hw3
shelton
ggplot2
Author

Dane Shelton

Published

August 2, 2022

Code 
library(tidyverse)
library(ggplot2)
library(alr4)
library(smss)
library(GGally)

knitr::opts_chunk$set(echo = FALSE, warning=FALSE, message = FALSE)

Homework 3

We are using UN11 data:

UN11
1.1.1

Predictor/Explanatory/IV - ppgdp Per Person GDP

Response/DV - fertility Fertility Rate per 1000

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No, our scatter plot appears to have a negative exponential relationship; as ppgdp increase, fertility decreases at a nonlinear rate.

NOTE: If anyone knows why it is printing the above output as well as the graph please send a comment on Google Classroom or Piazza!

Now, after using a log transformation on both x and y, our scatter plot appears to have a negative linear relationship; as ppgdp increase, fertility decreases at a linear rate. This transformation makes these variabels appropriate for linear regression.

USD to GBP

a) The slope of the regression line will be divided by 1.33 to represent the adjustment to GBP. \(1 USD * (1 GBP/1.33 USD)\) leaves us with just GBP. The slope is reduced by approximately 25 percent.

b) The correlation between the explanatory variable and the response will not change.

The rightmost column uses BSAAM as a response variable to the preciptation values at the various sites over the years 1948-1990. Inspecting the plots on this column closer, we can see that BSAAM has a strong positive correlation with OPSLAKE, OPRC, and OBPBC. There is a much weaker positive relationship between BSAAM and APSLAKE, APSAB, and APSMAM. If we were attempting to predict stream runoff volume, it would be best to observe and use the values of OPSLAKE, OPRC, and OBPBC to create our model. These locations’ precipitation values are highly correlated with stream runoff volume each year.

Using ggpairs of the GGally package, we can see the variables that correlate the highest with quality are helpfulness and clarity. Clarity and helpfulness have the third highest correlation with each other. If we were attempting to predict the quality rating of a course, we would strongly consider both clarity and helpfulness ratings.


Call:
lm(formula = pi_num ~ re_no, data = student.survey)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.8889 -0.5172 -0.2667  1.2040  2.7333 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)         2.2667     0.3394   6.678 1.18e-08 ***
re_nooccasionally   0.2506     0.4181   0.599 0.551374    
re_nomost weeks     2.1619     0.6017   3.593 0.000691 ***
re_noevery week     2.6222     0.5543   4.731 1.56e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.315 on 56 degrees of freedom
Multiple R-squared:  0.3872,    Adjusted R-squared:  0.3544 
F-statistic:  11.8 on 3 and 56 DF,  p-value: 4.282e-06

First using a box plot to visualize the relationship between a numeric and a nominal variable, it’s clear the distributions of those that attend church more frequently skew towards conservative values on the 7-point scale provided by the data. This is confirmed by inspecting the summary of the linear regression model relating Political Ideology to Religiosity. Both group means’ coefficients (scores) for those attending church “most weeks” and “weekly” are approximately 2 times greater that the intercept value that respresents those that attend “never”.


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

Observing the results of the linear regression model relating high-school GPA to hours spent watching TV, we see that for every one hour increase in hours of TV/wk, our model predicts high-school GPA to decrease by 0.018305 points. We see the weak negative linear relationship using both geom_point and geom_smooth to depict the regression line and the original data points.