Homework 5

Question 1

First, let’s load the relevant libraries and set all the graph themes to minimal.

Code

library(readxl)
library(tidyverse)

── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
✔ ggplot2 3.3.6      ✔ purrr   0.3.4 
✔ tibble  3.1.8      ✔ dplyr   1.0.10
✔ tidyr   1.2.1      ✔ stringr 1.4.1 
✔ readr   2.1.3      ✔ forcats 0.5.2 
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()

Code

library(dplyr)
library(alr4)

Loading required package: car
Loading required package: carData

Attaching package: 'car'

The following object is masked from 'package:dplyr':

    recode

The following object is masked from 'package:purrr':

    some

Loading required package: effects
lattice theme set by effectsTheme()
See ?effectsTheme for details.

Code

library(smss)
library(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=stargazer 

A

Variables Beds would be removed first. It’s P-value does not meet statistically significant threshold.

B

For the opposite reason, Size would be added first.

C

Beds is most likely auto-correlated with Size, as bedrooms make up a substantial amount of square footage in a house, driving up the price. However, that is not the only factor if pricing, as is most likely why the number – which can be high – does not necessarily mean we see an improved price. Conversely, this is not the case for bathrooms.

D

Code

data(house.selling.price.2)
model_1 <- lm(P ~ S + Ba, data = house.selling.price.2)
plot(model_1)

Code

stargazer(model_1)

% Table created by stargazer v.5.2.3 by Marek Hlavac, Social Policy Institute. E-mail: marek.hlavac at gmail.com
% Date and time: Fri, Dec 09, 2022 - 6:39:51 PM
\begin{table}[!htbp] \centering 
  \caption{} 
  \label{} 
\begin{tabular}{@{\extracolsep{5pt}}lc} 
\\[-1.8ex]\hline 
\hline \\[-1.8ex] 
 & \multicolumn{1}{c}{\textit{Dependent variable:}} \\ 
\cline{2-2} 
\\[-1.8ex] & P \\ 
\hline \\[-1.8ex] 
 S & 63.863$^{***}$ \\ 
  & (4.840) \\ 
  & \\ 
 Ba & 22.448$^{***}$ \\ 
  & (6.130) \\ 
  & \\ 
 Constant & $-$49.752$^{***}$ \\ 
  & (9.183) \\ 
  & \\ 
\hline \\[-1.8ex] 
Observations & 93 \\ 
R$^{2}$ & 0.833 \\ 
Adjusted R$^{2}$ & 0.829 \\ 
Residual Std. Error & 18.267 (df = 90) \\ 
F Statistic & 224.114$^{***}$ (df = 2; 90) \\ 
\hline 
\hline \\[-1.8ex] 
\textit{Note:}  & \multicolumn{1}{r}{$^{*}$p$<$0.1; $^{**}$p$<$0.05; $^{***}$p$<$0.01} \\ 
\end{tabular} 
\end{table} 

Code

PRESS <- function(model) {
  i <- residuals(model)/(1 - lm.influence(model)$hat)
  sum(i^2)
}

PRESS(model_1)

[1] 34174.5

Code

broom::glance(model_1)

# A tibble: 1 × 12
  r.squared adj.r.squa…¹ sigma stati…²  p.value    df logLik   AIC   BIC devia…³
      <dbl>        <dbl> <dbl>   <dbl>    <dbl> <dbl>  <dbl> <dbl> <dbl>   <dbl>
1     0.833        0.829  18.3    224. 1.12e-35     2  -401.  809.  819.  30033.
# … with 2 more variables: df.residual <int>, nobs <int>, and abbreviated
#   variable names ¹​adj.r.squared, ²​statistic, ³​deviance

Note: observation #5 is an outlier and violates many of these diagnostic plots. If we log transform either P or S, observation #7 does the same. Therefore, we will keep the model as-is and not transform it.

R2 = 0.83 Adjusted R2 = 0.83 PRESS = 34.174.5 AIC = 809.23 BIC = 819.36

E

I chose this model as the other two variables Beds and New either do not meet the P-value threshold or have a low correlation to Price. The other two variables have a high correlation with Price.

Question 2

Code

data(trees)
head(trees)

  Girth Height Volume
1   8.3     70   10.3
2   8.6     65   10.3
3   8.8     63   10.2
4  10.5     72   16.4
5  10.7     81   18.8
6  10.8     83   19.7

A

Code

model_q2 <- lm(Volume ~ Girth + Height, data = trees)

Fitted.

B

Code

plot(model_q2)

Both of the Residuals vs. Fitted plots are violated, as they form a U-shape instead of a horizontal line; Cook’s Distance plot is violated as row 31 is outside of the 0.5 dotted line. The Normal Q-Q plot seems fine. The Scale Location plot does not look good, as it has a U-shape as well.

Question 3

Code

data(florida)
head(florida)

           Gore   Bush Buchanan
ALACHUA   47300  34062      262
BAKER      2392   5610       73
BAY       18850  38637      248
BRADFORD   3072   5413       65
BREVARD   97318 115185      570
BROWARD  386518 177279      789

A

Code

model_q3a <- lm(Buchanan ~ Bush, data = florida)
plot(model_q3a)

Yes, Palm Beach County is an outlier. This is especially apparent with Cook’s Distance plot, as it is outside the 1.0 dotted line.

B

Code

model_q3b <- lm(log(Buchanan) ~ log(Bush), data = florida)
plot(model_q3b)

The findings do change, as all observations that violated the tests are now within the lines/meet assumptions.