Solution Library
Calculate And Test Hypotheses For Given Data
Question
Y_{i} |
X_{1i} |
X_{2i} |
X_{3i} |
X_{4i} |
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} = β_{0} + β_{l}X_{1i} + β_{2}X_{2i} + β_{3}X_{3i} + β_{4}X_{4i} + ε_{i}
a. Compute b_{0}, b_{1}, b_{2}, b_{3} and b_{4}.
b. Compute the predicted values for Y_{i}{Y_{t}).
c. Compute Se(b_{0}), Se(b_{1}), Se(b_{2}), Se(b_{3}) and Se(b_{4}).
d. Plot the residuals (e_{i}) against X_{1i} and then against Y_{i}
e. Test the hypothesis H_{0}: β_{1} = 0 against H_{1}: β_{1} ≠ 0 at 5% significance level.
f. Test the hypothesis H_{0}: β_{4} = 1 against H1: β_{4} ≠ 1 at 1% significance.
g. Compute the coefficient of determination R^{2} and Adjusted – R^{2}
h. Test the hypothesis that H_{0}: β_{1} = β_{2} = β_{3} = β_{4} = 0 against the H_{1}: H_{0} is not true at 1% significance level.
i. Test the hypothesis that H_{0}: β_{1} = β_{2} = β_{3} = 0 against the H_{1}: H_{0} is not true at 5% significance level.
j. Test the hypothesis that H_{0}: β_{1} = β_{2} = 0 against the H_{1}: H_{0} 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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