Newton North High School is interested in analyzing how many calories its studen
ID: 3142681 • Letter: N
Question
Newton North High School is interested in analyzing how many calories its students consume on an average day and whether it related to students being a male and an athlete. The following regression was obtained: Calories = beta_0 + beta_1 * Spring + beta_2 * Summer + beta_3 * Autumn + beta_4 * Male + beta_5 * Athlete + beta_6 * Male * Athlete + u_r, where Spring. Summer and Autumn are seasonal dummies. Male is a dummy equal to 1 if the student is male, and Athlete is a dummy equal to 1 if student is an athlete. Calories is the total number of calories consumed per day. What is the average number of calories consumed by a female non-athlete student in the Summer season? In the Winter season? How many calories do female students that are athletes eat on average per day in each of the seasons? How many calories do male students that aren't athletes eat on average per day in each of the seasons? How many calories do male students that are athletes eat on average per day in each of the seasons? How does this compare to female athletes? Which of the variables look insignificant in the model?Explanation / Answer
1) for female non-athllete in summer season -
spring = 0, summer =1 , autumn = 0 , male = 0 , athlete = 0 , male*athlete = 0
hence
calories = b0 + b2 = 864 + 116 = 980
in winter
b0 = 864
2) female ,athlete
i) winter
spring = 0, summer =0 , autumn = 0 , male = 0 , athlete = 1 , male*athlete = 0
= b0 + b5 = 864 + 72 = 936
ii)spring
b0+ b1+b5 = 936+50 = 986
summer
b0+b2+b5 = 936 +116 = 1052
autumn
b0+b3+b5 = 936 + 82 = 1018
3) male ,not athlete ,
winter
spring = 0, summer =0 , autumn = 0 , male = 1 , athlete = 0 , male*athlete = 0
= b0 + b4 = 864 + 54 = 918
spring
b0 + b1 + b4 = 918 + 50 =968
summer
b0+b2+b4 = 918 +116 = 1036
autumn
b0+b3+b4 = 918+ 82 = 1000
4) male athlete
winter
spring = 0, summer =0 , autumn = 0 , male = 1 , athlete = 1 , male*athlete = 1
= b0 + b4 + b5+ b6 = 864 + 54 + 72 +188 = 1178
spring
b0 + b1 + b4 + b5+ b6 = 1178 + 50 = 1228
summer
b0+b2+b4 + b5+ b6 = 1178 + 116 = 1294
autumn
b0+b3+b4 + b5+ b6 = 1178+82 = 1260
clealy this is more than female athletes (difference is due to factor of male + male *athlete)