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