Homework-

Assume we are interested in fitting an additive multiple regression model of Y on four potential covariates X₁, X₂, X₃, X₄ : , i.e. our model is Y_i = β₀ + β₁X_i1 + β₂X_i2 + β₃X_i3 + β₄X_i4 + ε_i, i = 1,...,n , where εi ~^i.i.d. N (0, σ²) . The sample size is n = 17 and SST0 = 1062.21.

a) Define C′ and m for the composite hypothesis that β₀ = 0, β₁ + β₂ = 0, and β₃ = β₄. That is, express as

H₀: C'β = m

H_a: C'β ≠ m

b) Give the rank of C′.

c) State the reduced model for the composite hypothesis in part (a).

d) The SSE for the model Y_i = β₀ + β₁X_i1 + β₂X_i2 + β₃X_i3 + β₄X_i4 + ε_i is 37.88 and the SSE for the reduced model in part (c) is 95.11. Use the general linear test to test the hypothesis in part (a). Compute the value of the test statistic, determine the rejection region, and state your conclusion.

Note: The test statistic should be expressed in fraction form: #/# ÷ #/# as well as computing the value.

e) Compute R² and R²_adj for the model Y_i = β₀ + β₁X_i1 + β₂X_i2 + β₃X_i3 + β₄X_i4 + ε_i.

A summary of influence measures for the model Y_i = β₀ + β₁X_i1 + β₂X_i2 + β₃X_i3 + β₄X_i4 + ε_i  is given below:

f) Identify which observation(s) is/are outliers, if any. Use a cutoff of 2.

g) Identify which observation(s) is/are high leverage points, if any.

h) Identify which observation(s) is/are influential on the fitted values, Y^ˆ_i , if any.

i) Identify which observation(s) is/are influential on the estimate of β₀, if any.

j) Identify which observation(s) is/are influential on the estimate of β₁, if any.

k) Identify which observation(s) is/are influential on the estimate of β₂, if any.

l) Identify which observation(s) is/are influential on the estimate of β₃, if any.

m) Identify which observation(s) is/are influential on the estimate of β₄, if any.

Attachment:- Assignment.rar