Reference no: EM13827675

Problem-

Yi	X1i	X2i	X3i	X4i
0.076	0.022	0.048	0.027	0.042
0.227	1.111	0.15	0.136	0.152
0.041	0.003	0.027	0.024	0.076
0.063	0.06	0.041	0.056	0.037
0.077	0.004	0.052	0.012	0.08
0.032	0.007	0.018	0.052	0.047
0.281	0.452	0.205	0.194	0.165
0.047	0.006	0.024	0.027	0.025
0.174	0.043	0.123	0.063	0.117
0.127	0.062	0.098	0.039	0.105
0.066	0.03	0.054	0.246	0.287
0.047	0.044	0.026	0.023	0.017
0.122	0.087	0.075	0.083	0.094
0.004	0.095	0.109	0.057	0.004
0.116	0.164	0.065	0.003	0.043
0.416	0.347	0.187	0.086	0.143
0.09	0.004	0.043	0.11	0.073
0.15	0.074	0.113	0.061	0.099
0.136	0.261	0.094	0.064	0.078
0.137	0.025	0.073	0.092	0.132
0.229	0.058	0.128	0.18	0.139
0.12	0.346	0.067	0.039	0.046

Consider the data, set in the above table to estimate the regression model

Y_i = β₀ + β_lX_1i + β₂X_2i + β₃X_3i + β₄X_4i + ε_i

a. Compute b₀, b₁, b₂, b₃ and b₄.

b. Compute the predicted values for Y_i{Y_t).

c. Compute Se(b₀), Se(b₁), Se(b₂), Se(b₃) and Se(b₄).

d. Plot the residuals (e_i) against X_1i and then against Y_i

e. Test the hypothesis H₀: β₁ = 0 against H₁: β₁ ≠ 0 at 5% significance level.

f. Test the hypothesis H₀: β₄ = 1 against H1: β₄ ≠ 1 at 1% significance.

g. Compute the coefficient of determination R² and Adjusted - R²

h. Test the hypothesis that H₀: β₁ = β₂ = β₃ = β₄ = 0 against the H₁: H₀ is not true at 1% significance level.

i. Test the hypothesis that H₀: β₁ = β₂ = β₃ = 0 against the H₁: H₀ is not true at 5% significance level.

j. Test the hypothesis that H₀: β₁ = β₂ = 0 against the H₁: H₀ is not true at 1% significance level.

Additional information-

The question related to Basic Statistics and it discuss about establishing and calculating null hypotheses given in the question.