Fikri Dwi Alpian - 120450022 - RB
Input dataset
library(readxl)## Warning: package 'readxl' was built under R version 4.2.2df = read_excel("C:/Users/Acer A514-53/Downloads/model linear.xlsx")# Linear Model
models1 <- lm(`population` ~ Time, data = df)
summary(models1)##
## Call:
## lm(formula = population ~ Time, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.20045 -0.50442 -0.01285 0.59852 1.30369
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 201.97274 0.27173 743.3 <2e-16 ***
## Time 2.32849 0.01531 152.1 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7256 on 28 degrees of freedom
## Multiple R-squared: 0.9988, Adjusted R-squared: 0.9987
## F-statistic: 2.314e+04 on 1 and 28 DF, p-value: < 2.2e-16models1##
## Call:
## lm(formula = population ~ Time, data = df)
##
## Coefficients:
## (Intercept) Time
## 201.973 2.328# Yt= 201.972 + 2.328 t
# r^2 = 0.9988Modelnya Yt = 201.972 + 2.328 t r-squared = 0.9988
# Log Linear Model
models2 <- lm(log(`population`) ~ Time, data = df)
summary(models2)##
## Call:
## lm(formula = log(population) ~ Time, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.0035723 -0.0007549 -0.0002391 0.0008144 0.0033002
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.317e+00 6.084e-04 8739 <2e-16 ***
## Time 9.801e-03 3.427e-05 286 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.001625 on 28 degrees of freedom
## Multiple R-squared: 0.9997, Adjusted R-squared: 0.9996
## F-statistic: 8.179e+04 on 1 and 28 DF, p-value: < 2.2e-16models2##
## Call:
## lm(formula = log(population) ~ Time, data = df)
##
## Coefficients:
## (Intercept) Time
## 5.317035 0.009801# ln Yt = 5.3170 + 0.0098t
# r^2 = 0.9997Modelnya Yt = 5.3170 + 0.0098t r-squared = 0.9997
# Logistik Growth Model
models3 <- nls(`population` ~ SSlogis(Time, phi1, phi2, phi3), data = df)
summary(models3)##
## Formula: population ~ SSlogis(Time, phi1, phi2, phi3)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## phi1 1574.951 635.529 2.478 0.0198 *
## phi2 165.300 52.016 3.178 0.0037 **
## phi3 86.638 6.263 13.833 8.99e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3537 on 27 degrees of freedom
##
## Number of iterations to convergence: 0
## Achieved convergence tolerance: 3.658e-06models3## Nonlinear regression model
## model: population ~ SSlogis(Time, phi1, phi2, phi3)
## data: df
## phi1 phi2 phi3
## 1574.95 165.30 86.64
## residual sum-of-squares: 3.378
##
## Number of iterations to convergence: 0
## Achieved convergence tolerance: 3.658e-06# Yt = 1574.95 / (1+3.658e-6)Modelnya Yt = 1574.95 / (1+3.658e-6)
Input dataset
df2 = read_excel("C:/Users/Acer A514-53/Downloads/14.9modellinear.xlsx")model <- lm(log(GDP) ~ log(Labor) + log(Capital), data=df2)
summary(model)##
## Call:
## lm(formula = log(GDP) ~ log(Labor) + log(Capital), data = df2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.057144 -0.016249 -0.005791 0.023511 0.038740
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.65242 0.60620 -2.726 0.0144 *
## log(Labor) 0.33973 0.18569 1.830 0.0849 .
## log(Capital) 0.84600 0.09335 9.062 6.42e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02829 on 17 degrees of freedom
## Multiple R-squared: 0.9951, Adjusted R-squared: 0.9945
## F-statistic: 1719 on 2 and 17 DF, p-value: < 2.2e-16model##
## Call:
## lm(formula = log(GDP) ~ log(Labor) + log(Capital), data = df2)
##
## Coefficients:
## (Intercept) log(Labor) log(Capital)
## -1.6524 0.3397 0.8460# Modelnya
# ln GDP = -1.6524 + 0.3397 ln Labor + 0.8460 ln Capital
# R-Squared = 0.9951ln GDP = -1.6524 + 0.3397 ln Labor + 0.8460 ln R-Squared = 0.9951
# 14.1.4
# Cobb-Douglass (C-D) Function multiplicative error
models = nls(GDP ~ A*Labor + Capital*(1-a),
data=df2, start = list(A = 1, a = 0.5))
a = coef(models)
summary(models) # A=1.12328, a=0.39346, 1-a=0.60654##
## Formula: GDP ~ A * Labor + Capital * (1 - a)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## A 1.12328 0.72784 1.543 0.14
## a 0.39346 0.02274 17.301 1.16e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6771 on 18 degrees of freedom
##
## Number of iterations to convergence: 1
## Achieved convergence tolerance: 1.647e-07A=1.12328, a=0.39346, 1-a=0.60654
# 14.1.2
# Cobb-Douglass (C-D) Function additive error
models = nls(GDP ~ A*Labor**a*Capital**(1-a),
data=df2, start = list(A = 1, a = 0.5))
b = coef(models)
summary(models) # A=0.80529, a=0.06520, 1-a=0.9384##
## Formula: GDP ~ A * Labor^a * Capital^(1 - a)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## A 0.80529 0.09891 8.142 1.91e-07 ***
## a 0.06520 0.03509 1.858 0.0796 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6592 on 18 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.558e-06A=0.80529, a=0.06520, 1-a=0.9384