sensor_data <- read.csv("/Users/manojdannana/Desktop/Manoj/IUPUI/class work/intro to statistics/datasets/Occupancy_Estimation.csv")

Response Variable:

The response variable I am picking for my analysis is Room_Occupancy_Count as the dataset I have tries to see how the Room Occupancy changes when all the other variables change.

Categorical Column for Explanatory Variable:

The explanatory categorical variable I am picking up is S6_PIR. S6_PIR is the value of Motion Detection Sensor that denotes whether there is motion in the room or not. It is a binary value.

Null Hypothesis:

H0: There is no significant difference in mean sensor readings (S6_PIR) across different categories (groups) in the dataset.

ANOVA Test

S6_PIR <- sensor_data$S6_PIR
Room_Occupancy_Count <- sensor_data$Room_Occupancy_Count

unique_values <- unique(S6_PIR)
cat("Unique Values in S6_PIR: \n")
## Unique Values in S6_PIR:
cat(unique_values)
## 0 1
cat("\n")
result_anova <- aov(S6_PIR ~ Room_Occupancy_Count, data=sensor_data)
cat("Summary of Results: \n")
## Summary of Results:
summary(result_anova)
##                         Df Sum Sq Mean Sq F value Pr(>F)    
## Room_Occupancy_Count     1  333.0     333    6775 <2e-16 ***
## Residuals            10127  497.7       0                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Conclusions from ANOVA Test:

The Two important values we have to look at from the above ANOVA Test are the F-Score and P-Score.

The F-Score is 6775 which is very high and It implies that there is significantly more variance in sensor readings (S6_PIR) between various room occupancy counts than there is within each occupancy count group. It indicates that sensor readings are strongly impacted by the room occupancy.

Since the p-value is extremely small (close to zero), much smaller than the typical significance level of 0.05, we reject the null hypothesis. This indicates that there is a significant difference in mean sensor readings (S6_PIR) across different room occupancy counts.

Continuous Column for Explanatory Variable:

The Continuous Explanatory Variable I am considering is Mean_Temp column. This column isn’t explicitly present in the dataset. I am going to create it by taking the mean of (S1_Temp, S2_Temp, S3_Temp and S4_Temp) columns since all these columns represent the same thing and have same units.

Creating the column

sensor_data$Mean_Temp <- rowMeans(sensor_data[, c("S1_Temp", "S2_Temp", "S3_Temp", "S4_Temp")])

Checking for the correlation between columns Mean_Temp and Room_Occupancy_count

room_occupancy <- sensor_data$Room_Occupancy_Count
mean_temp <- sensor_data$Mean_Temp

correlation_coefficient <- cor(room_occupancy, mean_temp)

print(correlation_coefficient)
## [1] 0.692698

The Correlation Coefficient is 0.7 which indicates a strong positive correlation between the two columns. Hence we can proceed with building a Linear Regression Model for the two columns.

Regression Model

model <- lm(mean_temp ~ room_occupancy, data=sensor_data)

summary(model)
## 
## Call:
## lm(formula = mean_temp ~ room_occupancy, data = sensor_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.74019 -0.23187 -0.01687  0.17063  1.17313 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    25.329374   0.003133 8085.83   <2e-16 ***
## room_occupancy  0.309440   0.003202   96.65   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2879 on 10127 degrees of freedom
## Multiple R-squared:  0.4798, Adjusted R-squared:  0.4798 
## F-statistic:  9342 on 1 and 10127 DF,  p-value: < 2.2e-16

Interpretation and Recommendations:

  • The intercept may not have a practical interpretation in this context since it represents an extrapolation to a hypothetical scenario where the mean temperature is zero, which is unlikely to occur in real-world situations. Therefore, interpretations and recommendations should focus on the coefficient for mean_temp.

  • Since the coefficient for mean_temp is positive and statistically significant (p < 0.001), it suggests that there is a positive linear relationship between mean temperature and Room_Occupancy_Count. In other words, as the mean temperature increases, the value of Room_Occupancy_Count tends to increase as well.