Consider a regression model of the following form: Y = b0 + b1x1 + b2x2 + b3x3 +

Question

Consider a regression model of the following form:

Y = b0 + b1x1 + b2x2 + b3x3 + e

Assume that 15 observations were collected to evaluate this model. Find the critical values for the following hypotheses for = 0.05 and = 0.01:
1. H0 : b2 = 0 vs H1 : b2 6= 0

2. H0 : b2 = 0 vs H1 : b2 > 0
3. H0 : b2 = 0 vs H1 : b2 < 0

4. H0 : b1 = b2 = b3 = b4 = 0 vs H1 : At least one bi 6= 0

5. H0 : = 0 vs H1 : > 0
6. H0 : = 0 vs H1 : < 0

Can you please fill below cells ?

Critical Values =0.05 =0.01 Hypothesis 1 Hypothesis 2 Hypothesis 3 Hypothesis 4 Hypothesis 5 Hypothesis 6

Explanation / Answer

for above degree of freedom =n-4=11

therefore

Critical Values =0.05 =0.01 Hypothesis 1 -/+2.2010 -/+3.1058 two tailed t test Hypothesis 2 1.7959 2.7181 right tail t test Hypothesis 3 -1.7959 -2.7181 left tail t test Hypothesis 4 3.5874 6.2167 ANOVA F test Hypothesis 5 1.7959 2.7181 right tail t test Hypothesis 6 -1.7959 -2.7181 left tail t test

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