discussionwk12
jim lung
11-14-2017
Data 605 Discussion week 12
Using R, build a multiple regression model for data that interests you. Include in this model at least one quadratic term, one dichotomous term, and one dichotomous vs. quantitative interaction term. Interpret all coefficients. Conduct residual analysis. Was the linear model appropriate? Why or why not?
Data:
New York Air Quality Measurements
Ozone numeric Ozone (ppb) Solar.R numeric Solar R (lang) Wind numeric Wind (mph) Temp numeric Temperature (degrees F) Month numeric Month (1–12) Day numeric Day of month (1–31)
#forest <- read.csv("forestfires.csv")
head(airquality)## Ozone Solar.R Wind Temp Month Day
## 1 41 190 7.4 67 5 1
## 2 36 118 8.0 72 5 2
## 3 12 149 12.6 74 5 3
## 4 18 313 11.5 62 5 4
## 5 NA NA 14.3 56 5 5
## 6 28 NA 14.9 66 5 6summary(airquality)## Ozone Solar.R Wind Temp
## Min. : 1.00 Min. : 7.0 Min. : 1.700 Min. :56.00
## 1st Qu.: 18.00 1st Qu.:115.8 1st Qu.: 7.400 1st Qu.:72.00
## Median : 31.50 Median :205.0 Median : 9.700 Median :79.00
## Mean : 42.13 Mean :185.9 Mean : 9.958 Mean :77.88
## 3rd Qu.: 63.25 3rd Qu.:258.8 3rd Qu.:11.500 3rd Qu.:85.00
## Max. :168.00 Max. :334.0 Max. :20.700 Max. :97.00
## NA's :37 NA's :7
## Month Day
## Min. :5.000 Min. : 1.0
## 1st Qu.:6.000 1st Qu.: 8.0
## Median :7.000 Median :16.0
## Mean :6.993 Mean :15.8
## 3rd Qu.:8.000 3rd Qu.:23.0
## Max. :9.000 Max. :31.0
## pairs(airquality)
Multiple Regression Model
To predict numeric Ozone (ppb)
one quadratic term: Temp ^2
# create quadratic term
temp_squared <- (airquality$Temp)^2
# create model
airqualitylm <- lm(airquality$Ozone ~ temp_squared + airquality$Solar.R + airquality$Wind, data = airquality)summary(airqualitylm)##
## Call:
## lm(formula = airquality$Ozone ~ temp_squared + airquality$Solar.R +
## airquality$Wind, data = airquality)
##
## Residuals:
## Min 1Q Median 3Q Max
## -39.830 -13.799 -3.252 10.089 96.996
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.718665 14.186985 -0.403 0.6877
## temp_squared 0.011208 0.001621 6.916 3.53e-10 ***
## airquality$Solar.R 0.059356 0.022733 2.611 0.0103 *
## airquality$Wind -3.218499 0.644853 -4.991 2.34e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 20.81 on 107 degrees of freedom
## (42 observations deleted due to missingness)
## Multiple R-squared: 0.6195, Adjusted R-squared: 0.6089
## F-statistic: 58.08 on 3 and 107 DF, p-value: < 2.2e-16The model is as follows: Ozone = \(Ozone = -5.718665 + 0.011208*Temp^{2} + 0.059356*Solar - 3.218499*Wind\)
It is a a statistically significant predictor of evaluation score with p-value less than 0.05. For Multiple R-squared, the model is around 61% fits the data.
Residual Analysis
plot(airqualitylm$fitted.values, airqualitylm$residuals)
abline(0,0)
# qqplot
qqnorm(airqualitylm$residuals)
qqline(airqualitylm$residuals)
Q-Q plot are not uniformly scattered and have deviation at lower and quantiles. The residuals does not show randomly.