Question

3. Derive from first principles using partial differentiation the expressions satisfied by the ?, ??, ?? and ?? in the following regression equation: y = ? + ??x? + ??x? + ??x? + u Where all symbols have their usual meaning. 4. Suppose you are given the following information: ?? = 49.6870 - 2.1586X? r² = 0.9757 (0.7463) (0.12113) df=8 T = (66.578) (-17.821) p-value = (0.000) (0.000) a) Conduct a two tailed hypothesis test that: i) The intercept is 49 and the slope coefficient is -2, use 1% significance. ii) Confirm your deductions to 4(a) (i) using a confidence interval approach b) What does the r² tell you? c) Perform a hypothesis using r², such that ?=0, what do you conclude?

          3. Derive from first principles using partial differentiation the expressions satisfied by the ?, ??, ?? and ?? in the following regression equation:
y = ? + ??x? + ??x? + ??x? + u
Where all symbols have their usual meaning.
4. Suppose you are given the following information:
?? = 49.6870 - 2.1586X? r² = 0.9757
(0.7463) (0.12113) df=8
T = (66.578) (-17.821)
p-value = (0.000) (0.000)
a) Conduct a two tailed hypothesis test that:
i) The intercept is 49 and the slope coefficient is -2, use 1% significance.
ii) Confirm your deductions to 4(a) (i) using a confidence interval approach
b) What does the r² tell you?
c) Perform a hypothesis using r², such that ?=0, what do you conclude?

3. Derive from first principles using partial differentiation the expressions satisfied by the ?, ??, ?? and ?? in the following regression equation:
y = ? + ??x? + ??x? + ??x? + u
Where all symbols have their usual meaning.
4. Suppose you are given the following information:
?? = 49.6870 - 2.1586X? r² = 0.9757
(0.7463) (0.12113) df=8
T = (66.578) (-17.821)
p-value = (0.000) (0.000)
a) Conduct a two tailed hypothesis test that:
i) The intercept is 49 and the slope coefficient is -2, use 1% significance.
ii) Confirm your deductions to 4(a) (i) using a confidence interval approach
b) What does the r² tell you?
c) Perform a hypothesis using r², such that ?=0, what do you conclude?

Added by Jack R.

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