Question

1.

When testing r linear restrictions imposed on the model y = β₀ + β₁x₁ + ... + β_kx_k + ε, the test statistic is assumed to follow the F(df₁, df₂) distribution with ____________________.

df1 = k and df₂ = n – k – 1

df₁ = k – 1 and df₂ = n – k – 1

df₁ = r and df₂ = n – k

df₁ = r and df₂ = n – k – 1

2.

(Round all intermediate calculations to at least 4 decimal places.)

Consider the following sample regressions for the linear, the quadratic, and the cubic models along with their respective R2 and adjusted R2.

  

	Linear	Quadratic	Cubic
Intercept	9.45	9.78	9.84
x	2.60	2.69	1.79
x2	NA	−0.30	−0.32
x3	NA	NA	0.25
R2	0.790	0.818	0.877
Adjusted R2	0.791	0.815	0.876

       
   

a.	Predict y for x = 2 and 3 with each of the estimated models. (Round your answers to 2 decimal places.)

  

	Linear yˆy^	Quadratic yˆy^	Cubic yˆy^
x = 2
x = 3

  

b.	Select the most appropriate model.
	Linear model Quadratic model Cubic model

Answer 1

1.

When testing r linear restrictions imposed on the model y = β₀ + β₁x₁ + ... + β_kx_k + ε, the test statistic is assumed to follow the F(df₁, df₂) distribution with df₁ = r and df₂ = n – k – 1

2. The predicted values are calculated as For linear model y(at2) 945+2.60x2 -14.65 y(at3) 9.45+2.60 x3 -17.25 For quadratic model y(at2) = 9.78 +2.69 x2-0.32x22 = 13.88 y(at3) 9.78+2.69x3-0.32x3* = 14.97 For cubic model )(at2) = 9.84 +1.79% 2-0.32x22 +0.25×23 =14.14 y(at3)-9.84 +1.79% 3-0.32x32 +0.25x33 -19.08 Therefore Linear yy Quadratic yy Cubic yy 13.88 14.97 x=21 x=3| 14.65 17.25 14.14 19.08 b. The most appropriate model is Cubic model because it has the highest value for adjusted R Square