Question

Description: The data are from a national sample of 6000 households with a male head earning less than $15,000 annually in 1966. The data were classified into 39 demographic groups for analysis. The study was undertaken in the context of proposals for a guaranteed annual wage (negative income tax). At issue was the response of labor supply (average hours) to increasing hourly wages. The study was undertaken to estimate this response from available data

SOLVE: Use SAS software to answer the following questions by using simple linear regression.

Research questions:

Do labor hours increase or decrease with wage rates?

What other factors affect the number of hours that people work?

The comparison between the correlation of wages and ages, and wages and schooling.

DATA BELOW:

HRS    RATE ERSP ERNO NEIN ASSET AGE DEP RACE SCHOOL

2157   2.905   1121   291   380   7250   38.5   2.340   32.1   10.5

2174   2.970   1128   301   398   7744   39.3   2.335   31.2   10.5

2062   2.350   1214   326   185   3068   40.1   2.851   *   8.9

2111   2.511   1203   49   117   1632   22.4   1.159   27.5   11.5

2134   2.791   1013   594   730   12710   57.7   1.229   32.5   8.8

2185   3.040   1135   287   382   7706   38.6   2.602   31.4   10.7

2210   3.222   1100   295   474   9338   39.0   2.187   10.1   11.2

2105   2.493   1180   310   255   4730   39.9   2.616   71.1   9.3

2267   2.838   1298   252   431   8317   38.9   2.024   9.7   11.1

2205   2.356   885   264   373   6789   38.8   2.662   25.2   9.5

2121   2.922   1251   328   312   5907   39.8   2.287   51.1   10.3

2109   2.499   1207   347   271   5069   39.7   3.193   *   8.9

2108   2.796   1036   300   259   4614   38.2   2.040   *   9.2

2047   2.453   1213   297   139   1987   40.3   2.545   *   9.1

2174   3.582   1141   414   498   10239   40.0   2.064   *   11.7

2067   2.909   1805   290   239   4439   39.1   2.301   *   10.5

2159   2.511   1075   289   308   5621   39.3   2.486   43.6   9.5

2257   2.516   1093   176   392   7293   37.9   2.042   *   10.1

1985   1.423   553   381   146   1866   40.6   3.833   *   6.6

2184   3.636   1091   291   560   11240   39.1   2.328   13.6   11.6

2084   2.983   1327   331   296   5653   39.8   2.208   58.4   10.2

2051   2.573   1194   279   172   2806   40.0   2.362   77.9   9.1

2127   3.262   1226   314   408   8042   39.5   2.259   39.2   10.8

2102   3.234   1188   414   352   7557   39.8   2.019   29.8   10.7

2098   2.280   973   364   272   4400   40.6   2.661   53.6   8.4

2042   2.304   1085   328   140   1739   41.8   2.444   83.1   8.2

2181   2.912   1072   304   383   7340   39.0   2.337   30.2   10.2

2186   3.015   1122   30   352   7292   37.2   2.046   29.5   10.9

2108   2.786   1757   *   506   9658   43.4   *   32.6   10.2

2188   3.010   990   366   374   7325   38.4   2.847   30.9   10.6

2203   3.273   *   *   430   8221   38.2   2.324   22.1   11.0

2077   1.901   350   209   95   1370   37.4   4.158   61.3   8.2

2196   3.009   947   294   342   6888   37.5   3.047   31.8   10.6

2093   1.899   342   311   120   1425   37.5   4.512   62.8   8.1

2173   2.959   1116   296   387   7625   39.2   2.342   31.0   10.5

2179   2.971   1128   312   397   7779   39.4   2.341   31.2   10.5

2200   2.980   1126   204   393   7885   39.2   2.341   31.0   10.6

2052   2.630   *   *   154   3331   40.5   *   45.8   10.3

2197   3.413   1078   300   512   10450   39.1   2.297   15.5   11.3

Answer 1

Sol:

use data step in SAS to create dataset.

input statement to declare variables

procedure corr to get the correlation matrix and var statement to anlayse which ever variable to analyse;:

Entire SAS Code:

data wage;
infile cards;
input
HRS RATE ERSP ERNO NEIN ASSET AGE DEP RACE SCHOOL;
cards;

2157 2.905 1121 291 380 7250 38.5 2.340 32.1 10.5

2174 2.970 1128 301 398 7744 39.3 2.335 31.2 10.5

2062 2.350 1214 326 185 3068 40.1 2.851 * 8.9

2111 2.511 1203 49 117 1632 22.4 1.159 27.5 11.5

2134 2.791 1013 594 730 12710 57.7 1.229 32.5 8.8

2185 3.040 1135 287 382 7706 38.6 2.602 31.4 10.7

2210 3.222 1100 295 474 9338 39.0 2.187 10.1 11.2

2105 2.493 1180 310 255 4730 39.9 2.616 71.1 9.3

2267 2.838 1298 252 431 8317 38.9 2.024 9.7 11.1

2205 2.356 885 264 373 6789 38.8 2.662 25.2 9.5

2121 2.922 1251 328 312 5907 39.8 2.287 51.1 10.3

2109 2.499 1207 347 271 5069 39.7 3.193 * 8.9

2108 2.796 1036 300 259 4614 38.2 2.040 * 9.2

2047 2.453 1213 297 139 1987 40.3 2.545 * 9.1

2174 3.582 1141 414 498 10239 40.0 2.064 * 11.7

2067 2.909 1805 290 239 4439 39.1 2.301 * 10.5

2159 2.511 1075 289 308 5621 39.3 2.486 43.6 9.5

2257 2.516 1093 176 392 7293 37.9 2.042 * 10.1

1985 1.423 553 381 146 1866 40.6 3.833 * 6.6

2184 3.636 1091 291 560 11240 39.1 2.328 13.6 11.6

2084 2.983 1327 331 296 5653 39.8 2.208 58.4 10.2

2051 2.573 1194 279 172 2806 40.0 2.362 77.9 9.1

2127 3.262 1226 314 408 8042 39.5 2.259 39.2 10.8

2102 3.234 1188 414 352 7557 39.8 2.019 29.8 10.7

2098 2.280 973 364 272 4400 40.6 2.661 53.6 8.4

2042 2.304 1085 328 140 1739 41.8 2.444 83.1 8.2

2181 2.912 1072 304 383 7340 39.0 2.337 30.2 10.2

2186 3.015 1122 30 352 7292 37.2 2.046 29.5 10.9

2108 2.786 1757 * 506 9658 43.4 * 32.6 10.2

2188 3.010 990 366 374 7325 38.4 2.847 30.9 10.6

2203 3.273 * * 430 8221 38.2 2.324 22.1 11.0

2077 1.901 350 209 95 1370 37.4 4.158 61.3 8.2

2196 3.009 947 294 342 6888 37.5 3.047 31.8 10.6

2093 1.899 342 311 120 1425 37.5 4.512 62.8 8.1

2173 2.959 1116 296 387 7625 39.2 2.342 31.0 10.5

2179 2.971 1128 312 397 7779 39.4 2.341 31.2 10.5

2200 2.980 1126 204 393 7885 39.2 2.341 31.0 10.6

2052 2.630 * * 154 3331 40.5 * 45.8 10.3

2197 3.413 1078 300 512 10450 39.1 2.297 15.5 11.3
;
run;
proc print data=wage;
run;

proc corr data=wage pearson plots=scatter(nvar=all);
run;
proc corr data=wage pearson plots=scatter;
var HRS;
with RATE ;
run;
proc corr data=wage pearson plots=scatter;
var RATE;
with AGE SCHOOL;
run;

Output:

There exists a positive relationship between HRS and RATE,as HRS increases RATE increases and vice versa.

The comparison between the correlation of wages and ages, and wages and schooling.

as

correlation coefficient between age and rate=0.03149

there exists a weak positive relationship between age and rate

p=0.8491,p>0.05

Relationship is not significant

correlation coefficient between school and rate=0.88397

there exists a strong positive relationship between school and rate

p<0.0001,p<0.05

Relationship  between school and rate is signifcant