Determinants of Literacy Rate
Alan Adelman, Scott Callahan, Omer Kutlubay
Presentation 2
Running the regression with all variables
fit <- lm(LTR ~ GDP+ UNEMP+ URBGR + MOBILE + LEXP + INTERNET , data = ltrdata10)
(sse <- deviance(fit))
[1] 0.7454
(df.residual(fit))
[1] 88
Call:
lm(formula = LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP + INTERNET,
data = ltrdata10)
Residuals:
Min 1Q Median 3Q Max
-0.3242 -0.0469 0.0023 0.0365 0.2274
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.064632 0.149502 0.43 0.6666
GDP 0.034831 0.013625 2.56 0.0123 *
UNEMP 0.239559 0.117059 2.05 0.0437 *
URBGR -1.274271 0.552218 -2.31 0.0234 *
MOBILE 0.000920 0.000317 2.90 0.0047 **
LEXP 0.006380 0.001879 3.40 0.0010 **
INTERNET -0.000652 0.000742 -0.88 0.3819
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.092 on 88 degrees of freedom
Multiple R-squared: 0.635, Adjusted R-squared: 0.61
F-statistic: 25.5 on 6 and 88 DF, p-value: <2e-16
Remove the INTERNET variable
fit2 <- lm(LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP, ltrdata10)
(sse2 <- deviance(fit2))
[1] 0.752
(fstat <- (deviance(fit2)-deviance(fit))/(deviance(fit)/df.residual(fit)))
[1] 0.772
1-pf(fstat,1,df.residual(fit)) # p-value
[1] 0.382
Call:
lm(formula = LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP, data = ltrdata10)
Residuals:
Min 1Q Median 3Q Max
-0.3301 -0.0451 0.0015 0.0345 0.2240
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.156962 0.106225 1.48 0.1430
GDP 0.027269 0.010551 2.58 0.0114
UNEMP 0.223462 0.115469 1.94 0.0561
URBGR -1.292914 0.551104 -2.35 0.0212
MOBILE 0.000900 0.000316 2.85 0.0055
LEXP 0.005727 0.001723 3.32 0.0013
Residual standard error: 0.0919 on 89 degrees of freedom
Multiple R-squared: 0.631, Adjusted R-squared: 0.611
F-statistic: 30.5 on 5 and 89 DF, p-value: <2e-16
GDP
(tstat <- summary(fit)$coef[2,3]) #t-stat
[1] 2.56
2*(1-pt(abs(tstat),88)) # p-value
[1] 0.0123
Analysis of Variance Table
Model 1: LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP
Model 2: LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP + INTERNET
Res.Df RSS Df Sum of Sq F Pr(>F)
1 89 0.752
2 88 0.745 1 0.00654 0.77 0.38
Remove GDP
fit3 <- lm(LTR ~ UNEMP+ URBGR + MOBILE + LEXP + INTERNET, ltrdata10)
Analysis of Variance Table
Model 1: LTR ~ UNEMP + URBGR + MOBILE + LEXP + INTERNET
Model 2: LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP + INTERNET
Res.Df RSS Df Sum of Sq F Pr(>F)
1 89 0.801
2 88 0.745 1 0.0554 6.53 0.012
we picked the larger model, but wont use INTERNET because of multicollinearity with GDP
g <- lm(LTR ~ GDP +UNEMP+ URBGR + MOBILE + LEXP , ltrdata10)
summary(g)
Call:
lm(formula = LTR ~ GDP + UNEMP + URBGR + MOBILE + LEXP, data = ltrdata10)
Residuals:
Min 1Q Median 3Q Max
-0.3301 -0.0451 0.0015 0.0345 0.2240
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.156962 0.106225 1.48 0.1430
GDP 0.027269 0.010551 2.58 0.0114
UNEMP 0.223462 0.115469 1.94 0.0561
URBGR -1.292914 0.551104 -2.35 0.0212
MOBILE 0.000900 0.000316 2.85 0.0055
LEXP 0.005727 0.001723 3.32 0.0013
Residual standard error: 0.0919 on 89 degrees of freedom
Multiple R-squared: 0.631, Adjusted R-squared: 0.611
F-statistic: 30.5 on 5 and 89 DF, p-value: <2e-16
Calculating CI for GDP the hard way
alpha <- (1-.95)
qt(1-alpha/2,df.residual(g))
[1] 1.99
c(.027269-1.99*.010551, .027269+1.99*.010551)
[1] 0.00627 0.04827
95% confidece interval
one-at-a-time
confint(g)
2.5 % 97.5 %
(Intercept) -0.054105 0.36803
GDP 0.006304 0.04823
UNEMP -0.005972 0.45290
URBGR -2.387946 -0.19788
MOBILE 0.000271 0.00153
LEXP 0.002303 0.00915
99% confidence interval
one-at-a-time
confint(g, level = 0.99)
0.5 % 99.5 %
(Intercept) -1.23e-01 0.43657
GDP -5.04e-04 0.05504
UNEMP -8.05e-02 0.52740
URBGR -2.74e+00 0.15771
MOBILE 6.74e-05 0.00173
LEXP 1.19e-03 0.01026
cor(ltrdata10$URBGR, ltrdata10$MOBILE)
[1] -0.311
summary(g, corr=TRUE)$corr
(Intercept) GDP UNEMP URBGR MOBILE LEXP
(Intercept) 1.000 -0.1216 -0.5078 -0.5028 0.2113 -0.726
GDP -0.122 1.0000 -0.1223 -0.0512 -0.3864 -0.531
UNEMP -0.508 -0.1223 1.0000 0.2508 0.0409 0.395
URBGR -0.503 -0.0512 0.2508 1.0000 0.1151 0.328
MOBILE 0.211 -0.3864 0.0409 0.1151 1.0000 -0.163
LEXP -0.726 -0.5305 0.3949 0.3276 -0.1629 1.000
Setting up for Prediction Intervals
x0 <- data.frame(URBGR=0.03,UNEMP=.04, MOBILE=75, LEXP=50 ,GDP=8)
str(predict(g,x0,se=TRUE))
List of 4
$ fit : Named num 0.699
..- attr(*, "names")= chr "1"
$ se.fit : num 0.0353
$ df : int 89
$ residual.scale: num 0.0919
Prediction Intervals
Mean Response (Average)
predict(g,x0,interval="confidence", level=.95)
fit lwr upr
1 0.699 0.629 0.769
New Response (One-at-a-time)
predict(g,x0,interval="prediction")
fit lwr upr
1 0.699 0.503 0.895
grid <- seq(0,300,1)
p <- predict(g, data.frame(URBGR=0.03,UNEMP=.04, MOBILE=grid, LEXP=50 ,GDP=8), se=T, interval="confidence")
