Question

The following table shows the hot dogs bought from a street vendor over the course of eight days​ ("Demand"). Also shown is the temperature for each day in degrees Celsius.

Complete parts a and b below. nbsp

Temperature (degrees C ) 18 13 22 18 8 13 18 20

Demand 45 31 35 38 19 22 43 32

a. Calculate the slope and​ y-intercept for the linear regression equation for these data.

b. Predict the demand for hot dogs on a day with a temperature of 10 °C.

Answer 1

x

y

18	45
13	31
22	35
18	38
8	19
13	22
18	43
20	32

a) The least square estimates for equation y=a+bx, where x=temperature and y=demand, are given by:

Using the values we've calculated, we get a=9.364, b=1.462

Therefore, the regression line of Demand on Temperature is given as : Y= 9.364+ 1.462x

b) The demand for hot dogs on a day with a temperature of 10 °C , that is when x=10, then Y=9.364+14.62=23.984