LAB REPORT 4 BSD3443 STATISTICAL MODELLING AND SIMULATIONS

library(readr)

## Warning: package 'readr' was built under R version 4.0.5

datalab4<- read.table("C:/Users/ADMIN/Downloads/UMP SEM 5/STATS MODELING/LAB REPORT 4/missile.txt",header=TRUE)

datalab4

##     x1      x2 y
## 1  400 2.58712 0
## 2  220 2.83445 1
## 3  490 2.95819 0
## 4  210 3.03145 1
## 5  500 3.12618 0
## 6  270 2.27379 0
## 7  200 1.75191 1
## 8  470 3.79009 0
## 9  480 4.72141 0
## 10 310 4.40155 1
## 11 240 3.85747 1
## 12 490 3.63706 0
## 13 420 3.22118 0
## 14 330 2.75392 1
## 15 280 3.31236 1
## 16 210 5.09166 1
## 17 300 6.21180 1
## 18 470 5.21862 1
## 19 230 2.58414 0
## 20 430 2.05767 0
## 21 460 1.66235 0
## 22 220 0.77621 1
## 23 250 0.89889 1
## 24 200 1.73104 1
## 25 390 1.92354 0

summary(datalab4)

##        x1              x2               y       
##  Min.   :200.0   Min.   :0.7762   Min.   :0.00  
##  1st Qu.:230.0   1st Qu.:2.0577   1st Qu.:0.00  
##  Median :310.0   Median :2.9582   Median :1.00  
##  Mean   :338.8   Mean   :3.0566   Mean   :0.52  
##  3rd Qu.:460.0   3rd Qu.:3.7901   3rd Qu.:1.00  
##  Max.   :500.0   Max.   :6.2118   Max.   :1.00

datalab4$y <- factor(datalab4$y)

logitmod <- glm(y ~ x1 , data = datalab4, family = "binomial")
summary(logitmod)

## 
## Call:
## glm(formula = y ~ x1, family = "binomial", data = datalab4)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -2.0620  -0.4868   0.3915   0.5476   2.1682  
## 
## Coefficients:
##              Estimate Std. Error z value Pr(>|z|)   
## (Intercept)  6.070884   2.108996   2.879  0.00399 **
## x1          -0.017705   0.006076  -2.914  0.00357 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 34.617  on 24  degrees of freedom
## Residual deviance: 20.364  on 23  degrees of freedom
## AIC: 24.364
## 
## Number of Fisher Scoring iterations: 4

i) Based on the output, write the equation of the logistic regression model.

• y = 6.0709 - 0.0177x1 + e

ii) Does the model deviance indicate that the logistic regression model from part (i) is adequate?.

• Null deviance: 34.617 on 24 degrees of freedom

• Residual deviance: 20.364 on 23 degrees of freedom

• Yes, based on the residuals deviance and the null deviance value, the model deviance do indicate that the logistic regression model from part(i) is adequate because the residuals deviance value is less than the null deviance value. Thus, the smaller the residuals deviance compared to null deviance, the better the model.

iii) Provide an interpretation of the parameter β1 of the model.

• For one knot increase in target speed, the log odds of test-firing results decrease by 0.0177

logitmod <- glm(y ~ x1 + x2 , data = datalab4, family = "binomial")
summary(logitmod)

## 
## Call:
## glm(formula = y ~ x1 + x2, family = "binomial", data = datalab4)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -2.21945  -0.43285   0.08161   0.46436   1.42620  
## 
## Coefficients:
##              Estimate Std. Error z value Pr(>|z|)   
## (Intercept)  5.126227   2.199315   2.331  0.01976 * 
## x1          -0.024672   0.009079  -2.717  0.00658 **
## x2           1.130875   0.674592   1.676  0.09366 . 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 34.617  on 24  degrees of freedom
## Residual deviance: 16.197  on 22  degrees of freedom
## AIC: 22.197
## 
## Number of Fisher Scoring iterations: 6

iv) Considering the predictor wind speed in the model, refit the model and write the updated logistic regression model.

• y = 5.1262 - 0.0247x1 + 1.1309x2 + e

v) Based on the updated logistic model, does the model deviance indicate that the model is adequate. Explain briefly.

• Yes, based on the updated logistic model residuals deviance, the model deviance do indicate that the updated logistic model is more adequate because the residuals deviance value of updated logistic model is less than the residuals deviance value of logistic model in (ii).