Page 8 - FINAL CFA II SLIDES JUNE 2019 DAY 3
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LOS 8.e: Calculate and interpret 1) a confidence interval for the
population value of a regression coefficient and 2) a predicted READING 8: MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS
value for the dependent variable, given an estimated regression
model and assumed values for the independent variables. MODULE 8.2: HYPOTHESIS TESTS AND CONFIDENCE INTERVALS
Confidence Intervals for a Regression Coefficient
Done same way as for simple linear regression., for say 95% SL
EXAMPLE: Calculating a confidence interval for a regression coefficient: Calculate the 90% confidence interval for the estimated coefficient for the
independent variable PR in the real earnings growth example.
Answer:
• The critical t-value is 1.68, the same as we used in testing the statistical significance at the 10% SL (90% confidence level).
• The estimated slope coefficient is 0.25 and the standard error is 0.032.
• The 90% confidence interval is: 0.25 ± (1.68)(0.032) = 0.25 ± 0.054 = 0.196 to 0.304
Zero is excluded! So?
the same conclusion we made when using
We can conclude that the PR coefficient is statistically significant at the 10% level— the t-test earlier. Any Lesson?
Constructing a confidence interval and conducting a t-test with an Ho = 0 will always result in the same conclusion regarding
the statistical significance of the regression coefficient.
