By Shlens J.
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Extra info for A tutorial on Principal Component Analysis
Let n equal the total number of observations. , n, where y, = the score for the ith observation and With this parameterization, the parameter ft is the mean of population 1 and B0 + fi\ is the mean of population 2. A two-tailed test of HO : B1 = 0 versus Ha : B1 = 0 can be performed by using a test statistic for a pooled two-sample t test that can be obtained in several ways. One way is to use the linear model and compute the usual test statistics for 15 16 Chapter 2. 1. Cancer data set. 1. A dot plot of the cancer data.
11)). We will express di in a general form in the next chapter, but for the two-sample test we can calculate the studentized deleted residual as where the mean squared error M S E ( i ) is based on the n — 1 observations remaining after removing the ith observation. In the next chapter we will give a shortcut formula for the calculation of di that does not require the recalculation of y(i) and M S E ( i ) for each observation. For example, if we want to compute the studentized deleted residual for i = 2 in our cancer data set with n = 47 observations, we first compute y(2) based on the model yi = B0 + Ei for i = 1, 3 , 4 , .
1. We want to test HO : B3 = 0 against Ha : B3 0 in the complete model where Yi, is the nitrogen concentration, xi 1 is the percentage of commercial land, xi,-,2 is the percentage of agricultural land, and Xi,-,3 is the percentage of forested land in the ith river basin. For our test of HO : Bj, = 0 we use the reduced model to compute the appropriate weights for the observations. 5. 3. Histogram of the studentized deleted residuals for the reduced model using the New York rivers data set. the percentage of commercial land, and the percentage of agricultural land.
A tutorial on Principal Component Analysis by Shlens J.