Homework_3

Library

Code

library(tidyverse)

── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr     1.1.1     ✔ readr     2.1.4
✔ forcats   1.0.0     ✔ stringr   1.5.0
✔ ggplot2   3.4.2     ✔ tibble    3.2.1
✔ lubridate 1.9.2     ✔ tidyr     1.3.0
✔ purrr     1.0.1     
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
ℹ Use the ]8;;http://conflicted.r-lib.org/conflicted package]8;; to force all conflicts to become errors

Code

library(dplyr)
library(ggplot2)
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 

Q.1)

A

• Predictor variable :- ppgdp

• Response variable :- fertility, birth rate

B

Code

ggplot(UN11, aes(ppgdp, fertility, color = "red")) +
  geom_point()

C

Code

ggplot(data = UN11, aes(x = log(ppgdp), y = log(fertility))) +
  geom_point()

we can imagine negatively sloped straight line and a plausible linear regression.

Q.2)

A)

the conversion from USD to British pound the numerical value will be divided by 1.23 to mitigate the effect slope will be divided by 1.23 as well.

B)

correlation will not change as it does not affect by measuring unit.

Q.3)

Code

data(water)
pairs(water)

Q.4)

Code

#data(Rateprof)
pairs(Rateprof[,c('quality', 'clarity', 'helpfulness',
                  'easiness', 'raterInterest')])

There is a strong correlation among quality, clarity, and helpfulness . easiness is correlated with the other three. raterInterest is also fairly correlated, but raters almost always say they are at least somewhat interested in the subject. Overall, the results might show that people do not differentiate all these dimensions very well in their minds—or that professors that do one in one dimension tend to do well on the others too.

Q.5)

A)

Code

data("student.survey")
ggplot(student.survey, aes(x = re, fill = pi)) +
    geom_bar()

Code

ggplot(data = student.survey, aes(x = tv, y = hi)) +
  geom_point() +
  theme_bw()

B)

Code

data("student.survey")

model_1 <- lm(as.numeric(pi) ~ as.numeric(re), 
         data = student.survey)
model_2 <- lm(hi ~ tv, data = student.survey)
summary(model_1)

Call:
lm(formula = as.numeric(pi) ~ as.numeric(re), data = student.survey)

Residuals:
     Min       1Q   Median       3Q      Max 
-2.81243 -0.87160  0.09882  1.12840  3.09882 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)      0.9308     0.4252   2.189   0.0327 *  
as.numeric(re)   0.9704     0.1792   5.416 1.22e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.345 on 58 degrees of freedom
Multiple R-squared:  0.3359,    Adjusted R-squared:  0.3244 
F-statistic: 29.34 on 1 and 58 DF,  p-value: 1.221e-06

Code

summary(model_2)

Call:
lm(formula = hi ~ tv, data = student.survey)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.2583 -0.2456  0.0417  0.3368  0.7051 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  3.441353   0.085345  40.323   <2e-16 ***
tv          -0.018305   0.008658  -2.114   0.0388 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.4467 on 58 degrees of freedom
Multiple R-squared:  0.07156,   Adjusted R-squared:  0.05555 
F-statistic: 4.471 on 1 and 58 DF,  p-value: 0.03879

There is a Positive and statistically significant relation between Religiosity and conservatism.

Watching TV for one more hour will decline the GPA by 0.018