Question

1. A convenience store manager notices that sales of soft drinks are higher on hotter days. He gathers some data, recording the high temperature of the day as x, and the number of cans sold as y. The samples used to create the model ranged from a temperature of 75^°F to  96^°F.  His data yielded the following LSRL:

   

   Part 1: (4 pts)

   Give the slope and interpret what it means in the context of the question (2 pts).

   Part 2:

   Give the y-intercept and interpret what it means in the context of the question (2 pts).

   Part 3:

   Use the model to predict the number of cans sold if the temperature reached 100^°F (4 pts), then comment on the usefulness of your solution

THERE WAS NO DATA SET PROVIDED.

Answer 1

From the given information, Let the random variable X represents the high temperature of the day. Let the random variable Y represents the number of cans sold. The least squares regression line of Yon X is given as follows: ŷ =-602.143+14.792X (a) From the given information slope of the regression line is 14.792. As the value of the high temperature of the day (X) increases by 1, the value of the Number of cans sold (Y) increases by 14.792. (b) From the given information Y-intercept of the regression line is -602.143. If the high temperature of the day is equal to 0, the expected number of cans sold is - 602.143. (C) When the temperature reached 100°F then the number of cans sold is predicted as follows: Y = -602.143 +14.792x = -602.143+14.792(100) = -602.143 +1479.2 = 877.057 Therefore, number of cans sold if the temperature reached 100°F is 877. Since, the model ranged from a temperature of 75°F and 96°F, and considering 100°F is out of the range. Therefore, the solution is useless.