Homework - 5

hw5

desriptive statistics

probability

Homework 5

Author

Hannah Rosenbaum

Published

May 4, 2023

Code

library(alr4)

Loading required package: car

Loading required package: carData

Loading required package: effects

lattice theme set by effectsTheme()
See ?effectsTheme for details.

Code

library(smss)

Question 1

Code

data("house.selling.price.2")

a

Using backward elimination, Beds would be removed first.

b

Using forward elimination, New would be selected first.

c

Because Beds is correlated to Size, which is correlated to Price, so inherently, more Beds has an impact on Price but still have a low p-value.

d

Code

fit <- lm(Price ~ . -Size -Beds -Baths -New, data=house.selling.price)

Error in is.data.frame(data): object 'house.selling.price' not found

Code

summary(fit)

Error in summary(fit): object 'fit' not found

Code

fit <- lm(Price ~ . -Size -Baths -New, data=house.selling.price)

Error in is.data.frame(data): object 'house.selling.price' not found

Code

summary(fit)

Error in summary(fit): object 'fit' not found

Code

fit <- lm(Price ~ . -Size -New, data=house.selling.price)

Error in is.data.frame(data): object 'house.selling.price' not found

Code

summary(fit)

Error in summary(fit): object 'fit' not found

Code

fit2 <- lm(Price ~ . -New, data=house.selling.price)

Error in is.data.frame(data): object 'house.selling.price' not found

Code

summary(fit)

Error in summary(fit): object 'fit' not found

Code

fit2 <- lm(Price ~ . -New -Size, data=house.selling.price)

Error in is.data.frame(data): object 'house.selling.price' not found

Code

summary(fit)

Error in summary(fit): object 'fit' not found

Code

fit2 <- lm(Price ~ . -New -Size -Beds, data=house.selling.price)

Error in is.data.frame(data): object 'house.selling.price' not found

Code

summary(fit)

Error in summary(fit): object 'fit' not found

Code

summary(fit)

Error in summary(fit): object 'fit' not found

Code

AIC(fit)

Error in AIC(fit): object 'fit' not found

Code

BIC(fit)

Error in BIC(fit): object 'fit' not found

Code

summary(fit2)

Error in summary(fit2): object 'fit2' not found

Code

AIC(fit2)

Error in AIC(fit2): object 'fit2' not found

Code

BIC(fit2)

Error in BIC(fit2): object 'fit2' not found

e

I prefer the model generated by backward elimination, since the AIC, BIC, and multiple R-squared statistics are higher.

Question 2

Code

data("trees")

a

Code

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


Call:
lm(formula = Volume ~ Girth + Height, data = trees)

Residuals:
    Min      1Q  Median      3Q     Max 
-6.4065 -2.6493 -0.2876  2.2003  8.4847 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) -57.9877     8.6382  -6.713 2.75e-07 ***
Girth         4.7082     0.2643  17.816  < 2e-16 ***
Height        0.3393     0.1302   2.607   0.0145 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 3.882 on 28 degrees of freedom
Multiple R-squared:  0.948, Adjusted R-squared:  0.9442 
F-statistic:   255 on 2 and 28 DF,  p-value: < 2.2e-16

b

Code

plot(fit)

Residuals vs Fitted violation: curvature

Scale-Location violation: positive trend

Question 3

Code

data(florida)

Code

fit <- lm(Gore ~ Bush, data=florida)
summary(fit)


Call:
lm(formula = Gore ~ Bush, data = florida)

Residuals:
   Min     1Q Median     3Q    Max 
-65960 -12515   4534   7181 182682 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -8.617e+03  4.744e+03  -1.816   0.0739 .  
Bush         1.198e+00  6.657e-02  18.002   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 30820 on 65 degrees of freedom
Multiple R-squared:  0.8329,    Adjusted R-squared:  0.8304 
F-statistic: 324.1 on 1 and 65 DF,  p-value: < 2.2e-16

Code

plot(fit)

Palm Beach County is an outlier based on falling out of the group in the residuals vs. fitted and Q-Q plots. The Residuals vs. Leverage is just on the line, but it still supports Palm Beach being an outlier.

b

Code

fit <- lm(log(Gore) ~ log(Bush), data=florida)
summary(fit)


Call:
lm(formula = log(Gore) ~ log(Bush), data = florida)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.92986 -0.19820  0.01858  0.19148  1.04574 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) -0.88437    0.31982  -2.765   0.0074 ** 
log(Bush)    1.06362    0.03234  32.885   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.384 on 65 degrees of freedom
Multiple R-squared:  0.9433,    Adjusted R-squared:  0.9424 
F-statistic:  1081 on 1 and 65 DF,  p-value: < 2.2e-16

Code

plot(fit)

Palm Beach County does not appear to be an outlier.