LFulton_Assignment12_PGatica
Peter Gatica
2022-11-13
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## âś– dplyr::filter() masks stats::filter()
## âś– dplyr::lag() masks stats::lag()The attached who.csv dataset contains real-world data from 2008. The variables included follow.
Country: name of the country
LifeExp: average life expectancy for the country in years
InfantSurvival: proportion of those surviving to one year or more
Under5Survival: proportion of those surviving to five years or more
TBFree: proportion of the population without TB.
PropMD: proportion of the population who are MDs
PropRN: proportion of the population who are RNs
PersExp: mean personal expenditures on healthcare in US dollars at average exchange rate
GovtExp: mean government expenditures per capita on healthcare, US dollars at average exchange rate
TotExp: sum of personal and government expenditures.
who_src = read.csv('who.csv', header = TRUE)
head(who_src)## Country LifeExp InfantSurvival Under5Survival TBFree PropMD
## 1 Afghanistan 42 0.835 0.743 0.99769 0.000228841
## 2 Albania 71 0.985 0.983 0.99974 0.001143127
## 3 Algeria 71 0.967 0.962 0.99944 0.001060478
## 4 Andorra 82 0.997 0.996 0.99983 0.003297297
## 5 Angola 41 0.846 0.740 0.99656 0.000070400
## 6 Antigua and Barbuda 73 0.990 0.989 0.99991 0.000142857
## PropRN PersExp GovtExp TotExp
## 1 0.000572294 20 92 112
## 2 0.004614439 169 3128 3297
## 3 0.002091362 108 5184 5292
## 4 0.003500000 2589 169725 172314
## 5 0.001146162 36 1620 1656
## 6 0.002773810 503 12543 13046- Provide a scatterplot of LifeExp~TotExp, and run simple linear regression. Do not transform the variables. Provide and interpret the F statistics, R^2, standard error,and p-values only. Discuss whether the assumptions of simple linear regression met.
plot(who_src$TotExp, who_src$LifeExp, xlab='TotalExpenditure', ylab='LifeExpectancy', main='scatterplot')
(who_src_lm <- lm(LifeExp ~ TotExp,data = who_src))##
## Call:
## lm(formula = LifeExp ~ TotExp, data = who_src)
##
## Coefficients:
## (Intercept) TotExp
## 6.475e+01 6.297e-05plot(who_src$TotExp, who_src$LifeExp, xlab='TotalExpenditure', ylab='LifeExpectancy', main='scatterplot')
abline(who_src_lm, col='red')
This doesn’t appear to be a good fit because not many observations fall
near the abline which suggests that there is not a good correlation
between life expectancy and total expenditures.
summary(who_src_lm)##
## Call:
## lm(formula = LifeExp ~ TotExp, data = who_src)
##
## Residuals:
## Min 1Q Median 3Q Max
## -24.764 -4.778 3.154 7.116 13.292
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.475e+01 7.535e-01 85.933 < 2e-16 ***
## TotExp 6.297e-05 7.795e-06 8.079 7.71e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.371 on 188 degrees of freedom
## Multiple R-squared: 0.2577, Adjusted R-squared: 0.2537
## F-statistic: 65.26 on 1 and 188 DF, p-value: 7.714e-14The median is high and the range is not consistent around the median. The residual standard error of 9.371 on 188 degrees of freedom seems high suggesting that even countries and their citizens that have a low total expenditure may still have a high life expectancy. This model does not support that thought.
- Raise life expectancy to the 4.6 power (i.e., LifeExp^4.6). Raise total expenditures to the 0.06 power (nearly a log transform, TotExp^.06). Plot LifeExp^4.6 as a function of TotExp^.06, and re-run the simple regression model using the transformed variables. Provide and interpret the F statistics, R^2, standard error, and p-values. Which model is “better?”
LifeExp_2 = who_src$LifeExp^4.6
TotExp_2 = who_src$TotExp^0.06
plot(TotExp_2, LifeExp_2, xlab = 'TotalExpenditure', ylab='LifeExpentancy', main='scatterplot', col=1)
life_tot_lm <- lm(LifeExp_2 ~ TotExp_2)
abline(life_tot_lm, col=2)
(life_tot_lm)##
## Call:
## lm(formula = LifeExp_2 ~ TotExp_2)
##
## Coefficients:
## (Intercept) TotExp_2
## -736527909 620060216Raising the life expectancy and total expenditures makes this regression model a better fit. Notice how the observations now align more closely to the abline.
summary(life_tot_lm)##
## Call:
## lm(formula = LifeExp_2 ~ TotExp_2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -308616089 -53978977 13697187 59139231 211951764
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -736527910 46817945 -15.73 <2e-16 ***
## TotExp_2 620060216 27518940 22.53 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 90490000 on 188 degrees of freedom
## Multiple R-squared: 0.7298, Adjusted R-squared: 0.7283
## F-statistic: 507.7 on 1 and 188 DF, p-value: < 2.2e-16The R-squared of 0.7298 and the ddjusted R-squared of 0.7283 has increased significantly which means that the values explain 73% of the variance. The low p-value still suggests that there is not a correlation between the total expenditures and life expectancy in this model.
- Using the results from 3, forecast life expectancy when TotExp^.06 =1.5. Then forecast life expectancy when TotExp^.06=2.5.
LifeExp_46 = -736527909 + 620060216 * 1.5
(LifeExp_15 = exp(log(LifeExp_46)/4.6))## [1] 63.31153LifeExp_46 = -736527909 + 620060216 * 2.5
(LifeExp_25 = exp(log(LifeExp_46)/4.6))## [1] 86.50645- Build the following multiple regression model and interpret the F Statistics, R^2, standard error, and p-values. How good is the model? LifeExp = b0+b1 x PropMd + b2 x TotExp +b3 x PropMD x TotExp
(prob4_lm <- lm(LifeExp ~ TotExp + PropMD + PropMD * TotExp,data = who_src))##
## Call:
## lm(formula = LifeExp ~ TotExp + PropMD + PropMD * TotExp, data = who_src)
##
## Coefficients:
## (Intercept) TotExp PropMD TotExp:PropMD
## 6.277e+01 7.233e-05 1.497e+03 -6.026e-03summary(prob4_lm)##
## Call:
## lm(formula = LifeExp ~ TotExp + PropMD + PropMD * TotExp, data = who_src)
##
## Residuals:
## Min 1Q Median 3Q Max
## -27.320 -4.132 2.098 6.540 13.074
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.277e+01 7.956e-01 78.899 < 2e-16 ***
## TotExp 7.233e-05 8.982e-06 8.053 9.39e-14 ***
## PropMD 1.497e+03 2.788e+02 5.371 2.32e-07 ***
## TotExp:PropMD -6.026e-03 1.472e-03 -4.093 6.35e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.765 on 186 degrees of freedom
## Multiple R-squared: 0.3574, Adjusted R-squared: 0.3471
## F-statistic: 34.49 on 3 and 186 DF, p-value: < 2.2e-16- Forecast LifeExp when PropMD=.03 and TotExp = 14. Does this forecast seem realistic? Why or why not?
(fcst_lfexp <- 62.8 + (.000072 * 14) + (1497 *.03) + (.006 * 14 * .03))## [1] 107.7135An increase in life expectancy to 108 years doesn’t seem possible even if the expenditures increases and you increase the number of doctors by 3%.