ECON 4706 B Winter 2020
Simon
Power

Assignment 1: Due February
11

BEFORE BEGINNING THIS ASSIGNMENT, PLEASE BE SURE TO READ THE
DOCUMENT ENTITLED “GENERAL ASSIGNMENT GUIDELINES”. ALL REFERENCES TO PAGE
NUMBERS, EQUATIONS, AND TABLES ARE TO THE 5th EDITION OF DOUGHERTY.

1. Consider the following
simple (linear) regression model:

together with the following data:

X |
Y |

2 |
8 |

3 |
14 |

1 |
6 |

5 |
18 |

9 |
34 |

i) Use equation (1.20) to
calculate the OLS estimate of

ii) Use equation (1.21) to calculate the OLS estimate of

iii) Write the fitted regression equation in the form of
equation (1.50)

iv) Use your various results from above to produce an
analogous table to Table 1.5

v) Use the results from your table, together with equation
(1.80), to calculate

vi) Re-estimate the regression model using the STATA “reg”
command and attach a copy of the relevant output

vii) Check that your results to parts i), ii), and v) above
match those produced by STATA. (Highlight and label the corresponding
quantities on your output.)

viii) Highlight and label the quantities equivalent to TSS,
ESS, and RSS on your output

ix) Use the data in your table to calculate the correlation
between and and verify that its square is equal to the
value of .

x) Use the data in your table to calculate the correlation
between and and verify that its square is equal to the
value of .

2. Following a similar sequence of steps to that used on pp.
96-97 to derive the OLS estimator of in the no-intercept model, derive the OLS
estimator of in the following intercept-only model:

(Be sure to check the second-order condition to ensure that
you have minimized RSS.)

3. It has often been claimed that the educational attainment
of the child depends on the educational attainment of the mother. Estimate a
suitable simple (linear) regression model, using the S and SM variables from
the EAWE22.dta dataset, in order to investigate this claim. Be sure to report
your estimated regression model in the form of equation (1.50), to supply your
STATA output from the regression command, and to interpret your results along
the lines of the discussion on pp. 98-99. (You do not have to conduct a formal
statistical test.)

4. Consider the following
simple (linear) regression model:

Demonstrate that, if BOTH
the units of are changed so that and the units of are changed so that , then the new intercept estimate will be equal to and the new slope estimate will
be equal to , where and are the OLS estimates from the
original model.

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