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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   6

# omit rows where 'Ozone' has missing values
airquality<-na.omit(airquality, cols="Ozone")
par(mfrow = c(3,2))
plot(airquality$Ozone~airquality$Solar.R)
plot(airquality$Ozone~airquality$Wind)
plot(airquality$Ozone~airquality$Temp)
plot(airquality$Ozone~airquality$Month)
plot(airquality$Ozone~airquality$Day)

• Predcitor : Temp
• Response : Ozone

Model_Ozon_Temp <- lm(airquality$Ozone ~ airquality$Temp,airquality)
summary(Model_Ozon_Temp)

## 
## Call:
## lm(formula = airquality$Ozone ~ airquality$Temp, data = airquality)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -40.922 -17.459  -0.874  10.444 118.078 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     -147.6461    18.7553  -7.872 2.76e-12 ***
## airquality$Temp    2.4391     0.2393  10.192  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 23.92 on 109 degrees of freedom
## Multiple R-squared:  0.488,  Adjusted R-squared:  0.4833 
## F-statistic: 103.9 on 1 and 109 DF,  p-value: < 2.2e-16

plot(airquality$Temp,airquality$Ozone)
abline(Model_Ozon_Temp)

• Predcitor : wind
• Response : Ozone

Model_Ozon_Win <- lm(airquality$Ozone ~ airquality$Wind,airquality)
summary(Model_Ozon_Win)

## 
## Call:
## lm(formula = airquality$Ozone ~ airquality$Wind, data = airquality)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -43.513 -18.597  -5.035  15.814  88.437 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      99.0413     7.4724   13.25  < 2e-16 ***
## airquality$Wind  -5.7288     0.7082   -8.09 9.09e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 26.42 on 109 degrees of freedom
## Multiple R-squared:  0.3752, Adjusted R-squared:  0.3694 
## F-statistic: 65.44 on 1 and 109 DF,  p-value: 9.089e-13

plot(airquality$Wind,airquality$Ozone)
abline(Model_Ozon_Win)

• Predcitor : airquality\(Wind*airquality\)Temp)*airquality$Solar.R,airquality
• Response : Ozone

Model_Ozon_WinTemp <- lm(airquality$Ozone ~ (log(airquality$Wind)*airquality$Temp)*(airquality$Solar.R),airquality)
summary(Model_Ozon_WinTemp)

## 
## Call:
## lm(formula = airquality$Ozone ~ (log(airquality$Wind) * airquality$Temp) * 
##     (airquality$Solar.R), data = airquality)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -37.339 -11.611  -1.718   7.892  75.204 
## 
## Coefficients:
##                                                           Estimate
## (Intercept)                                             -9.928e+01
## log(airquality$Wind)                                     3.185e+01
## airquality$Temp                                          1.699e+00
## airquality$Solar.R                                       1.843e-01
## log(airquality$Wind):airquality$Temp                    -4.822e-01
## log(airquality$Wind):airquality$Solar.R                 -2.072e-01
## airquality$Temp:airquality$Solar.R                       3.211e-03
## log(airquality$Wind):airquality$Temp:airquality$Solar.R  7.558e-04
##                                                         Std. Error t value
## (Intercept)                                              2.382e+02  -0.417
## log(airquality$Wind)                                     9.726e+01   0.327
## airquality$Temp                                          3.159e+00   0.538
## airquality$Solar.R                                       1.272e+00   0.145
## log(airquality$Wind):airquality$Temp                     1.307e+00  -0.369
## log(airquality$Wind):airquality$Solar.R                  5.300e-01  -0.391
## airquality$Temp:airquality$Solar.R                       1.646e-02   0.195
## log(airquality$Wind):airquality$Temp:airquality$Solar.R  6.923e-03   0.109
##                                                         Pr(>|t|)
## (Intercept)                                                0.678
## log(airquality$Wind)                                       0.744
## airquality$Temp                                            0.592
## airquality$Solar.R                                         0.885
## log(airquality$Wind):airquality$Temp                       0.713
## log(airquality$Wind):airquality$Solar.R                    0.697
## airquality$Temp:airquality$Solar.R                         0.846
## log(airquality$Wind):airquality$Temp:airquality$Solar.R    0.913
## 
## Residual standard error: 18.56 on 103 degrees of freedom
## Multiple R-squared:  0.7088, Adjusted R-squared:  0.689 
## F-statistic: 35.81 on 7 and 103 DF,  p-value: < 2.2e-16

Result shows that we are able to explain 68% of data with formula = Ozone ~ (Wind * Temp ) * Solar.R