Question

A movie theater decides to examine how ticket price impacts attendance. They examined the price per ticket and the amount of tickets sold. The table below shows the results. [Note that the second two columns say "continued" to denote that there are only two variables worth of data] Theater Attendance Data icket Price (in dollars) Tickets Sold (in hundreds) icket Price continued) ickets Sold continued) 50 25 25 10 10.50 12 32 24 24 50 113 50 19 36 12 30 10

A)What is the value of the correlation coefficient?

B)What is the value of the coefficient of determination?

C)When finding the least-squares regression for this line, what is the slope?

D)When finding the least-squares regression for this line, what is the y-intercept?

E)Give the equation for the least-squares regression line.

F)Interpret the slope for this equation.

G)Is it reasonable to give an interpretation of your y-intercept? If yes, please give one. If not, explain why.

Answer 1

A)

value of the correlation coefficient =-0.8648

b)

value of the coefficient of determination=r² =0.7478

c)

slope =-12.9193

d)

y-intercept =162.7077

e)

equation for the least-squares regression line :Yhat=162.7077+(-12.9193)*x

f)

here slope tells us that for 1 unit increase in ticket price ; sale of tickets decreased by 1291.93 tickets on average

g)

it is not reasonable as ticket price can not go down to 0 ; and intercept is the value for ticket value to be 0.