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Inferential Statistics for b and r

Answers


  1. The assumptions are linearity, homoscedasticity, and normally distributed errors. See the text for more information.

  2. Use the table in this section or the inverse t distribution calculator to find that the critical value is t(N-2) = t(10) = 2.23. The upper limit of the 95% CI = b + (t)(sb) = .8 + 2.23(.3) = 1.47.

  3. t = (r) sqrt(N-2)/sqrt(1-r2) = (0.5) sqrt(18)/sqrt(1-.25) = 2.45 (This is significant at the .05 level.)

  4. First, convert r to z' (so .75 -> .973). The standard error of z' is 1/sqrt(N-3) = .213. Lower limit of CI = .973 - 1.96(.213) = 0.556. Now convert back from z' to r. r = .505