Melbourne Rain Trends
By Gregory Baharis (s3545698), Harri Somakanthan (s3775653) & Syed Wajahath (s3750039)
Introduction & Problem Statement
Melbourne Weather trends. The following investigation takes a look at melbourne weather data from 2008-2017.
RPubs link information: RPubs Link
There were three primary questions that drove our investigation
- What is the effect of Rainfall on the variation of temperature in Melbourne.
- What is the effect of Sunshine on evaportation .
- What is the effect of Humidty on temperature.
The dataset that we used was the Rain in Australia dataset available on Kaggle: https://www.kaggle.com/jsphyg/weather-dataset-rattle-package.
We will use statistics to analyse the relationship between each of the 2 variables per question. We shall undergo this process in 3 steps. Firstly we will collect the descriptive statistics and construct a box plot to analyse the spread of the data and check for any noticeable outlier patterns. Secondly we will then complete a t.test to determine the accuracy of the sample and visualise it using granova. Thirdly we will construct scatter plots and complete a linear regression and correlation analysis determing if a relationship exists.
Hypothesis Tests for Linear Relationships and Correlation.
##
## Call:
## lm(formula = Rainonly$Rainfall ~ Rainonly$TempVar)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.808 -3.936 -2.618 0.764 78.287
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.2479 0.6555 9.532 < 2e-16 ***
## Rainonly$TempVar -0.2182 0.0841 -2.595 0.00961 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.408 on 902 degrees of freedom
## Multiple R-squared: 0.00741, Adjusted R-squared: 0.00631
## F-statistic: 6.734 on 1 and 902 DF, p-value: 0.009614
## 2.5 % 97.5 %
## (Intercept) 4.9614266 7.5343277
## Rainonly$TempVar -0.3833083 -0.0531826
## The corrolation constant for Rainfall vs TempVar is -0.0860813
##
## The confidence interval is -0.15044
## The confidence interval is -0.0209959
## Warning: Removed 1 rows containing non-finite values (stat_smooth).
## Warning: Removed 1 rows containing missing values (geom_point).
##
## Call:
## lm(formula = rain$Sunshine ~ rain$Evaporation)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.1054 -2.9271 0.2605 3.1254 8.0760
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.91759 0.12981 37.88 <2e-16 ***
## rain$Evaporation 0.33687 0.02288 14.72 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.756 on 2432 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.08185, Adjusted R-squared: 0.08147
## F-statistic: 216.8 on 1 and 2432 DF, p-value: < 2.2e-16
## 2.5 % 97.5 %
## (Intercept) 4.6630405 5.1721406
## rain$Evaporation 0.2920049 0.3817332
##
## The corrolation constant for Sunshine vs Evaportation is 0.289054
##
## The confidence interval is 0.251065
## The confidence interval is 0.326153
## Warning: Removed 3 rows containing non-finite values (stat_smooth).
## Warning: Removed 3 rows containing missing values (geom_point).
##
## Call:
## lm(formula = rain$Humidity9am ~ rain$Temp9am)
##
## Residuals:
## Min 1Q Median 3Q Max
## -39.848 -8.666 -0.313 8.352 40.999
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 91.42440 0.80794 113.2 <2e-16 ***
## rain$Temp9am -1.64705 0.05245 -31.4 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.43 on 2430 degrees of freedom
## (3 observations deleted due to missingness)
## Multiple R-squared: 0.2886, Adjusted R-squared: 0.2884
## F-statistic: 986 on 1 and 2430 DF, p-value: < 2.2e-16
## 2.5 % 97.5 %
## (Intercept) 89.840083 93.008718
## rain$Temp9am -1.749905 -1.544194
##
## The corrolation constant for Humdity vs Temp at 9am is -0.537186
##
## The confidence interval is -0.5657
## The confidence interval is -0.507389
## Warning: Removed 7 rows containing non-finite values (stat_smooth).
## Warning: Removed 7 rows containing missing values (geom_point).
##
## Call:
## lm(formula = rain$Humidity3pm ~ rain$Temp3pm)
##
## Residuals:
## Min 1Q Median 3Q Max
## -32.077 -8.648 -1.246 7.507 50.815
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 84.87367 0.88263 96.16 <2e-16 ***
## rain$Temp3pm -1.75672 0.04374 -40.17 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.41 on 2426 degrees of freedom
## (7 observations deleted due to missingness)
## Multiple R-squared: 0.3994, Adjusted R-squared: 0.3991
## F-statistic: 1613 on 1 and 2426 DF, p-value: < 2.2e-16
## 2.5 % 97.5 %
## (Intercept) 83.142894 86.604453
## rain$Temp3pm -1.842488 -1.670957
##
## The corrolation constant for Humdity vs Temp at 3pm is -0.634058
##
## The confidence interval is -0.657932
## The confidence interval is -0.608911
Interpretation
Summary Statistics
Following with the problem statement we first determined the descriptive statistics of the 8 relevant variables to our question: TempVar, Rainfall, Evaporation, Sunshine, Humidity (9am and 3pm) and Temp (9am and 3pm). TempVar was calculated by taking the maximum temperature of the day minus the minimum temperature and all other variables we used are present within the dataset.
Boxplots
We constructed boxplots for each of the variables and an additional one for Rainfall. We separated Rainfall into another boxplot to get a more accurate picture as the days where it did not rain were skewing the results towards 0 as indicated by the summary statistics.
Outliers
We kept all the outliers in our dataset. This is primarily done to ensure that no data points are missing in one variable and present in a corresponding point in another variable, as conceptually it does not make sense for a value to be missing (unless it is not collected). For example if a humidity data point was deleted, the temperature at 9:00 am or 3:00 pm would have no corresponding humidity value which does not make sense conceptually as humidity is on a scale from 0-100. A secondary reason is also that our data points for all eight variables are numeric and measurable. For example if we were comparing the prices of goods between two supermarkets, we would be selecting different objects (like meats or dairy products) where products can vary dramatically in type, whereas for example temperature cannot be divided into further subcategories.
Linear Regression
We constructed 4 different scatter plots and then conducted a linear regression and correlation test on each: (TempVar vs Rainfall, Evaporation vs Sunshine, Humidity (9am) vs Temp (9am) and Humidity (3pm) vs Temp (3pm). We found that Evaporation vs Sunshine had a positive trend and the others had negative trends. Testing the significance we found that all the curves are statistically significant for the constant and slope terms and that there is a statistically significant possibility that a relationship does indeed exist for these variables. Likewise for correlation we had a similar outcome with were Evaporation vs Sunshine were positively correlated and the other three were negatively correlated. Testing the confidence intervals, H0 (no correlation) was not between any of them which allows us to reject the hypothesis stating that there is statistically significant correlation between each of the pairs.
Discussion
Major Findings
Strengths
The strengths of our analysis is that we looked at the weather patterns of Melbourne city overall. With many saying as Melbourne has the most unpredictable weather, this analysis helps us to know how the factors of weather effects the weather pattern. Thus, from the results, one could plan his/her activities accordingly.
limitations
The limitation of our analysis is the sample size and number of weather factors. We have considered only few factors like temperature, rainfall, sunshine, humidity and evaporation. The reason for the selected factors is because they are the most common factors which define the weather of particular location.
Findings
1. What is the effect of Rainfall on the variation of temperature in Melbourne ?
- There is a negative linear relation between Temperature Variance and Rainfall. However, this trend is highly skewed by the dense amount of data at lower temperature variances. The data also shows that when the temperature variance is between 3 & 8 the most amount of rainfall occurs.
2. What is the effect of Sunshine on evaportation ?
- The effect of sunshine on evaporation was exactly as we predicted: A positive linear relation. The more hours of sunshine, the more evaporation occurred. The data is collected by the amount of mm of water evaporated from a pan.
3. What is the effect of Humidty on temperature ?
- In this relationship we expected a higher temperature for a lower humidity. The relationship was very linear. During 9am the humidity is higher and the temperature tends to be lower, however in the afternoon at 3pm the temperature is higher with a lower humidity.
Proposal for future investigations
- Cloud level vs Rainfall
- City Traffic flow vs Rainfall (Do people choose to drive less during times of Rainflow & does this have an impact?)
- Behavioural Mood of park visitors vs Sunshine (Does weather have a relationship with the mood of citizens?)
- Consider other weather defining factors like air pressure, windspeed and many more.
- Try to get more sample size
- Consider other locations of Australia
A take home message for the reader
- When people say Melbourne has unpredictable weather, the data agrees. When looking at Rainfall vs Temperature Variance there is a dense portion of the data under 5mm of rain between 4-8 C variance. Best to always have an umbrella ready!
Final Conclusion
- There was a clear relationship found in all 3 questions investigated. However, the relationship found for Tempreture Variation vs the Rainfall was not a strong relationship. Sunshine vs Evaporation was as expected a mildly strong relationship where as Humidity vs Tempreture by far was the strongest relationship.
