Question

The response is the tooth length in n = 60 guinea pigs. Each animal received a daily dose of vitamin C by one of two delivery methods (orange juice or ascorbic acid). The estimated mean function is E(length|source, dose) = 11.5 + 8.5 source + 8.0 dose + 4.0 source × dose where source takes the value 1 for ascorbic acid and 0 for orange juice.
Suppose the variable source was re-coded to take the value 1 for orange juice and 0 for ascorbic acid. Then the estimated mean function becomes what? Please include explaination.

Answer 1

E(length|source, dose) = 11.5 + 8.5 source + 8.0 dose + 4.0 source × dose

for ascorbic acid , source = 1

hence for ascorbic acid

E(length|source, dose) = 11.5 + 8.5 + 8.0 dose + 4.0 dose

= 20 + 12 dose

for orange juice

E(length|source, dose) = 11.5 + 8.0 dose

hence if we code source = 1 for orange juice

E(length|source, dose) = a + b source + c dose + d source × dose

for orange juice = a + b + (c+ d) dose

for ascorbic acid = a+ c dose

hence

a+b = 11.5 , c+d = 8 , a = 20 ,c = 12

b - -8.5 , d = -4

E(length|source, dose) = 20 -8.5 source + 12 dose -4 source × dose