Results of Multiple Regression Analysis Using Temperature as the Dependent Variable

Based on the results of correlation analysis of temperature data and factor data, we performed multiple regression analysis using the mean maximum daily temperature in August as the dependent variable. The size of woodland area and amount of anthropogenic heat emissions, which correlated highly with mean maximum daily temperatures in August, were used as explanatory variables.

Table 2.5 Results of multiple regression analysis by cell size

Explanatory variables

Range of collected data

A: 50-m cells

B: 150-m cells

C: 250-m cells

Coefficient

P value

Coefficient

P value

Coefficient

P value

Woodland area (m2)

-0.0009

0.025

-0.0001

0.018

-0.0001

0.013

Anthropogenic

-0.0003

0.979

0.0033

0.03

0.0002

0.678

heat emissions

(GJ/day)

Intercept

32.2398

32.0011

32.3125

Multiple correlation

0.4924

0.7276

0.5885

coefficient

P value

0.0715

0.0008

0.0176

Number of readings

22

22

22

Although the amount of green space also correlates highly with the mean maximum daily temperatures in August, a high correlation coefficient was found between the amount of woodland and amount of green space, which suggests a likelihood of multicollinearity. For this reason we chose to use data from woodland areas rather than green space, because the former has a higher correlation with mean maximum daily temperatures in August.

The most significant result of multiple regression analysis was found for B (150-m cells), which gave good P values and multiple correlation coefficients in Table 2.5. From this result we determined the multiple regression model in Eq. (2.1), where Y is the mean daily maximum temperature in August (°C), X1 is the woodland area (m2), and X2 is the amount of anthropogenic heat emissions (GJ/day):

Y = 32.0011 – 0.0001 (X1) + 0.0033(X2) (2.1)

It should be noted that the multiple regression model obtained in this study is applicable within a mean daily maximum temperature range in August between 30.4 ° and 33.4 °C when the data were actually collected.

The effects on temperature formation given in Eq. (2.1), as obtained from the correlation analysis results, show that the woodland area coefficient has a negative effect whereas the anthropogenic heat emissions coefficient has a positive effect. This result can be said to validate the hypothesis given in the introduction.