Page 16 - FINAL CFA II SLIDES JUNE 2019 DAY 3

MODULE 8.3: ANOVA AND THE F-TEST READING 8: MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS

Step 3:
Step 3: Determine the utility of the model as a whole.

2,
Coefficient of determination, R is used:
0.05SL < Fail to Reject!
GDP and ΔI explain 67.05% of the variation in annual sales.
0.05SL <
Tests of significance for the set of independent variables should be
> 0.05SL
performed using the F-test.

1TT F test structure:
H 0 : b ΔI = b GDP = 0
H a : b ΔI ≠ 0, or b GDP ≠ 0

F at the 5% SL with df numerator = 2 and df denominator = 19 is 3.52.
c

Decision rule: Reject H if F > 3.52.
0
Step 2: Reject Ho and conclude that at least one of the independent variables
significantly contributes to the dependent variable.
That is, changes in mortgage rates and the level of GDP together (but
Can be done using t-tests and p-values. not alone) explain a significant amount of the variation in BuildCo’s

p. values: ONLY ΔI contributes significantly to the level of annual sales. annual sales at the 5% significance level.
• Using t-statistics: H : b = 0 versus H : bj ≠ 0
j
0
a
The critical 2TT t-values with df = 19 (5% SL) are ± 2.093. Reject Ho
Fail to Reject Ho (for Intercept/GDP)
Decision rule: Reject H if –2.093 >t > 2.093 –2.093 < t=1.327, 1.333 < 2.093
0
–2.093 < -5.758
Reject Ho (for ΔI)
Once again: ONLY ΔI contributes significantly to the level of annual sales. Fail to Reject Ho

p-values or t-tests will always have results. In the exam, use p-value if it is We could have reached this same conclusion by observing that the
provided! ANOVA table reports that F is significant p < 0.005 whilst this all test
is using 5% (2.5% each side): SL > p-value of 0.005 = Reject Ho!