## 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.

### economics

##### Description

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.