In: Statistics and Probability
Consider the following data for two variables, x and
y.
xi | 140 | 110 | 130 | 150 | 175 | 160 | 125 |
yi | 150 | 100 | 125 | 120 | 135 | 135 | 115 |
a. Compute the standardized residuals for these data.
Observation 1 | |
Observation 2 | |
Observation 3 | |
Observation 4 | |
Observation 5 | |
Observation 6 | |
Observation 7 |
from above:
SSE =Syy-(Sxy)2/Sxx= | 910.5839 |
s2 =SSE/(n-2)= | 182.1168 | |
std error σ = | =s=√s2= | 13.4951 |
residual | standardized | ||||||
observations | et=(y-ŷ) | hi=1/n+(xi-x̅)2/SSx | si =s*√(1-hi) | residual=et/si | |||
observation 1 | 24.96 | 0.1436 | 12.4889 | 1.9988 | |||
observation 2 | -10.80 | 0.4793 | 9.7378 | -1.1094 | |||
observation 3 | 4.71 | 0.1873 | 12.1654 | 0.3870 | |||
observation 4 | -9.78 | 0.1679 | 12.3103 | -0.7945 | |||
observation 5 | -6.64 | 0.5268 | 9.2835 | -0.7155 | |||
observation 6 | 0.47 | 0.2603 | 11.6062 | 0.0409 | |||
observation 7 | -2.92 | 0.2348 | 11.8050 | -0.2473 |