Residual Plot vs Fitted, linearity and Heteroskedasticity I am working on a linear Regression Model right now,
it has the following format:
leisure = ß0 + ß1*age + ß2*log(rain +1) + ß3*log(temperature + 1) + ß4*km + ß5*time

So basically I want to know if rain and temperature has an impact on the number of leisure activities a person spends (leisure is a fractional number)
I had to add a small constant when taking the log, because rain and temperature can take zero values.
I plotted a Residual vs. Fitted Plot and I am wondering if I interpret it the right way.
The red line is nearly horizontal which should indicate that there is a linear relationship between my independent variables and my dependent variable leisure.
However the plot also shows me that I have a massiv problem with Heteroskedasticity.
I thought about using FGLS to deal with my Heteroskedasticity.
I am grateful for any suggestions and input.
Thank you


Since your reponse variable is a count, then you need to fit a model for count data, such as a poisson or negative binomial, for example:
glm(leisure ~ age + rain + temperature + km + time, family = poisson(link = "log", data = mydata) 

It appears from the residual plot that you have just used lm
Since your interest is on the impact of rain and temperature, you might want to consider an interaction between these, if you think the effect of one is different depending on the level of the other. Also, a nonlinear association may be indicated - for example when the weather is extremely cold or extremely hot, some exercise may be reduced. So perhaps a quadratic term, or splines would be a good idea.
