R Notebook

SLR on Physicians SLR on Literacy Rate Plot, significance of each predictor, confidence and prediction interval, partial f-test full f-test, t-test, correlation, residuals

(lplot<-plot(LIFEEXP~LITERATE,xlab="Literacy Rate",ylab="Life Expectancy",main= "Expected Life Based on Literacy Rate", data = Life))

NULL

abline(35.9664,.3802)

Prediction

73-.3802*14.2

[1] 67.60116

newdata <- data.frame(ILLITERATE = 14)
(distpredict <- predict.lm(lmod, newdata, interval="predict") )

Error in eval(predvars, data, env) : object 'mag' not found

Actual= 73.9 The linear model gives a much lower expected life.

cresid1<-lmod$residuals
cresid1

          1           2           3           4           5           6           7 
-17.6288023   9.8854749   6.3153232 -18.2605617  13.4745141  -0.2964257  -6.3926035 
          8           9          10          11          12          13          14 
  8.5931192   2.3922195 -10.7859706  10.0219562   2.2095900 -14.3517944  -3.9418450 
         15          16          17          18          19          20          21 
 10.9285891  -4.3539288   4.8944130  -1.1496009   8.0305002 -13.5136253   6.2120067 
         22          23          24          25          26          27          28 
 11.9352221  -5.2376288  -8.4055870 -11.2022705  -2.3738276 -10.7288023   9.6978411 
         29          30          31          32          33          34          35 
  8.9214505 -16.2605617  -9.3539288  13.1219562   7.4769309   5.7788420  -6.5804606 
         36          37          38          39          40          41          42 
-14.3155364  12.1338167 -12.7671947   3.1480939   7.3646763  -1.7793376   3.2168402 
         43          44          45          46          47          48          49 
 13.4697923   2.2409553   7.5072849   8.3631593   5.3470826 -10.6970430 -11.4901868 
         50          51          52          53          54          55          56 
 -7.9022705   3.0287008   3.2438777  -4.8453847  -9.9755155   2.1438777  -1.2221694 
         57          58          59          60          61          62          63 
 -3.2736044   6.0697923   5.5034627  -5.3155364   6.9081846  -3.8494893   3.2524218 
         64          65          66          67          68          69          70 
  1.0532099   9.4811471   6.1584374  -5.2567396   4.4400556   1.0192570  -0.9437561 
         71          72          73          74          75          76          77 
  8.2617539  12.5243729   1.8660817 -11.9343123  -8.1705111  -9.7428564  10.2423607 
         78          79          80          81          82          83          84 
  9.8489937  -6.9135137  -3.0964257 -17.2055870 -15.0022705   7.1887914  -7.5556166 
         85          86          87          88          89          90          91 
  5.1116127   2.9395499  -2.6453847 -13.3506123  10.5366275   2.7001462  -6.8605617 
         92          93          94          95          96          97          98 
  3.1253843   3.0844636   7.3769309   5.8243729   5.3532099  -4.7850708  -7.2334126 
         99         100         101         102         103         104         105 
  3.9111070   8.2181340 -16.9022705  -0.6069924  -9.4970430   1.9678812   3.3803590 
        106         107         108         109         110         111         112 
  8.0097016  10.4413494  -3.8506123 -14.4937265   4.0836755   8.6338167   1.2299945 
        113         114         115         116         117         118         119 
  7.8039684  -2.9055870   6.0186397   5.1086903   8.4565264   2.8931192   0.4855865 
        120         121         122         123         124         125         126 
  3.9845752   2.5376388 -16.5020473 -14.6055870   4.3053738 -13.1546052   7.0584374 
        127         128         129         130         131         132         133 
  7.6366275   2.8214505   5.5755255   2.4427548   3.4111070   5.3523101 -17.9022705 
        134         135         136         137         138         139         140 
 12.6205508  -1.7746157   6.2296005   2.7811471 -12.7249802   3.9054854   9.2115011 
        141         142         143         144         145         146         147 
 -3.2837771   7.7280835 -19.4738276   4.0088019   3.1040800   6.8205508  -3.7339183 
        148         149         150         151         152         153         154 
 -8.6506123   8.1413494  -0.3638782  -1.9539288  11.4963241   5.5717033   7.0305002 
        155         156         157         158         159         160         161 
  4.8788420 -18.5404396 -10.2605617  -7.0864762   8.3177400   7.5713093   5.1281951 
        162         163         164         165         166         167         168 
 -2.5025529  -6.9016532   9.1844636   3.6310059  11.4148175   0.2479823 -19.6671947 
        169 
-19.4738276 

hist(cresid1,xlab="residual", main="Plot of Residuals")

qqnorm(cresid1)
qqline(cresid1)

There is a relationship but maybe linear isn’t the best way to describe it. Correlation

summary(lmod)

Call:
lm(formula = LIFEEXP ~ PHYSICIAN, data = Life)

Residuals:
    Min      1Q  Median      3Q     Max 
-19.667  -6.580   2.781   6.908  13.475 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 59.547296   0.993539   59.94   <2e-16 ***
PHYSICIAN    0.051658   0.004927   10.48   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 8.666 on 167 degrees of freedom
Multiple R-squared:  0.397, Adjusted R-squared:  0.3934 
F-statistic: 109.9 on 1 and 167 DF,  p-value: < 2.2e-16

looks like they might have a log normal relationship because it’s clearly not linear. We don’t have to do any of the other testings to see if linear is the best model since we can clearly see from the plot.

?stepAIC