Read in Denver average rent, denver rental trend and denver vacancy rate data

   Col1 Denver.Average.Rents Denver.Rental.Trend Denver.Vacancy.Rate
1  2005                  971                  NA              0.0970
2  2006                  969        -0.002059732              0.0756
3  2007                  950        -0.019607843              0.0840
4  2008                 1016         0.069473684              0.0719
5  2009                 1006        -0.009842520              0.0775
6  2010                  998        -0.007952286              0.0647
7  2011                 1000         0.002004008              0.0510
8  2012                 1019         0.019000000              0.0494
9  2013                 1051         0.031403337              0.0400
10 2014                 1111         0.057088487              0.0397
11 2015                 1226         0.103510351              0.0341
   Denver.GDP...bn. Denver.GDP.Growth Denver.HH.Median.Income
1            134.79        0.08950000                   66625
2            141.19        0.04748127                   64649
3            147.17        0.04235427                   67302
4            154.50        0.04980635                   66430
5            150.09       -0.02854369                   65184
6            155.60        0.03671131                   63848
7            160.97        0.03451157                   62421
8            169.20        0.05112754                   63439
9            177.18        0.04716312                   63861
10           188.17        0.06202732                   66947
11           193.17        0.02657172                   70283
   Median.Income.Trend Annual.Rent.Median.Income WR.Median.Home.Price
1                   NA                 0.1748893                   NA
2         -0.029658537                 0.1798636                   NA
3          0.041036984                 0.1693858               222000
4         -0.012956524                 0.1835315               219000
5         -0.018756586                 0.1851988               215000
6         -0.020495827                 0.1875705               212000
7         -0.022349956                 0.1922430               207000
8          0.016308614                 0.1927521               215000
9          0.006652059                 0.1974914               238000
10         0.048323703                 0.1991426               269000
11         0.049830463                 0.2093252               306000
   WR.Home.Appreciation
1                    NA
2                    NA
3                    NA
4           -0.01351351
5           -0.01826484
6           -0.01395349
7           -0.02358491
8            0.03864734
9            0.10697674
10           0.13025210
11           0.13754647

Provide a summary of the Denver real estate stats

      Col1      Denver.Average.Rents Denver.Rental.Trend
 Min.   :2005   Min.   : 950.0       Min.   :-0.019608  
 1st Qu.:2008   1st Qu.: 984.5       1st Qu.:-0.006479  
 Median :2010   Median :1006.0       Median : 0.010502  
 Mean   :2010   Mean   :1028.8       Mean   : 0.024302  
 3rd Qu.:2012   3rd Qu.:1035.0       3rd Qu.: 0.050667  
 Max.   :2015   Max.   :1226.0       Max.   : 0.103510  
                                     NA's   :1          
 Denver.Vacancy.Rate Denver.GDP...bn. Denver.GDP.Growth 
 Min.   :0.03410     Min.   :134.8    Min.   :-0.02854  
 1st Qu.:0.04470     1st Qu.:148.6    1st Qu.: 0.03561  
 Median :0.06470     Median :155.6    Median : 0.04716  
 Mean   :0.06226     Mean   :161.1    Mean   : 0.04170  
 3rd Qu.:0.07655     3rd Qu.:173.2    3rd Qu.: 0.05047  
 Max.   :0.09700     Max.   :193.2    Max.   : 0.08950  
                                                        
 Denver.HH.Median.Income Median.Income.Trend Annual.Rent.Median.Income
 Min.   :62421           Min.   :-0.029659   Min.   :0.1694           
 1st Qu.:63854           1st Qu.:-0.020061   1st Qu.:0.1817           
 Median :65184           Median :-0.003152   Median :0.1876           
 Mean   :65544           Mean   : 0.005793   Mean   :0.1883           
 3rd Qu.:66786           3rd Qu.: 0.034855   3rd Qu.:0.1951           
 Max.   :70283           Max.   : 0.049830   Max.   :0.2093           
                         NA's   :1                                    
 WR.Median.Home.Price WR.Home.Appreciation
 Min.   :207000       Min.   :-0.02358    
 1st Qu.:215000       1st Qu.:-0.01503    
 Median :219000       Median : 0.01257    
 Mean   :233667       Mean   : 0.04301    
 3rd Qu.:238000       3rd Qu.: 0.11280    
 Max.   :306000       Max.   : 0.13755    
 NA's   :2            NA's   :3

Create standard deviation for each data point

[1] 78.62674
[1] NA
[1] 0.02068382

Create bar charts for each data point

Warning in arrange_impl(.data, dots): '.Random.seed' is not an integer
vector but of type 'NULL', so ignored
Warning: Ignoring 1 observations

Warning: Ignoring 1 observations

Creating scatter plots of rent, rent trends and vacancy rates against nominal GDP and GDP growth 

Warning: Ignoring 1 observations

Warning: Ignoring 1 observations

Summary linear model statistics Denver GDP vs. Rental Trends


Call:
lm(formula = denReData$Denver.GDP...bn. ~ rent.rate, data = denReData)

Residuals:
    Min      1Q  Median      3Q     Max 
-24.166  -2.262   2.895   6.578  13.601 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  163.724      3.846  42.569 1.02e-10 ***
rent.rate    330.776     99.994   3.308   0.0107 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 12.16 on 8 degrees of freedom
  (1 observation deleted due to missingness)
Multiple R-squared:  0.5777,    Adjusted R-squared:  0.5249 
F-statistic: 10.94 on 1 and 8 DF,  p-value: 0.01073

Summary linear model Statistics Denver GDP vs. Vacancy Rates


Call:
lm(formula = denReData$Denver.GDP...bn. ~ vacancy.rate, data = denReData)

Residuals:
   Min     1Q Median     3Q    Max 
-9.870 -3.281  1.744  4.318  7.708 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)   161.094      1.908  84.449 2.32e-14 ***
vacancy.rate -865.250     96.728  -8.945 8.98e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 6.327 on 9 degrees of freedom
Multiple R-squared:  0.8989,    Adjusted R-squared:  0.8877 
F-statistic: 80.02 on 1 and 9 DF,  p-value: 8.975e-06

Creating scatter plots of rent, rent trends and vacancy rates against Denver HHI and Denver Median HHI Trend 

Warning: Ignoring 1 observations

Warning: Ignoring 1 observations
Warning: Ignoring 1 observations
Warning: Ignoring 1 observations

Creating scatter plots of rent, rent trends and vacancy rates against Annual Rent/Median Income Ratio

Warning: Ignoring 1 observations

Summary linear model Statistics Denver Rent/Income Ratio vs. Rental Trends


Call:
lm(formula = denReData$Annual.Rent.Median.Income ~ rent.ratio, 
    data = denReData)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.015100 -0.002825  0.003449  0.004289  0.007026 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 0.189650   0.002594  73.120 1.36e-12 ***
rent.ratio  0.198829   0.067433   2.949   0.0185 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.008202 on 8 degrees of freedom
  (1 observation deleted due to missingness)
Multiple R-squared:  0.5208,    Adjusted R-squared:  0.4609 
F-statistic: 8.694 on 1 and 8 DF,  p-value: 0.01847

Summary linear model Statistics Denver Rent/Income Ratio vs. Rental Trends


Call:
lm(formula = denReData$Annual.Rent.Median.Income ~ vacancy.ratio, 
    data = denReData)

Residuals:
       Min         1Q     Median         3Q        Max 
-0.0076051 -0.0020922 -0.0009143  0.0025989  0.0063525 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)    0.188309   0.001276 147.535  < 2e-16 ***
vacancy.ratio -0.520678   0.064720  -8.045 2.12e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.004233 on 9 degrees of freedom
Multiple R-squared:  0.8779,    Adjusted R-squared:  0.8644 
F-statistic: 64.72 on 1 and 9 DF,  p-value: 2.116e-05

Prediction model for Rental Rate Trends vs. GDP

#creating the training and test data
set.seed(100)
trainingRowIndex1<- sample(1:nrow(denReData), 0.80*nrow(denReData))
trainingData1<- denReData[trainingRowIndex1,]
testDataI<- denReData[-trainingRowIndex1,]

#building the model on the test data
model1<- lm(denReData$Denver.Rental.Trend ~ denReData$Denver.GDP...bn.)
distPred1<- predict(model1, testDataI)
## Warning: 'newdata' had 3 rows but variables found have 11 rows
summary(model1)
## 
## Call:
## lm(formula = denReData$Denver.Rental.Trend ~ denReData$Denver.GDP...bn.)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.018066 -0.016048 -0.012599  0.007268  0.061281 
## 
## Coefficients:
##                              Estimate Std. Error t value Pr(>|t|)  
## (Intercept)                -0.2616281  0.0868875  -3.011   0.0168 *
## denReData$Denver.GDP...bn.  0.0017464  0.0005279   3.308   0.0107 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.02795 on 8 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.5777, Adjusted R-squared:  0.5249 
## F-statistic: 10.94 on 1 and 8 DF,  p-value: 0.01073
#calculating preciction accuracy and error rates
actual_preds1<- data.frame(cbind(actuals=testDataI$Denver.Rental.Trend, predicteds=distPred1))
## Warning in cbind(actuals = testDataI$Denver.Rental.Trend, predicteds =
## distPred1): number of rows of result is not a multiple of vector length
## (arg 1)
corr_accuracy1<- cor(actual_preds1)
head(actual_preds1)
##        actuals   predicteds
## 1 -0.007952286 -0.026228994
## 2  0.002004008 -0.015051945
## 3  0.019000000 -0.004608389
## 4 -0.007952286  0.008192826
## 5  0.002004008  0.000491140
## 6  0.019000000  0.010113881

Prediction model for Vacancy Rate vs. Denver GDP

#creating the training and test data
set.seed(100)
trainingRowIndex2<- sample(1:nrow(denReData), 0.80*nrow(denReData))
trainingData2<- denReData[trainingRowIndex2,]
testData2<- denReData[-trainingRowIndex2,]

#building the model on the test data
model2<- lm(denReData$Denver.Vacancy.Rate ~ denReData$Denver.GDP...bn.)
distPred2<- predict(model2, testData2)
## Warning: 'newdata' had 3 rows but variables found have 11 rows
summary(model2)
## 
## Call:
## lm(formula = denReData$Denver.Vacancy.Rate ~ denReData$Denver.GDP...bn.)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.011392 -0.004997  0.002786  0.005363  0.007410 
## 
## Coefficients:
##                              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                 0.2296215  0.0188256  12.197 6.70e-07 ***
## denReData$Denver.GDP...bn. -0.0010389  0.0001161  -8.945 8.98e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.006933 on 9 degrees of freedom
## Multiple R-squared:  0.8989, Adjusted R-squared:  0.8877 
## F-statistic: 80.02 on 1 and 9 DF,  p-value: 8.975e-06
#calculating preciction accuracy and error rates
actual_preds2<- data.frame(cbind(actuals=testDataI$Denver.Vacancy.Rate, predicteds=distPred2))
## Warning in cbind(actuals = testDataI$Denver.Vacancy.Rate, predicteds =
## distPred2): number of rows of result is not a multiple of vector length
## (arg 1)
corr_accuracy2<- cor(actual_preds2)
head(actual_preds2)
##   actuals predicteds
## 1  0.0647 0.08959010
## 2  0.0510 0.08294123
## 3  0.0494 0.07672870
## 4  0.0647 0.06911367
## 5  0.0510 0.07369515
## 6  0.0494 0.06797089

Prediction model for Rental Rate Trends vs. Denver Rent/Income Ratio

#creating the training and test data
set.seed(100)
trainingRowIndex3<- sample(1:nrow(denReData), 0.80*nrow(denReData))
trainingData3<- denReData[trainingRowIndex3,]
testData3<- denReData[-trainingRowIndex3,]

#building the model on the test data
model3<- lm(denReData$Denver.Rental.Trend ~ denReData$Annual.Rent.Median.Income)
distPred3<- predict(model3, testData3)
## Warning: 'newdata' had 3 rows but variables found have 11 rows
summary(model3)
## 
## Call:
## lm(formula = denReData$Denver.Rental.Trend ~ denReData$Annual.Rent.Median.Income)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.029088 -0.020222 -0.007076  0.008858  0.061199 
## 
## Coefficients:
##                                     Estimate Std. Error t value Pr(>|t|)  
## (Intercept)                          -0.4724     0.1687  -2.800   0.0232 *
## denReData$Annual.Rent.Median.Income   2.6193     0.8883   2.949   0.0185 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.02977 on 8 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.5208, Adjusted R-squared:  0.4609 
## F-statistic: 8.694 on 1 and 8 DF,  p-value: 0.01847
#calculating preciction accuracy and error rates
actual_preds3<- data.frame(cbind(actuals=testDataI$Denver.Rental.Trend, predicteds=distPred3))
## Warning in cbind(actuals = testDataI$Denver.Rental.Trend, predicteds =
## distPred3): number of rows of result is not a multiple of vector length
## (arg 1)
corr_accuracy3<- cor(actual_preds3)
head(actual_preds3)
##        actuals   predicteds
## 1 -0.007952286 -0.014361592
## 2  0.002004008 -0.001332671
## 3  0.019000000 -0.028776856
## 4 -0.007952286  0.008274706
## 5  0.002004008  0.012641768
## 6  0.019000000  0.018853770

Prediction model for Vacancy vs. Denver Rent/Income Ratio

#creating the training and test data
set.seed(100)
trainingRowIndex4<- sample(1:nrow(denReData), 0.80*nrow(denReData))
trainingData4<- denReData[trainingRowIndex4,]
testData4<- denReData[-trainingRowIndex4,]

#building the model on the test data
model4<- lm(denReData$Denver.Vacancy.Rate ~ denReData$Annual.Rent.Median.Income)
distPred4<- predict(model4, testData4)
## Warning: 'newdata' had 3 rows but variables found have 11 rows
summary(model4)
## 
## Call:
## lm(formula = denReData$Denver.Vacancy.Rate ~ denReData$Annual.Rent.Median.Income)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -0.0101695 -0.0050005 -0.0009028  0.0044273  0.0121101 
## 
## Coefficients:
##                                     Estimate Std. Error t value Pr(>|t|)
## (Intercept)                          0.37977    0.03953   9.606 4.99e-06
## denReData$Annual.Rent.Median.Income -1.68611    0.20958  -8.045 2.12e-05
##                                        
## (Intercept)                         ***
## denReData$Annual.Rent.Median.Income ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.007618 on 9 degrees of freedom
## Multiple R-squared:  0.8779, Adjusted R-squared:  0.8644 
## F-statistic: 64.72 on 1 and 9 DF,  p-value: 2.116e-05
#calculating preciction accuracy and error rates
actual_preds4<- data.frame(cbind(actuals=testDataI$Denver.Vacancy.Rate, predicteds=distPred4))
## Warning in cbind(actuals = testDataI$Denver.Vacancy.Rate, predicteds =
## distPred4): number of rows of result is not a multiple of vector length
## (arg 1)
corr_accuracy4<- cor(actual_preds4)
head(actual_preds4)
##   actuals predicteds
## 1  0.0647 0.08488994
## 2  0.0510 0.07650277
## 3  0.0494 0.09416955
## 4  0.0647 0.07031817
## 5  0.0510 0.06750694
## 6  0.0494 0.06350806

Arima based model for rental rates

Arima based model for vacancy rates