Question

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 different commercial types and their respective trip attractions are listed in the following table.

Zonal Employment

Trip Attraction Zone Manuf. Ret&Ser Others Total X1 X2 X3 X Y 1 6820 2547 115 9482 9428 2 111 1899 0 2010 2192 3 228 87 259 574 330 4 0 127 0 127 153 5 2729 813 294 3836 3948

a) Determine a single linear regression equation between dependent variable Y and each of independent variables X, X1, X2, and X3. (The use of Excel or a similar tool is suggested, but the manual calculation is acceptable.) b) Determine a multiple linear regression equation between dependent variable Y and independent variables X1, X2, and X3. (The use of Excel or a similar tool is suggested.) c) Summarize the constants and coefficients of variables and coefficients of correlation derived from a) and b) into a single table. Select the equations that might be acceptable for use in trip generation and give the reasons

Answer 1

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.