Chapter 9: More on Specification and Data Issues

Franz Mohr, Created: February 4, 2018, Last update: February 4, 2018

library(wooldridge)

Example 9.1

data("crime1")

lm.9.1.1 <- lm(narr86 ~ pcnv + avgsen + tottime + ptime86 + 
                 qemp86 + inc86 + black + hispan, data = crime1)
summary(lm.9.1.1)

## 
## Call:
## lm(formula = narr86 ~ pcnv + avgsen + tottime + ptime86 + qemp86 + 
##     inc86 + black + hispan, data = crime1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.0108 -0.4518 -0.2392  0.2707 11.5284 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.5686855  0.0360461  15.777  < 2e-16 ***
## pcnv        -0.1332344  0.0403502  -3.302 0.000973 ***
## avgsen      -0.0113177  0.0122401  -0.925 0.355233    
## tottime      0.0120224  0.0094352   1.274 0.202698    
## ptime86     -0.0408417  0.0088120  -4.635 3.74e-06 ***
## qemp86      -0.0505398  0.0144397  -3.500 0.000473 ***
## inc86       -0.0014887  0.0003406  -4.370 1.29e-05 ***
## black        0.3265035  0.0454156   7.189 8.38e-13 ***
## hispan       0.1939144  0.0397113   4.883 1.10e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8286 on 2716 degrees of freedom
## Multiple R-squared:  0.07232,    Adjusted R-squared:  0.06959 
## F-statistic: 26.47 on 8 and 2716 DF,  p-value: < 2.2e-16

# Seems to be an error in the book.
# Although all coefficients and their standard errors are equal
# the intercept term is 0.569 instead of 0.596.

lm.9.1.2 <- lm(narr86 ~ pcnv + avgsen + tottime + ptime86 + 
                 qemp86 + inc86 + black + hispan + pcnvsq + 
                 pt86sq + inc86sq, data = crime1)
summary(lm.9.1.2)

## 
## Call:
## lm(formula = narr86 ~ pcnv + avgsen + tottime + ptime86 + qemp86 + 
##     inc86 + black + hispan + pcnvsq + pt86sq + inc86sq, data = crime1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.5248 -0.4646 -0.2151  0.2276 11.4286 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  5.046e-01  3.684e-02  13.699  < 2e-16 ***
## pcnv         5.525e-01  1.542e-01   3.582 0.000347 ***
## avgsen      -1.702e-02  1.205e-02  -1.412 0.158028    
## tottime      1.195e-02  9.282e-03   1.288 0.197924    
## ptime86      2.874e-01  4.426e-02   6.494 9.88e-11 ***
## qemp86      -1.409e-02  1.736e-02  -0.812 0.416970    
## inc86       -3.415e-03  8.037e-04  -4.249 2.22e-05 ***
## black        2.923e-01  4.483e-02   6.520 8.35e-11 ***
## hispan       1.636e-01  3.945e-02   4.147 3.47e-05 ***
## pcnvsq      -7.302e-01  1.561e-01  -4.677 3.05e-06 ***
## pt86sq      -2.961e-02  3.863e-03  -7.664 2.50e-14 ***
## inc86sq      7.186e-06  2.556e-06   2.811 0.004969 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8151 on 2713 degrees of freedom
## Multiple R-squared:  0.1035, Adjusted R-squared:  0.09982 
## F-statistic: 28.46 on 11 and 2713 DF,  p-value: < 2.2e-16

anova(lm.9.1.1, lm.9.1.2)

## Analysis of Variance Table
## 
## Model 1: narr86 ~ pcnv + avgsen + tottime + ptime86 + qemp86 + inc86 + 
##     black + hispan
## Model 2: narr86 ~ pcnv + avgsen + tottime + ptime86 + qemp86 + inc86 + 
##     black + hispan + pcnvsq + pt86sq + inc86sq
##   Res.Df    RSS Df Sum of Sq      F    Pr(>F)    
## 1   2716 1865.0                                  
## 2   2713 1802.4  3    62.589 31.404 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Example 9.2

data("hprice1")

lm.9.2.1 <- lm(price ~ lotsize + sqrft + bdrms, data = hprice1)
fit2.1 <- lm.9.2.1$fitted.values^2
fit3.1 <- lm.9.2.1$fitted.values^3
lm.9.2.1.reset <- lm(price ~ lotsize + sqrft + bdrms + fit2.1 + fit3.1, data = hprice1)
anova(lm.9.2.1, lm.9.2.1.reset)

## Analysis of Variance Table
## 
## Model 1: price ~ lotsize + sqrft + bdrms
## Model 2: price ~ lotsize + sqrft + bdrms + fit2.1 + fit3.1
##   Res.Df    RSS Df Sum of Sq      F  Pr(>F)  
## 1     84 300724                              
## 2     82 269984  2     30740 4.6682 0.01202 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

lm.9.2.2 <- lm(lprice ~ llotsize + lsqrft + bdrms, data = hprice1)
fit2.2 <- lm.9.2.2$fitted.values^2
fit3.2 <- lm.9.2.2$fitted.values^3
lm.9.2.2.reset <- lm(lprice ~ llotsize + lsqrft + bdrms + fit2.2 + fit3.2, data = hprice1)
anova(lm.9.2.2, lm.9.2.2.reset)

## Analysis of Variance Table
## 
## Model 1: lprice ~ llotsize + lsqrft + bdrms
## Model 2: lprice ~ llotsize + lsqrft + bdrms + fit2.2 + fit3.2
##   Res.Df    RSS Df Sum of Sq     F  Pr(>F)  
## 1     84 2.8626                             
## 2     82 2.6940  2   0.16854 2.565 0.08308 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Table 9.2

data("wage2")

lm.t9.2.1 <- lm(lwage ~ educ + exper + tenure + married + south + urban + 
                  black, data = wage2)
summary(lm.t9.2.1)

## 
## Call:
## lm(formula = lwage ~ educ + exper + tenure + married + south + 
##     urban + black, data = wage2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.98069 -0.21996  0.00707  0.24288  1.22822 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  5.395497   0.113225  47.653  < 2e-16 ***
## educ         0.065431   0.006250  10.468  < 2e-16 ***
## exper        0.014043   0.003185   4.409 1.16e-05 ***
## tenure       0.011747   0.002453   4.789 1.95e-06 ***
## married      0.199417   0.039050   5.107 3.98e-07 ***
## south       -0.090904   0.026249  -3.463 0.000558 ***
## urban        0.183912   0.026958   6.822 1.62e-11 ***
## black       -0.188350   0.037667  -5.000 6.84e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3655 on 927 degrees of freedom
## Multiple R-squared:  0.2526, Adjusted R-squared:  0.2469 
## F-statistic: 44.75 on 7 and 927 DF,  p-value: < 2.2e-16

lm.t9.2.2 <- lm(lwage ~ educ + exper + tenure + married + south + urban + 
                  black + IQ, data=wage2)
summary(lm.t9.2.2)

## 
## Call:
## lm(formula = lwage ~ educ + exper + tenure + married + south + 
##     urban + black + IQ, data = wage2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.01203 -0.22244  0.01017  0.22951  1.27478 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  5.1764392  0.1280006  40.441  < 2e-16 ***
## educ         0.0544106  0.0069285   7.853 1.12e-14 ***
## exper        0.0141458  0.0031651   4.469 8.82e-06 ***
## tenure       0.0113951  0.0024394   4.671 3.44e-06 ***
## married      0.1997644  0.0388025   5.148 3.21e-07 ***
## south       -0.0801695  0.0262529  -3.054 0.002325 ** 
## urban        0.1819463  0.0267929   6.791 1.99e-11 ***
## black       -0.1431253  0.0394925  -3.624 0.000306 ***
## IQ           0.0035591  0.0009918   3.589 0.000350 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3632 on 926 degrees of freedom
## Multiple R-squared:  0.2628, Adjusted R-squared:  0.2564 
## F-statistic: 41.27 on 8 and 926 DF,  p-value: < 2.2e-16

lm.t9.2.3 <- lm(lwage ~ educ + exper + tenure + married + south + urban + 
                black + IQ + IQ*educ, data = wage2)
summary(lm.t9.2.3)

## 
## Call:
## lm(formula = lwage ~ educ + exper + tenure + married + south + 
##     urban + black + IQ + IQ * educ, data = wage2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.00733 -0.21715  0.01177  0.23456  1.27305 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  5.6482483  0.5462963  10.339  < 2e-16 ***
## educ         0.0184559  0.0410608   0.449 0.653192    
## exper        0.0139072  0.0031768   4.378 1.34e-05 ***
## tenure       0.0113929  0.0024397   4.670 3.46e-06 ***
## married      0.2008658  0.0388267   5.173 2.82e-07 ***
## south       -0.0802354  0.0262560  -3.056 0.002308 ** 
## urban        0.1835758  0.0268586   6.835 1.49e-11 ***
## black       -0.1466989  0.0397013  -3.695 0.000233 ***
## IQ          -0.0009418  0.0051625  -0.182 0.855289    
## educ:IQ      0.0003399  0.0003826   0.888 0.374564    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3632 on 925 degrees of freedom
## Multiple R-squared:  0.2634, Adjusted R-squared:  0.2563 
## F-statistic: 36.76 on 9 and 925 DF,  p-value: < 2.2e-16

Example 9.4

data("crime2")

lm.9.4.1 <- lm(lcrmrte ~ unem + llawexpc, data = crime2, subset = (d87==1))
summary(lm.9.4.1)

## 
## Call:
## lm(formula = lcrmrte ~ unem + llawexpc, data = crime2, subset = (d87 == 
##     1))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.64786 -0.22955 -0.06368  0.22183  0.71164 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  3.34290    1.25053   2.673   0.0106 *
## unem        -0.02900    0.03234  -0.897   0.3748  
## llawexpc     0.20337    0.17265   1.178   0.2453  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3231 on 43 degrees of freedom
## Multiple R-squared:  0.05712,    Adjusted R-squared:  0.01326 
## F-statistic: 1.302 on 2 and 43 DF,  p-value: 0.2824

lm.9.4.2 <- lm(lcrmrte ~ unem + llawexpc + lcrmrt_1, data = crime2, subset = (d87==1))
summary(lm.9.4.2)

## 
## Call:
## lm(formula = lcrmrte ~ unem + llawexpc + lcrmrt_1, data = crime2, 
##     subset = (d87 == 1))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.48081 -0.12202  0.00659  0.14658  0.34428 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.076451   0.821143   0.093    0.926    
## unem         0.008621   0.019517   0.442    0.661    
## llawexpc    -0.139576   0.108641  -1.285    0.206    
## lcrmrt_1     1.193923   0.132099   9.038  2.1e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1905 on 42 degrees of freedom
## Multiple R-squared:  0.6798, Adjusted R-squared:  0.657 
## F-statistic: 29.73 on 3 and 42 DF,  p-value: 1.799e-10

Example 9.8

data("rdchem")

lm.9.8.1 <- lm(rdintens ~ sales + profmarg, data = rdchem)
summary(lm.9.8.1)

## 
## Call:
## lm(formula = rdintens ~ sales + profmarg, data = rdchem)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.2221 -1.1414 -0.6068  0.5008  6.3702 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 2.625e+00  5.855e-01   4.484 0.000106 ***
## sales       5.338e-05  4.407e-05   1.211 0.235638    
## profmarg    4.462e-02  4.618e-02   0.966 0.341966    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.862 on 29 degrees of freedom
## Multiple R-squared:  0.07612,    Adjusted R-squared:  0.0124 
## F-statistic: 1.195 on 2 and 29 DF,  p-value: 0.3173

# See the outliers
with(rdchem, plot(sales, rdintens, pch = 16))

# Test without the biggest firm
lm.9.8.2 <- lm(rdintens ~ sales + profmarg, data = rdchem, subset = (sales < 30000))
summary(lm.9.8.2)

## 
## Call:
## lm(formula = rdintens ~ sales + profmarg, data = rdchem, subset = (sales < 
##     30000))
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.0687 -1.1867 -0.7956  0.6486  6.0811 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 2.2968508  0.5918045   3.881 0.000577 ***
## sales       0.0001856  0.0000842   2.204 0.035883 *  
## profmarg    0.0478411  0.0444831   1.075 0.291336    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.792 on 28 degrees of freedom
## Multiple R-squared:  0.1728, Adjusted R-squared:  0.1137 
## F-statistic: 2.925 on 2 and 28 DF,  p-value: 0.07022

Hmmm, slightly different result than in the book

# Dummy for the biggest firm
big <- as.numeric(rdchem$sales == max(rdchem$sales))
lm.9.8.3 <- lm(rdintens ~ sales + profmarg + big, data = rdchem)
summary(lm.9.8.3)

## 
## Call:
## lm(formula = rdintens ~ sales + profmarg + big, data = rdchem)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.0687 -1.1218 -0.6207  0.6384  6.0811 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.2968508  0.5918045   3.881 0.000577 ***
## sales        0.0001856  0.0000842   2.204 0.035883 *  
## profmarg     0.0478411  0.0444831   1.075 0.291336    
## big         -6.5717169  3.6147274  -1.818 0.079773 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.792 on 28 degrees of freedom
## Multiple R-squared:  0.1737, Adjusted R-squared:  0.08513 
## F-statistic: 1.962 on 3 and 28 DF,  p-value: 0.1427

# Dummy for highest rdintens
hi.rdint <- as.numeric(rdchem$rdintens == max(rdchem$rdintens))
lm.9.8.4 <- lm(rdintens ~ sales + profmarg + hi.rdint, data = rdchem)
summary(lm.9.8.4)

## 
## Call:
## lm(formula = rdintens ~ sales + profmarg + hi.rdint, data = rdchem)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.1920 -1.0442 -0.3307  0.5016  3.5413 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 2.193e+00  4.615e-01   4.753 5.45e-05 ***
## sales       5.057e-05  3.400e-05   1.487   0.1481    
## profmarg    6.829e-02  3.600e-02   1.897   0.0681 .  
## hi.rdint    6.718e+00  1.475e+00   4.555 9.35e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.436 on 28 degrees of freedom
## Multiple R-squared:  0.4693, Adjusted R-squared:  0.4125 
## F-statistic: 8.255 on 3 and 28 DF,  p-value: 0.0004321

lm.9.8.5 <- lm(rdintens ~ sales + profmarg, data = rdchem, subset = (rdintens  < max(rdintens)))
summary(lm.9.8.5)

## 
## Call:
## lm(formula = rdintens ~ sales + profmarg, data = rdchem, subset = (rdintens < 
##     max(rdintens)))
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.1920 -1.0711 -0.5777  0.5182  3.5413 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 2.193e+00  4.615e-01   4.753 5.45e-05 ***
## sales       5.057e-05  3.400e-05   1.487   0.1481    
## profmarg    6.829e-02  3.600e-02   1.897   0.0681 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.436 on 28 degrees of freedom
## Multiple R-squared:  0.1716, Adjusted R-squared:  0.1125 
## F-statistic:   2.9 on 2 and 28 DF,  p-value: 0.07165

# Without first and tenth firm
lm.9.8.6 <- lm(rdintens ~ sales + profmarg, 
               data = rdchem,
               subset = (sales < max(sales) & rdintens < max(rdintens)))
summary(lm.9.8.6)

## 
## Call:
## lm(formula = rdintens ~ sales + profmarg, data = rdchem, subset = (sales < 
##     max(sales) & rdintens < max(rdintens)))
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.0667 -1.0609 -0.3414  0.6422  3.1439 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 1.939e+00  4.588e-01   4.226 0.000243 ***
## sales       1.596e-04  6.457e-05   2.472 0.020029 *  
## profmarg    7.007e-02  3.433e-02   2.041 0.051116 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.369 on 27 degrees of freedom
## Multiple R-squared:  0.2711, Adjusted R-squared:  0.2171 
## F-statistic: 5.021 on 2 and 27 DF,  p-value: 0.014

Hmm, slighty different results

lm.9.8.7 <- lm(rdintens ~ sales + profmarg + big + hi.rdint, data = rdchem)
summary(lm.9.8.7)

## 
## Call:
## lm(formula = rdintens ~ sales + profmarg + big + hi.rdint, data = rdchem)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.0667 -1.0604 -0.1891  0.6416  3.1439 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.939e+00  4.588e-01   4.226 0.000243 ***
## sales        1.596e-04  6.457e-05   2.472 0.020029 *  
## profmarg     7.007e-02  3.433e-02   2.041 0.051116 .  
## big         -5.414e+00  2.773e+00  -1.953 0.061306 .  
## hi.rdint     6.467e+00  1.412e+00   4.581  9.4e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.369 on 27 degrees of freedom
## Multiple R-squared:  0.535,  Adjusted R-squared:  0.4661 
## F-statistic: 7.766 on 4 and 27 DF,  p-value: 0.0002664

Example 9.9

data("rdchem")

lm.9.9.1 <- lm(lrd ~ lsales + profmarg, data = rdchem)
summary(lm.9.9.1)

## 
## Call:
## lm(formula = lrd ~ lsales + profmarg, data = rdchem)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.97681 -0.31502 -0.05828  0.39020  1.21783 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -4.37827    0.46802  -9.355 2.93e-10 ***
## lsales       1.08422    0.06020  18.012  < 2e-16 ***
## profmarg     0.02166    0.01278   1.694    0.101    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5136 on 29 degrees of freedom
## Multiple R-squared:  0.918,  Adjusted R-squared:  0.9123 
## F-statistic: 162.2 on 2 and 29 DF,  p-value: < 2.2e-16

# Without the largest firm
lm.9.9.2 <- lm(lrd ~ lsales + profmarg, data = rdchem, subset = (lsales  < max(lsales)))
summary(lm.9.9.2)

## 
## Call:
## lm(formula = lrd ~ lsales + profmarg, data = rdchem, subset = (lsales < 
##     max(lsales)))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.97871 -0.31809 -0.05582  0.38978  1.21104 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -4.40414    0.51102  -8.618 2.30e-09 ***
## lsales       1.08805    0.06711  16.212 9.21e-16 ***
## profmarg     0.02176    0.01302   1.670    0.106    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5225 on 28 degrees of freedom
## Multiple R-squared:  0.9037, Adjusted R-squared:  0.8968 
## F-statistic: 131.4 on 2 and 28 DF,  p-value: 5.877e-15

Example 9.10

data("infmrt")

lm.9.10.1 <- lm(infmort ~ lpcinc + lphysic + lpopul, data = infmrt, subset = (year==1990))
summary(lm.9.10.1)

## 
## Call:
## lm(formula = infmort ~ lpcinc + lphysic + lpopul, data = infmrt, 
##     subset = (year == 1990))
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.0811 -1.2064 -0.0521  1.0639  7.9589 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept) 33.85931   20.42785   1.658  0.10408   
## lpcinc      -4.68466    2.60412  -1.799  0.07845 . 
## lphysic      4.15326    1.51266   2.746  0.00853 **
## lpopul      -0.08782    0.28725  -0.306  0.76116   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.058 on 47 degrees of freedom
## Multiple R-squared:  0.1391, Adjusted R-squared:  0.08413 
## F-statistic: 2.531 on 3 and 47 DF,  p-value: 0.06841

lm.9.10.2 <- lm(infmort ~ lpcinc + lphysic + lpopul, data = infmrt, subset = (year==1990 & DC==0))
summary(lm.9.10.2)

## 
## Call:
## lm(formula = infmort ~ lpcinc + lphysic + lpopul, data = infmrt, 
##     subset = (year == 1990 & DC == 0))
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.49645 -0.81641 -0.05117  0.94204  2.60772 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  23.9548    12.4195   1.929  0.05994 . 
## lpcinc       -0.5669     1.6412  -0.345  0.73134   
## lphysic      -2.7418     1.1908  -2.303  0.02588 * 
## lpopul        0.6292     0.1911   3.293  0.00191 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.246 on 46 degrees of freedom
## Multiple R-squared:  0.2732, Adjusted R-squared:  0.2258 
## F-statistic: 5.763 on 3 and 46 DF,  p-value: 0.001967