Question

Exercise 4.7: Using the data set in Exhibit 1.20, construct a single model for infant mortality rate (IMR), using suitably defined indicator variables for rural-urban and male-female distinctions.

Answer 1

Answer:

Given data

Rearrraged before we bulid a model for the IMR:

State Gender Rural_Urban IMR UP Male Rural 159 Female Rural 187 UP Male Urban 110 UP Female Urban 111 MP Male Rural 148 MP Female Rural 134 MP Male Urban MP Female Urban Orissa Male Rural 131 Orissa Female Rural 142 Orissa Male Urban Orissa Female Urban Rajasthan Male Rural 135 Rajasthan Female Rural 142 Rajasthan Male Urban Rajasthan Female Urban Gujarat Male Rural 120 Gujarat Female Rural 135 Gujarat Male Urban

Gujarat Female Urban 84 AP Male Rural 138 AP Female Rural 101 AP Male Urban АР Female Urban Haryana Male Rural 107 Haryana Female Rural 128 Haryana Male Urban 57 Haryana Female Urban 60 Assam Male Rural 133 Assam Female Rural 106 Assam Male Urban 87 Assam Female Urban Punjab Male Rural 115 Punjab Female Rural 108 Punjab Male Urban 58 Punjab Female Urban 73 TN Male Rural 125 TN Female Rural 115 TN Male Urban TN Female Urban

Karnataka Male Rural Karnataka Female Rural Karnataka Male Urban Karnataka Female Urban Maharashtra Male Rural Maharashtra Female Rural Maharashtra Male Urban Maharashtra Female Urban Kerala Male Rural Kerala Female Rural Kerala Male Urban Kerala Female Urban

  This data is then imported into R and a quick program gives us the IMR model as a function of the Gender and Rural/Urban status:

> IMRD <- read.csv("clipboard", sep="\t", header=TRUE) > head(IMRD) State Gender Rural_Urban IMR 1 UP Male Rural 159 2 UP Female Rural 187 3 UP Male Urban 110 4 UP Female Urban 111 5 MP Male Rural 148 6 MP Female Rural 134 > IMRDSState <-as.character(IMRD$State) > IMRDSGender <-as.character(IMRDSGender) > IMRDSRural_Urban <-as.character(IMRDSRural_Urban) > IMRD_Model <- Im(IMR-,IMRD) > summary(IMRD_Model) Call: Im(formula = IMR-., data = IMRD) Residuals: Min 10 Median 3Q Max -23.2115 -7.5096 -0.7019 7.9567 24.0577

Coefficients: Estimate Std. Errort value Pr(>It) (Intercept) 112.192 7.707 14.557 < 2e-16 *** State Assam 11.750 9.825 1.196 0.2395 StateGujarat 16.750 9.825 1.705 0.0968. State Haryana -3.000 9.825 -0.305 0.7619 StateKarnataka -23.000 9.825 -2.341 0.0249 * StateKerala -57.000 9.825 -5.802 1.28e-06 *** State Maharashtra -21.250 9.825 -2.163 0.0373 * StateMP 22.250 9.825 2.265 0.0297* StateOrissa 17.000 9.825 1.730 0.0921. StatePunjab -2.500 9.825 -0.254 0.8006 StateRajasthan 11.250 9.825 1.145 0.2597 StateTN 0.500 9.825 0.051 0.9597 StateUP 50.750 9.825 5.165 9.05e-06 *** GenderFemale 5.692 7.707 0.739 0.4650 Gender Male 4.462 5.450 0.819 0.4184 Rural_UrbanUrban -49.692 5.450 -9.118 6.89e-11 *** --- Signif. codes: O ****' 0.001 '**' 0.01 *'0.05 0.11 Residual standard error: 13.89 on 36 degrees of freedom Multiple R-squared: 0.8979, Adjusted R-squared: 0.8553 F-statistic: 21.1 on 15 and 36 DF, p-value: 1.945e-13 Since the complete model does not make sense, we drop the State variable and redo the analysis: > IMRD_GUR_Model <- Im(IMR-Gender + +Rural_Urban + ,IMRD) > summary(IMRD_GUR_Model) Call: Im(formula = IMR - Gender + Rural_Urban, data = IMRD) Residuals: Min 10 Median 3Q Max -76.462 -12.077 2.269 16.962 73.000

Coefficients: Estimate Std. Errort value Pr(>1t) (Intercept) 114.000 7.944 14.350 < 2e-16 *** GenderFemale 5.692 15.888 0.358 0.722 Gender Male 4.462 11.235 0.397 0.693 Rural_UrbanUrban -49.692 11.235 -4.423 5.57e-05 *** Signif. codes: 0 ***' 0.001 '**' 0.01 * 0.05 0. 1 1 Residual standard error: 28.64 on 48 degrees of freedom Multiple R-squared: 0.4213, Adjusted R-squared: 0.3851 F-statistic: 11.65 on 3 and 48 DF, p-value: 7.446e-06

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