# Calculate And Test Hypotheses For Given Data

Question

 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

Yi = β0 + βlX1i + β2X2i + β3X3i + β4X4i + εi

a. Compute b0, b1, b2, b3 and b4.

b. Compute the predicted values for Yi{Yt).

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

d. Plot the residuals (ei) against X1i and then against Yi

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.

Summary

The question belongs to Statistics and it discusses about calculating and establishing null hypotheses given in the question.

Total Word Count 632

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