Final answer:
The relationship between hours after sunset and temperature is often negative and can be modeled with a linear function. As hours after sunset increase, temperature generally decreases. This negative correlation can be represented in a linear equation and verified by a correlation coefficient significantly different from zero.
Step-by-step explanation:
The relationship between the hours after sunset, x, and the temperature, y, is typically modeled using a linear function. The correlation between these two data sets is most often negative. This means that, in general, as the number of hours after sunset increases, the temperature tends to decrease. This negative correlation is observed because typically the atmosphere cools after the sun has set, due to the lack of incoming solar radiation to maintain the daytime temperatures.
A linear relationship can be constructed in the form of a linear equation ŷ = a + bx, where 'a' represents the y-intercept and 'b' is the slope of the line. The slope in this context would likely be negative, indicating that for every hour after sunset, the temperature drops by a certain amount. To further confirm the relationship, one would calculate the correlation coefficient, which if significantly different from zero, would indicate a significant linear relationship.