(without using lm command, instead use OLS formulas) (please show your code)

(Multivariate Regression) In order to study the eect of change in hourly wage (WPH) on the supply

of labor (hours worked, HRS), we have data on the 38 demographic groups. There are other factors

that will aect the supply of labor, which include spouse's annual income (ERSP) and the number

of years of education (SCL). We have data saved in le W age.txt. You are asked to estimate the

supply equation. Note, in all the following regressions, you should include a constant term.

(a) Estimate a univariate regression of HRS on WPH. What is the impact of a dollar change in wage

on the supply, and does the sign of the coecient makes sense? Is your estimate signicant?

(b) The supply of labor may depend on how much spouse makes. In other words, we should estimate

the following multivariate regression model instead,

HRS = 1 + 2 W P H + 3 ERSP + u.

What sign do you expect for 2 and 3 ? Are the corresponding coecient estimates signicant

and have the right sign?

(c) What if you delete the 19th observation, and rerun the multivariate regression, what do you

observe when comparing with those of (b)?

(d) Suppose, on average, a spouse worked 700 hours a year, we can study whether there is a

complete substitution eect of spouse by testing how would you formulate the hypothesis of

2 + 3 700 = 0. Is the complete substitution hypothesis true?

(e) Finally, since both HRS and WPH are endogenous, we may interested in estimating the following

multivariate regression model,

(W P H HRS) = 1 + 2 SCL + 3 N EIN + v,

where N EIN is non-wage income. Interpret your coecient estimates, and test their signicance. Does the sign of coeceint estimates make sense?

DATA

HRS WPH ERSP SCH NEIN

2157 2.905 1121 10.5 380

2174 2.97 1128 10.5 398

2062 2.35 1214 8.9 185

2111 2.511 1203 11.5 117

2134 2.791 1013 8.8 730

2185 3.04 1135 10.7 382

2210 3.222 1100 11.2 474

2105 2.493 1180 9.3 255

2267 2.838 1298 11.1 431

2205 2.356 885 9.5 373

2121 2.922 1251 10.3 312

2109 2.499 1207 8.9 271

2108 2.796 1036 9.2 259

2047 2.453 1213 9.1 139

2174 3.582 1141 11.7 498

2067 2.909 1805 10.5 239

2159 2.511 1075 9.5 308

2257 2.516 1093 10.1 392

1985 1.423 553 6.6 146

2184 3.636 1091 11.6 560

2084 2.983 1327 10.2 296

2051 2.573 1194 9.1 172

2127 3.262 1226 10.8 408

2102 3.234 1188 10.7 352

2098 2.28 973 8.4 272

2042 2.304 1085 8.2 140

2181 2.912 1072 10.2 383

2186 3.015 1122 10.9 352

2108 2.786 1757 10.2 506

2188 3.01 990 10.6 374

2203 3.273 1109 11 430

2077 1.901 350 8.2 95

2196 3.009 947 10.6 342

2093 1.899 342 8.1 120

2173 2.959 1116 10.5 387

2179 2.971 1128 10.5 397

2200 2.98 1126 10.6 393

2197 3.413 1078 11.3 512