Question

2. Hot dog sales during day games at the baseball stadium and the high temperatures during the games are approximately linearly related. Suppose the average high temperature at day games is 80 (degrees Farenheit) with a standard deviation of 10, and that average hot dog sales are 30 (thousands of dogs) with a standard deviation of 5. The correlation between temperature and sales is -0.25.

a) Suppose the high temperature at a particular day game is 80 degrees. How many hot dogs do you predict will be sold at that game?

b) Suppose the high temperature at a particular day game is 96 degrees. What is your best prediction for hot dog sales?

c) What fraction of the variation in hot dog sales is accounted for by the variation in predicted hot dog sales?

Answer 1

here let x and y are temperature and hot dog sales variable

here slope b1=r*$\sigma$_y/$\sigma$_x =(-0.25)*5/10=-0.125

and intercept =$\mu$y-b1*$\mu$x =30-(-0.125)*80=40

hence line equation: Y =40-0.125*x

a)

predicted sales =40-0.125*80=30

b)

predicted sales =40-0.125*96=28

c)

fraction of the variation in hot dog sales is accounted for by the variation in predicted hot dog sales =r²=(-0.25)² =0.0625