1. Build at least three sets of variable combinations
  • For each set of variables, include at least one column that you created (i.e., calculated based on others)
  • All variables for this data dive should be either continuous (i.e., numeric) or ordered (e.g., [‘small’, ‘medium’, ‘large’] is okay, but [“apples”, “oranges”, “bananas”] is not)
  • For each set, there should be one response variable with the others as explanatory variables
  1. Plot a visualization for each response-explanatory relationship, and draw some conclusions based on the plot
  • Use what we’ve covered so far in class to scrutinize the plot (e.g., are there any outliers?)
  1. Calculate the appropriate correlation coefficient for each of these combinations
  • Explain why the value makes sense (or doesn’t) based on the visualization(s)
  1. Build a confidence interval for each of the response variables. Provide a detailed conclusion of the response variable (i.e., the population) based on your confidence interval.

Building Variable Combinations

Below are the three sets of variable combinations:

Set 1: Temperature and Weather Conditions

Response Variable: temperature_celsius Explanatory Variables: humidity, pressure_mb, wind_kph, calculated_heat_index (a calculated variable based on temperature and humidity).

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## $humidity

## 
## $pressure_mb

## 
## $wind_kph

## temperature_celsius            humidity         pressure_mb            wind_kph 
##           1.0000000          -0.1095037          -0.6666068           0.1796794

Observations

The variable with the strongest negative correlation with temperature is pressure_mb, with a correlation coefficient of -0.667. This means that there is a strong negative relationship between the two variables. In other words, as temperature increases, pressure_mb decreases.

The correlation coefficients for humidity and wind_kph are both relatively weak, indicating that there is no strong relationship between either of these variables and temperature.

Overall, these results suggest that temperature is a strong negative predictor of pressure_mb, but not a strong predictor of humidity or wind_kph.

Set 2: Visibility and Environmental Factors

Response Variable: visibility_km Explanatory Variables: cloud, precip_mm, air_quality_PM2.5, calculated_dew_point (calculated from temperature and humidity).

## $cloud

## 
## $precip_mm

## 
## $air_quality_PM2.5

## 
## $calculated_dew_point

##        visibility_km                cloud            precip_mm 
##           1.00000000           0.17230747          -0.08527476 
##    air_quality_PM2.5 calculated_dew_point 
##          -0.18506400           0.04144997

Observations

In this case, the correlation coefficient between visibility and cloud cover is weak and positive, indicating that visibility tends to increase as cloud cover increases. This is pracically counterintuitive as clouds block sunlight, which can reduce visibility.

The correlation coefficient between visibility and precipitation is negative, indicating that visibility tends to decrease as precipitation increases. This is likely because precipitation particles can scatter and absorb light, which can reduce visibility.

The correlation coefficients between visibility and PM2.5 concentration and calculated dew point are negative and relatively weak. This suggests that there is a weak negative relationship between visibility and PM2.5 concentration and calculated dew point. This is likely because PM2.5 particles can scatter and absorb light, which can reduce visibility.

Visibility has a weak positive correlation with calculated dew point, meaning that there is a weak relationship between the two variables. This suggests that dew point may not be a significant factor in determining visibility.

Set 3: Air Quality Index and Pollutants

Response Variable: air_quality_us_epa_index

Explanatory Variables: air_quality_Carbon_Monoxide, air_quality_Nitrogen_dioxide, air_quality_Sulphur_dioxide, air_quality_PM10, calculated_pollution_factor (a calculated composite index of various pollutants).

## $air_quality_Carbon_Monoxide

## 
## $air_quality_Nitrogen_dioxide

## 
## $air_quality_Sulphur_dioxide

## 
## $air_quality_PM10

## 
## $calculated_pollution_factor

##  air_quality_Carbon_Monoxide air_quality_Nitrogen_dioxide 
##                    0.6224032                    0.5288290 
##  air_quality_Sulphur_dioxide             air_quality_PM10 
##                    0.4810241                    0.7932714 
##  calculated_pollution_factor 
##                    0.6495639

All of the air quality variables are positively correlated with each other. This means that they tend to move in the same direction. For example, if carbon monoxide levels increase, then nitrogen dioxide levels are also likely to increase.

Calculating Confidence Interval

Confidence Interval for Temperature (Celsius)

## Mean Temperature: 22.49432
## 95% Confidence Interval: [ 22.242 , 22.74663 ]

Visualization of Temperature Distribution

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## generated.

### Conclusion

The confidence interval for temperature suggests that the average temperature across the locations in the dataset is between 22.24°C and 22.75°C with 95% confidence. This interval indicates a relatively stable temperature range across the dataset’s locations, implying consistent weather conditions.

Confidence Interval for Visibility (Kilometers)

## Mean Visibility: 9.810221
## 95% Confidence Interval: [ 9.710713 , 9.909729 ]

Visualization for Visibility Distribution

### Conclusion

The confidence interval for visibility indicates that the average visibility is between 9.71 km and 9.91 km. This narrow range suggests high consistency in visibility conditions across different locations. High visibility, as indicated by the mean and interval, could imply generally clear weather conditions.

Confidence Interval for Air Quality Index (US EPA Index)

## Mean Air Quality Index: 1.463694
## 95% Confidence Interval: [ 1.428055 , 1.499332 ]

Visualization for Air Quality Index

### Conclusion

The confidence interval for the air quality index is very narrow, ranging from 1.43 to 1.50, suggesting a consistent air quality level across the dataset. The low mean value (close to 1) indicates generally good air quality in the sampled locations.

General Observation

All the confidence intervals are relatively narrow, indicating that the mean values are likely to be a reliable representation of the conditions.