Question 2 A survey of the commercial activities was conducted for five zones in
ID: 3042109 • Letter: Q
Question
Question 2 A survey of the commercial activities was conducted for five zones in an analysis area The data were collected based on three types of employment, namely manufacturing, retail and service, and others The resulted zonal employment of three dfferent commercial types and their respective trip attractions are listed in the following table Zonal Employment Trip Attraction ZoneManuf. Ret&Ser; Others Total X2 X3 X X1 6820 2547 115 9482 9428 1899 0 2010 2192 87 259 574 330 127 0 127153 813 29 3836 3948 228 2729 a) Determine a single linear regression equation between dependent variable Y and each of between dependent variable Y and independent the constants and coefficients of variables and coefficients of correlation derived from 1-6 independent varables XX.x.2 ad X3. hes of Exe manual calculation is acceptable.) Determine a multiple linear regression equation variables X1, X2, and X3. (The use of Excel or a similar tool is suggested.) l b) a) and b) into a single table. Select the equations that might be acceptable for use in trip generation and give the reasons.Explanation / Answer
using R
x1 <- c( 6820,111,228,0,2729)
x2 <- c(2547 , 1899 , 87 , 127 , 813)
x3 <- c( 115,0,259,0,294)
> x <- c(9482,2010,574,127,1836)
> model <- lm (y~x)
> summary(model)
Call:
lm(formula = y ~ x)
Residuals:
1 2 3 4 5
1.624 -13.327 4.721 2.425 4.557
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.6594628 5.0592008 1.119 0.345
x -0.0006627 0.0011447 -0.579 0.603
Residual standard error: 8.741 on 3 degrees of freedom
Multiple R-squared: 0.1005, Adjusted R-squared: -0.1993
F-statistic: 0.3352 on 1 and 3 DF, p-value: 0.6032
model1 <- lm (y~x1)
> summary(model1)
Call:
lm(formula = y ~ x1)
Residuals:
1 2 3 4 5
-2.110 -13.066 5.951 3.918 5.307
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.0818353 5.1526688 0.792 0.486
x1 -0.0001425 0.0015676 -0.091 0.933
Residual standard error: 9.203 on 3 degrees of freedom
Multiple R-squared: 0.002748, Adjusted R-squared: -0.3297
F-statistic: 0.008265 on 1 and 3 DF, p-value: 0.9333
model2 <- lm (y~x2)
> summary(model2)
Call:
lm(formula = y ~ x2)
Residuals:
1 2 3 4 5
5.1300 -8.4080 0.6986 -1.0830 3.6625
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 9.776418 4.101619 2.384 0.0973 .
x2 -0.005460 0.002794 -1.954 0.1456
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 6.112 on 3 degrees of freedom
Multiple R-squared: 0.5601, Adjusted R-squared: 0.4135
F-statistic: 3.82 on 1 and 3 DF, p-value: 0.1456
model3 <- lm (y~x3)
> summary(model3)
Call:
lm(formula = y ~ x3)
Residuals:
1 2 3 4 5
-2.1250 -7.9513 1.6489 9.0487 -0.6214
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1.04873 4.68043 -0.224 0.837
x3 0.03629 0.02563 1.416 0.252
Residual standard error: 7.135 on 3 degrees of freedom
Multiple R-squared: 0.4006, Adjusted R-squared: 0.2008
F-statistic: 2.005 on 1 and 3 DF, p-value: 0.2517
b)
model_mult <- lm (y~x1+x2+x3)
> summary(model_mult)
Call:
lm(formula = y ~ x1 + x2 + x3)
Residuals:
1 2 3 4 5
-0.004109 0.001059 -0.010807 0.002729 0.011128
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 9.234e+00 1.731e-02 533.62 0.001193 **
x1 2.360e-03 4.813e-06 490.38 0.001298 **
x2 -9.741e-03 1.323e-05 -736.43 0.000864 ***
x3 4.192e-03 7.572e-05 55.37 0.011497 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.01631 on 1 degrees of freedom
Multiple R-squared: 1, Adjusted R-squared: 1
F-statistic: 3.192e+05 on 3 and 1 DF, p-value: 0.001301
c) make table yourself ,
all results are given.
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