran Parthiban Rajendran 2 2 silver badges 10 10 bronze badges. Real Statistics is a branch of mathematics. Mathematics is differ from other discipline. In math, you need to go step by step, cannot jump. So for statistics, the required basic math background is calculus, linear algebra, probability, mathematical statistics.
After you familiar with these math materials, the answers to your question can be found from textbook of general linear model. The books refer them as introductory and they start so as well from scratch, which I have been able to follow well. And any basic topic could involve advanced math, so I also define my borders like here. There are two methods of making the decision. The two methods are equivalent and give the same result. Compare r to the appropriate critical value in the table.
If r is not between the positive and negative critical values, then the correlation coefficient is significant. If r is significant, then you may want to use the line for prediction. If you view this example on a number line, it will help you.
Therefore, r is significant. Can the line be used for prediction? Why or why not? The critical values are —0. Since —0. Suppose you computed the following correlation coefficients. Using the table at the end of the chapter, determine if r is significant and the line of best fit associated with each r can be used to predict a y value. If it helps, draw a number line.
Testing the significance of the correlation coefficient requires that certain assumptions about the data are satisfied. The premise of this test is that the data are a sample of observed points taken from a larger population. We have not examined the entire population because it is not possible or feasible to do so. We are examining the sample to draw a conclusion about whether the linear relationship that we see between x and y in the sample data provides strong enough evidence so that we can conclude that there is a linear relationship between x and y in the population.
The regression line equation that we calculate from the sample data gives the best-fit line for our particular sample. We want to use this best-fit line for the sample as an estimate of the best-fit line for the population. Examining the scatterplot and testing the significance of the correlation coefficient helps us determine if it is appropriate to do this.
The y values for each x value are normally distributed about the line with the same standard deviation. For each x value, the mean of the y values lies on the regression line.
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