Paper II - Homeownership
Candace Jennings
2024-01-15
Black Homeownership in Historical Context
r = getOption("repos")
r["CRAN"] = "http://cran.us.r-project.org"
options(repos = r)
install.packages("tidyverse")## Installing package into 'C:/Users/canda/AppData/Local/R/win-library/4.3'
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## C:\Users\canda\AppData\Local\Temp\RtmpqubneP\downloaded_packageslibrary(ggplot2)## Warning: package 'ggplot2' was built under R version 4.3.2library(stats)
library(car)## Loading required package: carDatalibrary(dplyr)##
## Attaching package: 'dplyr'## The following object is masked from 'package:car':
##
## recode## The following objects are masked from 'package:stats':
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## filter, lag## The following objects are masked from 'package:base':
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## intersect, setdiff, setequal, unionlibrary(stargazer)##
## Please cite as:## Hlavac, Marek (2022). stargazer: Well-Formatted Regression and Summary Statistics Tables.## R package version 5.2.3. https://CRAN.R-project.org/package=stargazerlibrary(lavaan)## Warning: package 'lavaan' was built under R version 4.3.2## This is lavaan 0.6-17
## lavaan is FREE software! Please report any bugs.cities <- read.csv('C:/Users/canda/DEM Dissertation Data/citiesALLYRS.csv', na.strings=c("NA"))
cities <- cities %>% mutate_if(is.character, as.numeric)## Warning: There were 25 warnings in `mutate()`.
## The first warning was:
## ℹ In argument: `cityname = .Primitive("as.double")(cityname)`.
## Caused by warning:
## ! NAs introduced by coercion
## ℹ Run `dplyr::last_dplyr_warnings()` to see the 24 remaining warnings.cities$Proximity<-as.factor(ifelse(cities$Proximity==1, "In Proximity", "Not in Prox"))stargazer(cities, header=FALSE, type='text', title="Descriptive Statistics",digits=2, out="Descript.htm")##
## Descriptive Statistics
## ===================================================
## Statistic N Mean St. Dev. Min Max
## ---------------------------------------------------
## Miles 114 6.50 5.53 0.00 21.00
## gini_20 262 0.42 0.05 0.29 0.54
## gini_10 264 0.42 0.06 0.26 0.57
## pboo_20 262 8.42 10.61 0.00 67.12
## pboo_10 240 8.58 11.03 0.05 65.63
## pboo_00 256 7.07 9.08 0.00 61.00
## pboo_90 257 6.45 8.59 0.00 60.64
## pboo_80 241 5.32 7.07 0.00 33.94
## chg_t20 235 10,355.00 24,403.75 -3,487 205,129
## chg_pb20 235 1.08 2.36 -8.59 15.95
## t_20 261 75,666.40 207,759.00 10,070 2,304,580
## pb_20 261 12.15 11.86 0.03 71.27
## dbw_20 261 25.38 12.07 0.00 69.14
## chg_t10 204 12,128.63 26,631.64 -9,504 206,512
## chg_pb10 204 1.36 3.65 -8.32 23.16
## t_10 240 70,884.63 194,929.20 10,127 2,099,451
## pb_10 240 11.39 12.10 0.03 69.35
## dbw_10 240 27.19 14.07 0.00 82.22
## chg_t00 174 13,749.87 36,706.30 -2,072 323,078
## chg_pb00 174 1.23 3.85 -5.08 25.02
## t_00 204 68,784.74 190,685.10 10,302 1,953,631
## pb_00 204 10.19 10.99 0.03 57.26
## dbw_00 204 30.84 15.98 0.00 75.64
## chg_t90 153 9,878.79 22,303.25 -4,247 150,053
## chg_pb90 153 1.49 4.02 -5.08 24.12
## t_90 180 62,714.99 167,886.90 10,023 1,630,553
## pb_90 180 9.46 10.45 0.00 60.56
## dbw_90 180 34.40 18.49 0.00 80.76
## t_80 154 60,676.74 165,936.10 10,197 1,595,138
## pb_80 154 8.62 9.85 0.01 40.12
## dbw_80 154 43.36 22.13 0.00 93.17
## ---------------------------------------------------stargazer(cities[c("pboo_20","t_20","pb_20","chg_t20","chg_pb20")], header=FALSE, type='text',
title="Descriptive Statistics 2020", digits=2,
covariate.labels=c("Black Homeownership","City Population","Percent Black Population","Change in City Population","Change in Percent Black Population"),
out="Descriptive Homeowner 2020.htm"
)##
## Descriptive Statistics 2020
## ============================================================================
## Statistic N Mean St. Dev. Min Max
## ----------------------------------------------------------------------------
## Black Homeownership 262 8.42 10.61 0.00 67.12
## City Population 261 75,666.40 207,759.00 10,070 2,304,580
## Percent Black Population 261 12.15 11.86 0.03 71.27
## Change in City Population 235 10,355.00 24,403.75 -3,487 205,129
## Change in Percent Black Population 235 1.08 2.36 -8.59 15.95
## ----------------------------------------------------------------------------table(cities$Proximity)##
## In Proximity Not in Prox
## 107 162install.packages("ggcorrplot")## Installing package into 'C:/Users/canda/AppData/Local/R/win-library/4.3'
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## C:\Users\canda\AppData\Local\Temp\RtmpqubneP\downloaded_packageslibrary(ggcorrplot)## Warning: package 'ggcorrplot' was built under R version 4.3.2library(ggplot2)#Change proximity to numeric to run correlation matrix
cities <- cities %>% mutate_if(is.character, as.numeric)
cities <- cities %>% mutate_if(is.integer, as.numeric)
cities <- cities %>% mutate_if(is.factor, as.numeric)
cities$t_20 <- log(cities$t_20)
cor_matrix <- cor(cities, use = "pairwise.complete.obs", method = "pearson") %>%
ggcorrplot(show.diag=FALSE, type="lower", lab=TRUE, lab_size=2)
print(cor_matrix)
df <- data.frame(cities)
sel20_vars <- c("pboo_20", "t_20","pb_20", "chg_t20","chg_pb20")
df_select20 <- df[sel20_vars]
cor_matrix20 <- cor(df_select20, use = "pairwise.complete.obs", method = "pearson") %>%
ggcorrplot(show.diag=FALSE, type="lower", lab=TRUE, lab_size=4)
print(cor_matrix20)
#Run regression with Logged Total population on Percent Black homeownership. No signifigance for any year.
tpop20<- lm(cities$pboo_20 ~ log(cities$t_20))
summary(tpop20)##
## Call:
## lm(formula = cities$pboo_20 ~ log(cities$t_20))
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.270 -6.448 -4.056 3.111 58.063
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -17.554 16.467 -1.066 0.287
## log(cities$t_20) 11.125 7.038 1.581 0.115
##
## Residual standard error: 10.58 on 259 degrees of freedom
## (8 observations deleted due to missingness)
## Multiple R-squared: 0.009556, Adjusted R-squared: 0.005732
## F-statistic: 2.499 on 1 and 259 DF, p-value: 0.1152coef(tpop20)["log(cities$t_20)"]/100## log(cities$t_20)
## 0.111247tpop10<- lm(cities$pboo_10 ~ log(cities$t_10))
summary(tpop10)##
## Call:
## lm(formula = cities$pboo_10 ~ log(cities$t_10))
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.303 -6.725 -4.234 3.273 56.897
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.7654 7.3455 -0.240 0.810
## log(cities$t_10) 0.9997 0.7066 1.415 0.158
##
## Residual standard error: 11.01 on 238 degrees of freedom
## (29 observations deleted due to missingness)
## Multiple R-squared: 0.00834, Adjusted R-squared: 0.004173
## F-statistic: 2.002 on 1 and 238 DF, p-value: 0.1584coef(tpop10)["log(cities$t_10)"]/100## log(cities$t_10)
## 0.00999737tpop00<- lm(cities$pboo_00 ~ log(cities$t_00))
summary(tpop00)##
## Call:
## lm(formula = cities$pboo_00 ~ log(cities$t_00))
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.365 -6.078 -3.391 2.804 54.268
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.4256 7.0160 -0.488 0.626
## log(cities$t_00) 1.0728 0.6756 1.588 0.114
##
## Residual standard error: 9.392 on 198 degrees of freedom
## (69 observations deleted due to missingness)
## Multiple R-squared: 0.01257, Adjusted R-squared: 0.007586
## F-statistic: 2.521 on 1 and 198 DF, p-value: 0.1139coef(tpop00)["log(cities$t_00)"]/100## log(cities$t_00)
## 0.01072754tpop90<- lm(cities$pboo_90 ~ log(cities$t_90))
summary(tpop90)##
## Call:
## lm(formula = cities$pboo_90 ~ log(cities$t_90))
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.420 -6.262 -3.160 4.192 54.227
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.5214 7.3197 -0.754 0.4517
## log(cities$t_90) 1.2766 0.7115 1.794 0.0745 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.218 on 177 degrees of freedom
## (90 observations deleted due to missingness)
## Multiple R-squared: 0.01787, Adjusted R-squared: 0.01232
## F-statistic: 3.22 on 1 and 177 DF, p-value: 0.07446coef(tpop90)["log(cities$t_90)"]/100## log(cities$t_90)
## 0.01276642tpop80<- lm(cities$pboo_80 ~ log(cities$t_80))
summary(tpop80)##
## Call:
## lm(formula = cities$pboo_80 ~ log(cities$t_80))
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.515 -5.458 -2.950 4.121 28.452
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7.3996 6.5234 -1.134 0.2584
## log(cities$t_80) 1.3760 0.6371 2.160 0.0324 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.697 on 152 degrees of freedom
## (115 observations deleted due to missingness)
## Multiple R-squared: 0.02978, Adjusted R-squared: 0.02339
## F-statistic: 4.665 on 1 and 152 DF, p-value: 0.03236coef(tpop80)["log(cities$t_80)"]/100## log(cities$t_80)
## 0.01376022#Run regression with Logged Total population on Percent Black population. Slight signifigance in 2020 and 1980.
tpop20B<- lm(cities$pb_20 ~ log(cities$t_20))
summary(tpop20B)##
## Call:
## lm(formula = cities$pb_20 ~ log(cities$t_20))
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.354 -8.050 -3.541 5.225 58.074
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -33.034 18.265 -1.809 0.0717 .
## log(cities$t_20) 19.325 7.806 2.476 0.0139 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.74 on 259 degrees of freedom
## (8 observations deleted due to missingness)
## Multiple R-squared: 0.02312, Adjusted R-squared: 0.01935
## F-statistic: 6.129 on 1 and 259 DF, p-value: 0.01394coef(tpop20B)["log(cities$t_20)"]/100## log(cities$t_20)
## 0.1932485tpop10B<- lm(cities$pb_10 ~ log(cities$t_10))
summary(tpop10B)##
## Call:
## lm(formula = cities$pb_10 ~ log(cities$t_10))
##
## Residuals:
## Min 1Q Median 3Q Max
## -14.032 -7.937 -4.269 4.124 57.746
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.2881 8.0375 -0.409 0.6828
## log(cities$t_10) 1.4183 0.7732 1.834 0.0679 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.05 on 238 degrees of freedom
## (29 observations deleted due to missingness)
## Multiple R-squared: 0.01394, Adjusted R-squared: 0.009798
## F-statistic: 3.365 on 1 and 238 DF, p-value: 0.06785coef(tpop10B)["log(cities$t_10)"]/100## log(cities$t_10)
## 0.01418331tpop00B<- lm(cities$pb_00 ~ log(cities$t_00))
summary(tpop00B)##
## Call:
## lm(formula = cities$pb_00 ~ log(cities$t_00))
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.563 -7.499 -4.037 4.522 48.296
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.7408 8.0813 -0.587 0.5581
## log(cities$t_00) 1.4469 0.7795 1.856 0.0649 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.93 on 202 degrees of freedom
## (65 observations deleted due to missingness)
## Multiple R-squared: 0.01677, Adjusted R-squared: 0.0119
## F-statistic: 3.445 on 1 and 202 DF, p-value: 0.06489coef(tpop00B)["log(cities$t_00)"]/100## log(cities$t_00)
## 0.01446904tpop90B<- lm(cities$pb_90 ~ log(cities$t_90))
summary(tpop90B)##
## Call:
## lm(formula = cities$pb_90 ~ log(cities$t_90))
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.606 -7.087 -4.198 3.658 52.431
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.7914 8.2396 -0.703 0.4831
## log(cities$t_90) 1.4886 0.8007 1.859 0.0647 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.38 on 178 degrees of freedom
## (89 observations deleted due to missingness)
## Multiple R-squared: 0.01905, Adjusted R-squared: 0.01354
## F-statistic: 3.457 on 1 and 178 DF, p-value: 0.06465coef(tpop90B)["log(cities$t_90)"]/100## log(cities$t_90)
## 0.01488605tpop80B<- lm(cities$pb_80 ~ log(cities$t_80))
summary(tpop80B)##
## Call:
## lm(formula = cities$pb_80 ~ log(cities$t_80))
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.915 -6.934 -4.312 5.507 29.895
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -11.0056 8.2193 -1.339 0.1826
## log(cities$t_80) 1.9256 0.8027 2.399 0.0177 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.698 on 152 degrees of freedom
## (115 observations deleted due to missingness)
## Multiple R-squared: 0.03648, Adjusted R-squared: 0.03014
## F-statistic: 5.754 on 1 and 152 DF, p-value: 0.01766coef(tpop80B)["log(cities$t_80)"]/100## log(cities$t_80)
## 0.01925604#Run regression with Logged Total population on Proximity. Some signifigance for all years except 2010.
#change proximity back to factor variable
cities$Proximity<-as.factor(ifelse(cities$Proximity==1, "In Proximity", "Not in Prox"))
str(cities)## 'data.frame': 269 obs. of 34 variables:
## $ cityname : num NA NA NA NA NA NA NA NA NA NA ...
## $ Proximity: Factor w/ 2 levels "In Proximity",..: 2 1 2 2 2 2 1 2 2 2 ...
## $ Miles : num NA 3 NA NA NA NA 13.7 NA NA NA ...
## $ FC.name : num NA NA NA NA NA NA NA NA NA NA ...
## $ gini_20 : num 0.45 0.395 0.461 0.423 0.471 0.39 0.456 0.417 0.469 0.44 ...
## $ gini_10 : num 0.45 0.475 0.42 0.411 0.456 0.358 0.424 0.436 0.457 0.523 ...
## $ pboo_20 : num 4.74 4.08 0.26 3.13 0.65 6.5 0.13 2.73 3.56 1.08 ...
## $ pboo_10 : num 4.73 2.53 0.19 3.31 0.57 7.01 0.19 1.49 3.69 1.53 ...
## $ pboo_00 : num 4.68 1.73 0 4.42 0.48 3.58 0 1.15 3.76 2.69 ...
## $ pboo_90 : num 5.34 6.51 0 2.63 0.72 2.68 0 0.9 4.06 2.46 ...
## $ pboo_80 : num 4.36 4.23 0 0.21 0.97 2.14 0 1.03 3.77 2.13 ...
## $ chg_t20 : num 8119 3605 1140 130 -1213 ...
## $ chg_pb20 : num 1.34343 5.30048 0.00392 -0.40411 0.14071 ...
## $ t_20 : num 11.74 9.72 9.88 9.68 9.79 ...
## $ pb_20 : num 11.36 17.364 0.2 2.406 0.732 ...
## $ dbw_20 : num 28.7 25 35.3 32.8 38.2 ...
## $ chg_t10 : num 1133 -1110 3593 1890 94 ...
## $ chg_pb10 : num 0.925 2.265 0.081 -2.991 -0.15 ...
## $ t_10 : num 117063 13056 18353 15869 19104 ...
## $ pb_10 : num 10.017 12.063 0.196 2.811 0.591 ...
## $ dbw_10 : num 34.8 21.4 55.3 36 27.6 ...
## $ chg_t00 : num 9276 NA NA 2846 -778 ...
## $ chg_pb00 : num 2.2753 NA NA 2.1368 -0.0416 ...
## $ t_00 : num 115930 14166 14760 13979 19010 ...
## $ pb_00 : num 9.092 9.798 0.115 5.802 0.742 ...
## $ dbw_00 : num 37.7 38.8 23.4 28.7 27.4 ...
## $ chg_t90 : num 8339 NA NA -1490 -1173 ...
## $ chg_pb90 : num 0.2325 NA NA 1.5337 -0.0707 ...
## $ t_90 : num 106654 NA NA 11133 19788 ...
## $ pb_90 : num 6.816 NA NA 3.665 0.783 ...
## $ dbw_90 : num 38.1 NA NA 24.7 41.2 ...
## $ t_80 : num 98315 NA NA 12623 20961 ...
## $ pb_80 : num 6.584 NA NA 2.131 0.854 ...
## $ dbw_80 : num 48.2 NA NA 29.9 52.6 ...Make “Not in Proximity” the reference category
cities$Proximity <- relevel(cities$Proximity, ref = "Not in Prox")
table(cities$Proximity)##
## Not in Prox In Proximity
## 162 107tpop20Bx<- lm(as.numeric(cities$Proximity) ~ log(cities$t_20))
summary(tpop20Bx)##
## Call:
## lm(formula = as.numeric(cities$Proximity) ~ log(cities$t_20))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.5487 -0.3861 -0.3336 0.5907 0.6832
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.07095 0.75527 -0.094 0.9252
## log(cities$t_20) 0.62357 0.32278 1.932 0.0545 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4854 on 259 degrees of freedom
## (8 observations deleted due to missingness)
## Multiple R-squared: 0.01421, Adjusted R-squared: 0.0104
## F-statistic: 3.732 on 1 and 259 DF, p-value: 0.05447coef(tpop20Bx)["log(cities$t_20)"]/100## log(cities$t_20)
## 0.006235658tpop10Bx<- lm(as.numeric(cities$Proximity) ~ log(cities$t_10))
summary(tpop10Bx)##
## Call:
## lm(formula = as.numeric(cities$Proximity) ~ log(cities$t_10))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.5452 -0.4012 -0.3668 0.5838 0.6422
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.94206 0.32796 2.872 0.00444 **
## log(cities$t_10) 0.04507 0.03155 1.428 0.15448
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4915 on 238 degrees of freedom
## (29 observations deleted due to missingness)
## Multiple R-squared: 0.0085, Adjusted R-squared: 0.004334
## F-statistic: 2.04 on 1 and 238 DF, p-value: 0.1545coef(tpop10Bx)["log(cities$t_10)"]/100## log(cities$t_10)
## 0.0004506704tpop00Bx<- lm(as.numeric(cities$Proximity) ~ log(cities$t_00))
summary(tpop00Bx)##
## Call:
## lm(formula = as.numeric(cities$Proximity) ~ log(cities$t_00))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.6068 -0.3868 -0.3355 0.5879 0.6796
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.65621 0.35988 1.823 0.0697 .
## log(cities$t_00) 0.07179 0.03471 2.068 0.0399 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4866 on 202 degrees of freedom
## (65 observations deleted due to missingness)
## Multiple R-squared: 0.02073, Adjusted R-squared: 0.01588
## F-statistic: 4.276 on 1 and 202 DF, p-value: 0.03992coef(tpop00Bx)["log(cities$t_00)"]/100## log(cities$t_00)
## 0.0007178517tpop90Bx<- lm(as.numeric(cities$Proximity) ~ log(cities$t_90))
summary(tpop90Bx)##
## Call:
## lm(formula = as.numeric(cities$Proximity) ~ log(cities$t_90))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.6849 -0.3635 -0.3050 0.5875 0.7163
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.34578 0.38110 0.907 0.36547
## log(cities$t_90) 0.10181 0.03703 2.749 0.00659 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4801 on 178 degrees of freedom
## (89 observations deleted due to missingness)
## Multiple R-squared: 0.04073, Adjusted R-squared: 0.03534
## F-statistic: 7.559 on 1 and 178 DF, p-value: 0.006589coef(tpop90Bx)["log(cities$t_90)"]/100## log(cities$t_90)
## 0.001018135tpop80Bx<- lm(as.numeric(cities$Proximity) ~ log(cities$t_80))
summary(tpop80Bx)##
## Call:
## lm(formula = as.numeric(cities$Proximity) ~ log(cities$t_80))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.6419 -0.3694 -0.3163 0.5917 0.6982
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.46039 0.40908 1.125 0.2622
## log(cities$t_80) 0.09117 0.03995 2.282 0.0239 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4827 on 152 degrees of freedom
## (115 observations deleted due to missingness)
## Multiple R-squared: 0.03312, Adjusted R-squared: 0.02676
## F-statistic: 5.207 on 1 and 152 DF, p-value: 0.02389coef(tpop80Bx)["log(cities$t_80)"]/100## log(cities$t_80)
## 0.0009116513#Run regression with percent Black population on Proximity. Significance
#Run regression with percent Black population on logged city population. Significance
proxpb20<- lm(as.numeric(Proximity)~pb_20,data=cities)
logtpb20<- lm(log(t_20)~pb_20,data=cities)
summary(proxpb20)##
## Call:
## lm(formula = as.numeric(Proximity) ~ pb_20, data = cities)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.0530 -0.3211 -0.2202 0.4807 0.8001
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.195302 0.040063 29.836 < 2e-16 ***
## pb_20 0.015777 0.002362 6.678 1.47e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4516 on 259 degrees of freedom
## (8 observations deleted due to missingness)
## Multiple R-squared: 0.1469, Adjusted R-squared: 0.1436
## F-statistic: 44.6 on 1 and 259 DF, p-value: 1.466e-10summary(logtpb20)##
## Call:
## lm(formula = log(t_20) ~ pb_20, data = cities)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.12198 -0.07040 -0.02304 0.04690 0.33338
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.3235144 0.0081942 283.556 <2e-16 ***
## pb_20 0.0011962 0.0004832 2.476 0.0139 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.09237 on 259 degrees of freedom
## (8 observations deleted due to missingness)
## Multiple R-squared: 0.02312, Adjusted R-squared: 0.01935
## F-statistic: 6.129 on 1 and 259 DF, p-value: 0.01394#Run regression with Proximity on percent black population. Highly Significant all years.
pbx20=lm(pb_20 ~ Proximity,cities)
summary(pbx20)##
## Call:
## lm(formula = pb_20 ~ Proximity, data = cities)
##
## Residuals:
## Min 1Q Median 3Q Max
## -17.565 -6.880 -2.417 3.975 53.409
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.5452 0.8673 9.852 < 2e-16 ***
## ProximityIn Proximity 9.3114 1.3942 6.678 1.47e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.97 on 259 degrees of freedom
## (8 observations deleted due to missingness)
## Multiple R-squared: 0.1469, Adjusted R-squared: 0.1436
## F-statistic: 44.6 on 1 and 259 DF, p-value: 1.466e-10pbx10=lm(pb_10 ~ Proximity,cities)
summary(pbx10)##
## Call:
## lm(formula = pb_10 ~ Proximity, data = cities)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.785 -6.725 -2.739 3.358 52.413
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.5541 0.9408 8.030 4.49e-14 ***
## ProximityIn Proximity 9.3850 1.4722 6.375 9.42e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.21 on 238 degrees of freedom
## (29 observations deleted due to missingness)
## Multiple R-squared: 0.1458, Adjusted R-squared: 0.1423
## F-statistic: 40.64 on 1 and 238 DF, p-value: 9.424e-10pbx00=lm(pb_00 ~ Proximity,cities)
summary(pbx00)##
## Call:
## lm(formula = pb_00 ~ Proximity, data = cities)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.176 -5.906 -2.490 2.612 41.624
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.6092 0.9095 7.267 7.87e-12 ***
## ProximityIn Proximity 9.0227 1.4434 6.251 2.38e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.09 on 202 degrees of freedom
## (65 observations deleted due to missingness)
## Multiple R-squared: 0.1621, Adjusted R-squared: 0.1579
## F-statistic: 39.08 on 1 and 202 DF, p-value: 2.379e-09pbx90=lm(pb_90 ~ Proximity,cities)
summary(pbx90)##
## Call:
## lm(formula = pb_90 ~ Proximity, data = cities)
##
## Residuals:
## Min 1Q Median 3Q Max
## -14.264 -5.885 -2.536 4.423 45.938
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.1778 0.9182 6.728 2.27e-10 ***
## ProximityIn Proximity 8.4397 1.4724 5.732 4.17e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.63 on 178 degrees of freedom
## (89 observations deleted due to missingness)
## Multiple R-squared: 0.1558, Adjusted R-squared: 0.1511
## F-statistic: 32.86 on 1 and 178 DF, p-value: 4.171e-08pbx80=lm(pb_80 ~ Proximity,cities)
summary(pbx80)##
## Call:
## lm(formula = pb_80 ~ Proximity, data = cities)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.815 -5.591 -2.976 4.212 34.316
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.7997 0.9508 6.100 8.41e-09 ***
## ProximityIn Proximity 7.2424 1.5232 4.755 4.57e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.218 on 152 degrees of freedom
## (115 observations deleted due to missingness)
## Multiple R-squared: 0.1295, Adjusted R-squared: 0.1238
## F-statistic: 22.61 on 1 and 152 DF, p-value: 4.572e-06##Logistic Regression
#The models indicate that there is a positive relationship between the percent of Black homeownership and whether the city is within proximity to a freedom colony. Cities with high percent of Black homeowners are more likely to be within proximity to a freedom colony for years 2000, 2010, and 2020.
#model 1 #A multiple regression was performed starting with proximity to freedom colonies (Table 4). This variable proved to yield statistically significant results. Proximity to freedom colonies provided an increase in Black homeownership by 7.935 percentage points.
model1_20<- lm(pboo_20~Proximity,data=cities)
summary(model1_20)##
## Call:
## lm(formula = pboo_20 ~ Proximity, data = cities)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.791 -5.199 -2.581 2.164 54.199
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.6037 0.7887 7.105 1.16e-11 ***
## ProximityIn Proximity 7.3177 1.2703 5.760 2.36e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.01 on 260 degrees of freedom
## (7 observations deleted due to missingness)
## Multiple R-squared: 0.1132, Adjusted R-squared: 0.1098
## F-statistic: 33.18 on 1 and 260 DF, p-value: 2.363e-08#model 2 - add in total popualtion logged #When the logged variable of city population was introduced in Model 2, there was a slight increase in homeownership although population was not statistically significant. Proximity remained a significant factor.
model2_20 <- lm(pboo_20~Proximity+log(t_20),data=cities)
summary(model2_20)##
## Call:
## lm(formula = pboo_20 ~ Proximity + log(t_20), data = cities)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.924 -4.983 -2.568 2.154 53.931
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9.916 15.652 -0.634 0.527
## ProximityIn Proximity 7.131 1.283 5.560 6.74e-08 ***
## log(t_20) 6.678 6.711 0.995 0.321
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.02 on 258 degrees of freedom
## (8 observations deleted due to missingness)
## Multiple R-squared: 0.1155, Adjusted R-squared: 0.1087
## F-statistic: 16.85 on 2 and 258 DF, p-value: 1.327e-07#As established, percent of Black population is highly correlated with Black homeownership. As expected, an initial regression with this variable yielded a significant result, but only a small increase in homeownership. Due to this high correlation, proximity lost its significance when percent of Black population was introduced to the model. Therefore, this variable was omitted from the regression.
citpb20=lm(pboo_20~pb_20,cities)
citpb10=lm(pboo_10~pb_10,cities)
citpb00=lm(pboo_00~pb_00,cities)
citpb90=lm(pboo_90~pb_90,cities)
citpb80=lm(pboo_80~pb_80,cities)
summary(citpb20)##
## Call:
## lm(formula = pboo_20 ~ pb_20, data = cities)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.0194 -1.2180 0.5173 1.5513 12.6654
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.9730 0.2680 -7.362 2.41e-12 ***
## pb_20 0.8585 0.0158 54.322 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.021 on 259 degrees of freedom
## (8 observations deleted due to missingness)
## Multiple R-squared: 0.9193, Adjusted R-squared: 0.919
## F-statistic: 2951 on 1 and 259 DF, p-value: < 2.2e-16summary(citpb10)##
## Call:
## lm(formula = pboo_10 ~ pb_10, data = cities)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.6954 -1.2473 0.3532 1.4362 13.3214
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.4811 0.2406 -6.155 3.17e-09 ***
## pb_10 0.8834 0.0145 60.941 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.713 on 238 degrees of freedom
## (29 observations deleted due to missingness)
## Multiple R-squared: 0.9398, Adjusted R-squared: 0.9395
## F-statistic: 3714 on 1 and 238 DF, p-value: < 2.2e-16summary(citpb00)##
## Call:
## lm(formula = pboo_00 ~ pb_00, data = cities)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.5147 -0.8487 0.2933 0.8873 14.6523
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.83415 0.23633 -3.53 0.000518 ***
## pb_00 0.82406 0.01565 52.64 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.441 on 198 degrees of freedom
## (69 observations deleted due to missingness)
## Multiple R-squared: 0.9333, Adjusted R-squared: 0.933
## F-statistic: 2771 on 1 and 198 DF, p-value: < 2.2e-16summary(citpb90)##
## Call:
## lm(formula = pboo_90 ~ pb_90, data = cities)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.9046 -0.7423 0.2832 0.7728 8.9028
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.66915 0.20261 -3.303 0.00116 **
## pb_90 0.86542 0.01436 60.287 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.004 on 177 degrees of freedom
## (90 observations deleted due to missingness)
## Multiple R-squared: 0.9536, Adjusted R-squared: 0.9533
## F-statistic: 3634 on 1 and 177 DF, p-value: < 2.2e-16summary(citpb80)##
## Call:
## lm(formula = pboo_80 ~ pb_80, data = cities)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.9313 -0.4940 0.0426 0.3423 5.6163
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.10014 0.13794 -0.726 0.469
## pb_80 0.78014 0.01056 73.888 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.286 on 152 degrees of freedom
## (115 observations deleted due to missingness)
## Multiple R-squared: 0.9729, Adjusted R-squared: 0.9727
## F-statistic: 5459 on 1 and 152 DF, p-value: < 2.2e-16