Are you trying to color the points based on the number of stars?
Load the data frame:
df <- read.table(text=' business_id longitude stars latitude duration
1 --5jkZ3-nUPZxUvtcbr8Uw -111.9269 4.5 33.46337 381
2 --BlvDO_RG2yElKu9XA1_g -111.8983 4.0 33.62146 690
3 -Ke8q969OAwEE-U0qUjw -112.1863 4.5 33.65387 604
4 -_npP9XdyzILAjtFfX8UAQ -112.0739 3.0 33.44990 1916
5 -2xCV0XGD9NxfWaVwA1-DQ -112.2766 4.0 33.56626 226
6 -3WVw1TNQbPBzaKCaQQ1AQ -112.0692 3.5 33.48585 2190')
And plot your image while defining a color gradient for the points (yellow to red as you stated).
ggmap(Phoenix) + geom_point(aes(x=longitude, y=latitude, color=stars), size=5, data=df, alpha=.3) + scale_color_gradient(low="yellow",high="red")
which will produce the following (I've increased the alpha and size to make it easier to see):