Loading my data set:
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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorsdataset <-read_delim("C:/Users/MSKR/MASTERS_ADS/STATISTICS_SEM1/DATA_SET_1.csv", delim = ",")## Rows: 4424 Columns: 37
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): Target
## dbl (36): Marital status, Application mode, Application order, Course, Dayti...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.Creating a custom table with mutating necessary categorical columns:
dataset_1<-dataset
dataset_1<-mutate(dataset_1, marital_status = ifelse(dataset$`Marital status` == 1, "single",
ifelse(`Marital status` == 2, "married",
ifelse(`Marital status` == 3, "widower",
ifelse(`Marital status` == 4, "divorced",
ifelse(`Marital status` == 5, "facto union",
ifelse(`Marital status` == 6, "legally seperated", "no")))))))dataset_1<-mutate(dataset_1, day_eve_class= ifelse(dataset_1$`Daytime/evening attendance ` == 1, "day","evening"))dataset_1<-mutate(dataset_1, day_eve_class= ifelse(dataset_1$`Daytime/evening attendance ` == 1, "day","evening"))dataset_1<-mutate(dataset_1, sem_results= rowMeans(select(dataset_1,`Curricular units 1st sem (grade)`, `Curricular units 2nd sem (grade)`)))dataset_1<-mutate(dataset_1, target = ifelse(dataset$Target == "Graduate",1,
ifelse(Target == "Enrolled",2,
ifelse(Target == "Dropout", 0, "no"))))df_bin<-filter(dataset_1,target!=2)
df_bin## # A tibble: 3,630 × 41
## `Marital status` `Application mode` `Application order` Course
## <dbl> <dbl> <dbl> <dbl>
## 1 1 17 5 171
## 2 1 15 1 9254
## 3 1 1 5 9070
## 4 1 17 2 9773
## 5 2 39 1 8014
## 6 2 39 1 9991
## 7 1 1 1 9500
## 8 1 18 4 9254
## 9 1 1 3 9238
## 10 1 1 1 9238
## # ℹ 3,620 more rows
## # ℹ 37 more variables: `Daytime/evening attendance\t` <dbl>,
## # `Previous qualification` <dbl>, `Previous qualification (grade)` <dbl>,
## # Nacionality <dbl>, `Mother's qualification` <dbl>,
## # `Father's qualification` <dbl>, `Mother's occupation` <dbl>,
## # `Father's occupation` <dbl>, `Admission grade` <dbl>, Displaced <dbl>,
## # `Educational special needs` <dbl>, Debtor <dbl>, …df_bin$target<-as.numeric(df_bin$target)# Logistic regression model
logit_model <- glm(target ~ `Previous qualification (grade)` + `Admission grade` + `Curricular units 1st sem (grade)` + `Curricular units 2nd sem (grade)`, data = df_bin, family = binomial)
summary(logit_model)##
## Call:
## glm(formula = target ~ `Previous qualification (grade)` + `Admission grade` +
## `Curricular units 1st sem (grade)` + `Curricular units 2nd sem (grade)`,
## family = binomial, data = df_bin)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -5.686198 0.507221 -11.210 < 2e-16 ***
## `Previous qualification (grade)` 0.010695 0.004076 2.624 0.008695 **
## `Admission grade` 0.012588 0.003817 3.298 0.000973 ***
## `Curricular units 1st sem (grade)` 0.020274 0.019223 1.055 0.291567
## `Curricular units 2nd sem (grade)` 0.282426 0.018089 15.613 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 4859.8 on 3629 degrees of freedom
## Residual deviance: 3369.5 on 3625 degrees of freedom
## AIC: 3379.5
##
## Number of Fisher Scoring iterations: 5The intercept value -5.69 represents the log-odds of graduating (the binary outcome = 1) when all other predictors are zero. A large negative intercept suggests that, without favorable values in predictors, the likelihood of graduating is low.
For each one-unit increase in previous qualification grade, the log-odds of graduating increases by 0.0107. Since the p-value is 0.0087 (significant at the 0.01 level), this variable has a statistically significant positive association with graduation likelihood. This suggests that better prior grades moderately increase the likelihood of graduation.
A one-unit increase in admission grade is associated with a 0.0126 increase in the log-odds of graduating. This is statistically significant at the 0.001 level, indicating that higher admission grades are strongly associated with a higher likelihood of graduation. This result could imply that students who perform better on admission exams are more likely to succeed.
For semester1_grades, the coefficient is positive but not statistically significant (p = 0.291). This suggests that grades in the first semester do not have a statistically meaningful impact on the likelihood of graduation. It may imply that early grades alone aren’t a strong predictor of final graduation outcomes, though further investigation could help clarify this.
For semester2_grades, the coefficient is positive and highly significant (p < 0.001), indicating that for each one-unit increase in second-semester grades, the log-odds of graduation increase by 0.2824. This suggests a strong positive relationship between second-semester performance and graduation likelihood, implying that academic performance in the second semester may be crucial for successful graduation
Null deviance of 4859.8 and Residual deviance of 3369.5 suggest that the model explains a substantial amount of variability compared to the baseline (null) model.
To construct the confidence interval for semester2_grades attribute, I am using the standard error from the model summary
coef_estimate <- coef(logit_model)["`Curricular units 2nd sem (grade)`"]
std_error <- summary(logit_model)$coefficients["`Curricular units 2nd sem (grade)`", "Std. Error"]# Calculate the 95% CI
ci_lower <- coef_estimate - 1.96 * std_error
ci_upper <- coef_estimate + 1.96 * std_error
c(ci_lower, ci_upper)## `Curricular units 2nd sem (grade)` `Curricular units 2nd sem (grade)`
## 0.2469712 0.3178807The 95% confidence interval for the coefficient of semester2_grades is [0.2470,0.3179]. Since the entire interval is positive and does not include zero, it strongly suggests a significant positive effect of second-semester grades on the likelihood of graduation. This aligns with the earlier finding that this predictor is highly statistically significant (p < 0.001).
With this interval, we can interpret that, for each additional unit in second-semester grades, the log-odds of graduation increase by somewhere between 0.2470 and 0.3179. This reflects a consistent impact, indicating that better performance in the second semester is associated with a higher probability of graduating.
It suggests that students who perform well in the second semester are considerably more likely to graduate.