Summary of model returning NA - r

Question

I'm new to r and not sure how fix the error I'm getting.
Here is the summary of my data:
> summary(data)
Metro MrktRgn MedAge numHmSales
Abilene : 1 Austin-Waco-Hill Country : 6 20-25: 3 Min. : 302
Amarillo : 1 Far West Texas : 1 25-30: 6 1st Qu.: 1057
Arlington: 1 Gulf Coast - Brazos Bottom:10 30-35:28 Median : 2098
Austin : 1 Northeast Texas :14 35-40: 6 Mean : 7278
Bay Area : 1 Panhandle and South Plains: 5 45-50: 2 3rd Qu.: 5086
Beaumont : 1 South Texas : 7 50-55: 1 Max. :83174
(Other) :40 West Texas : 3
AvgSlPr totNumLs MedHHInc Pop
Min. :123833 Min. : 1257 Min. :37300 Min. : 2899
1st Qu.:149117 1st Qu.: 6028 1st Qu.:53100 1st Qu.: 56876
Median :171667 Median : 11106 Median :57000 Median : 126482
Mean :188637 Mean : 24302 Mean :60478 Mean : 296529
3rd Qu.:215175 3rd Qu.: 25472 3rd Qu.:66200 3rd Qu.: 299321
Max. :303475 Max. :224230 Max. :99205 Max. :2196000
NA's :1
then I make a model with AvSlPr as the y variable and other the other variables as x variables
> model1 = lm(AvgSlPr ~ Metro + MrktRgn + MedAge + numHmSales + totNumLs + MedHHInc + Pop)
but when I do a summary of the model, I get NA for the Std. Error, t value, and t p-values.
> summary(model1)
Call:
lm(formula = AvgSlPr ~ Metro + MrktRgn + MedAge + numHmSales +
totNumLs + MedHHInc + Pop)
Residuals:
ALL 45 residuals are 0: no residual degrees of freedom!
Coefficients: (15 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
(Intercept) 143175 NA NA NA
MetroAmarillo 24925 NA NA NA
MetroArlington 35258 NA NA NA
MetroAustin 160300 NA NA NA
MetroBay Area 68642 NA NA NA
MetroBeaumont 5942 NA NA NA
...
MrktRgnWest Texas NA NA NA NA
MedAge25-30 NA NA NA NA
MedAge30-35 NA NA NA NA
MedAge35-40 NA NA NA NA
MedAge45-50 NA NA NA NA
MedAge50-55 NA NA NA NA
numHmSales NA NA NA NA
totNumLs NA NA NA NA
MedHHInc NA NA NA NA
Pop NA NA NA NA
Residual standard error: NaN on 0 degrees of freedom
(1 observation deleted due to missingness)
Multiple R-squared: 1, Adjusted R-squared: NaN
F-statistic: NaN on 44 and 0 DF, p-value: NA
Does anyone know whats going wrong and how I can fix this? Also, I'm not supposed to be using dummy variables.

Answer 1

Your Metro variable always refers to a single line for each factor level. You need at least two points to fit a line. Let me demonstrate with an example:
dat = data.frame(AvgSlPr=runif(4), Metro = factor(LETTERS[1:4]), MrktRgn = runif(4))
model1 = lm(AvgSlPr ~ Metro + MrktRgn, data = dat)
summary(model1)
#Call:
#lm(formula = AvgSlPr ~ Metro + MrktRgn, data = dat)
#Residuals:
#ALL 4 residuals are 0: no residual degrees of freedom!
#Coefficients: (1 not defined because of singularities)
# Estimate Std. Error t value Pr(>|t|)
#(Intercept) 0.33801 NA NA NA
#MetroB 0.47350 NA NA NA
#MetroC -0.04118 NA NA NA
#MetroD 0.20047 NA NA NA
#MrktRgn NA NA NA NA
#Residual standard error: NaN on 0 degrees of freedom
#Multiple R-squared: 1, Adjusted R-squared: NaN
#F-statistic: NaN on 3 and 0 DF, p-value: NA
But if we add more data so that at least some of the factor levels have more than one row of data, the linear model can be calculated:
dat = rbind(dat, data.frame(AvgSlPr=2:4, Metro=factor(LETTERS[2:4]), MrktRgn = 3:5))
model2 = lm(AvgSlPr ~ Metro + MrktRgn, data=dat)
summary(model2)
#Call:
#lm(formula = AvgSlPr ~ Metro + MrktRgn, data = dat)
#Residuals:
# 1 2 3 4 5 6 7
# 9.021e-17 2.643e-01 7.304e-03 -1.498e-01 -2.643e-01 -7.304e-03 1.498e-01
#Coefficients:
# Estimate Std. Error t value Pr(>|t|)
#(Intercept) 0.24279 0.30406 0.798 0.50834
#MetroB -0.10207 0.38858 -0.263 0.81739
#MetroC -0.06696 0.39471 -0.170 0.88090
#MetroD 0.06804 0.41243 0.165 0.88413
#MrktRgn 0.70787 0.06747 10.491 0.00896 **
#---
#Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#Residual standard error: 0.3039 on 2 degrees of freedom
#Multiple R-squared: 0.9857, Adjusted R-squared: 0.9571
#F-statistic: 34.45 on 4 and 2 DF, p-value: 0.02841
The data used to fit the model need be re-thought. What is the goal of the analysis? What data are needed to achieve the goal?