Question

10a

A sports analyst wants to exam the factors that may influence a tennis player’s chances of winning. Over four tournaments, he collects data on 30 tennis players and estimates the following model:

Win = β₀ + β₁Double Faults + β₂ Aces + ε, where Win is the proportion of winning, Double Faults is the percentage of double faults made, and Aces is the number of aces. A portion of the regression results are shown in the accompanying table.

	df	SS	MS	F	Significance F
Regression	2	1.24	0.620	41.85	5.34E−09
Residual	27	0.40	0.015
Total	29	1.64
	Coefficients	Standard Error	t-stat	p-value
Intercept	0.451	0.080	5.646	5.4E-06
Double Faults	−0.007	0.0024	−2.875	0.0078
Aces	0.015	0.003	4.65	7.8E-05

When testing whether the explanatory variables jointly influence the response variable, the null hypothesis is ________.

Multiple Choice

• H₀ : β₁ = β₂ = 0

• H₀ : β₀ = β₁ = β₂ = 0

• H₀ : β₁ + β₂ = 0

• H₀ : β₀ + β₁ + β₂ = 0

Answer 1

Solution :

When testing whether the explanatory variables jointly influence the response variable,

the null hypothesis is H₀ : β₀ = β₁ = β₂ = 0