Question: 'Give an interpretation of the estimated coefficient of tempC'
My answer: holding fixed the type of event, an increase in temperature by 1 degree C means the winning race time will increase by 0.232 minutes.
Apparently the correct answer: for the man's race, an increase in temperature by 1 degree C means the winning race time will increase by 0.232 minutes.
Why is it for the man's race? My understanding was that we hold the other variables (excluding tempC) fixed, which doesn't mean using a value of 0 for the dummy variable, which is what would be needed to get the correct interpretation in my mind. Does anyone know why?
Your model is $$ y_i = \beta_0 + \beta_1wrace_i + \beta_2tempC_i + \beta_3tempC_i\times wrace_i + \epsilon_i, $$ thus for womens' race you have $$ y_i = \beta_0 + \beta_1 + (\beta_2 + \beta_3)tempC_i + \epsilon_i, $$ and for men $$ y_i = \beta_0 + \beta_2tempC_i + \epsilon_i. $$ Namely, for women $$ \frac{\partial}{\partial tempC}\mathbb{E}[y|tempC, wrace=1]=\beta_2+\beta_3, $$ while for men $$ \frac{\partial}{\partial tempC}\mathbb{E}[y|tempC, wrace=0]=\beta_2. $$