Independent variables: SSOverall, STOverall, and SCOverall
Dependent variable: GWA(1st sem SY: 2021-2022)

library(readxl)
withage <- read_excel("withage.xlsx")
withage

Q1. How many of the observations whose age is at least 21 years old?

library(dplyr)

Attaching package: 'dplyr'
The following objects are masked from 'package:stats':

    filter, lag
The following objects are masked from 'package:base':

    intersect, setdiff, setequal, union
Ian <- withage%>%
  mutate(Agecode=ifelse(Age>=21, "at least 21 years old", "Less than 21 years old"))%>%
  group_by(Agecode)%>%
  summarise(count=n())%>%
  mutate(Percentage =round((count/sum(count)*100),2))
Ian

There are 72 of them whose age is at least 21 years old.

Q2. How many of the observations whose grades are above 1.25 to 1.75?

Ian1.1 <- withage%>%
  mutate(GWAcode=ifelse(`GWA (1st sem SY: 2021-2022)`>=1.25 & `GWA (1st sem SY: 2021-2022)`<=1.75, "GWA is the interval [1.25, 1.75]", "Not in the given interval of GWA"))%>%
  group_by(GWAcode)%>%
  summarise(count=n())%>%
  mutate(Percentage =round((count/sum(count)*100),2))
Ian1.1

There are 92 observations whose GWA is in the interval [1.25, 1.75].

Q3. Provide the results in checking the assumptions in running multiple regression analysis.

library(performance)
multiple <- lm(`GWA (1st sem SY: 2021-2022)` ~ SSOverall + STOverall + SCOverall, data = withage)
multiple

Call:
lm(formula = `GWA (1st sem SY: 2021-2022)` ~ SSOverall + STOverall + 
    SCOverall, data = withage)

Coefficients:
(Intercept)    SSOverall    STOverall    SCOverall  
   1.996962    -0.047674    -0.067324    -0.005764  
check_model(multiple)

Q4. Which of the independent variables significantly predicts the dependent variable?

summary(multiple)

Call:
lm(formula = `GWA (1st sem SY: 2021-2022)` ~ SSOverall + STOverall + 
    SCOverall, data = withage)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.45511 -0.11195 -0.02104  0.10446  0.57345 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.996962   0.173046  11.540   <2e-16 ***
SSOverall   -0.047674   0.038355  -1.243    0.217    
STOverall   -0.067324   0.047959  -1.404    0.163    
SCOverall   -0.005764   0.048030  -0.120    0.905    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.1993 on 109 degrees of freedom
Multiple R-squared:  0.07516,   Adjusted R-squared:  0.0497 
F-statistic: 2.953 on 3 and 109 DF,  p-value: 0.03583

As gleaned above, the results show that the independent variable STOverall significantly predicts the dependent variable GWA(1st sem SY: 2021-2022) with p-value results of 0.163 and has the coefficient with the largest absolute value of 0.067324.