Question

1. movieplay is an online movie rental service. they have a sliding price list based upon the popularity of the movies. the table below shows the rentals by price category for the month of september. let x represent the price and y represent the number of movies rented at that price.

price	# of rentals
4.99	1,000
3.99	1,200
2.99	1,380
1.99	1,672
0.99	1,903

a. examine the data without drawing a scatter plot, describe any trends that you see.

b. draw a scatter plot, describe the correlation.

c. based on this information how many rental might be anticipated if the company instituted a new price category of $6.99. explain your reasoning.

Explanation:

Step1: Analyze price - rentals relationship

As the price ($x$) decreases from $5.99$ to $0.99$, the number of rentals ($y$) increases from 800 to 1903. There is an inverse - relationship trend.

Step2: Consider scatter - plot correlation

When drawing a scatter plot, with price on the x - axis and number of rentals on the y - axis, the points will show a negative correlation. As the value of $x$ (price) goes up, the value of $y$ (number of rentals) goes down.

Step3: Predict rentals for new price

Since the trend is an inverse relationship, and the price of $6.99$ is higher than the highest price in the table ($5.99$). We can assume that the number of rentals will be less than 800. A reasonable estimate could be around 700 (this is an estimate based on the observed trend of decreasing rentals with increasing price).

Answer:

a. As the price of movie rentals decreases, the number of rentals increases.
b. The scatter - plot would show a negative correlation. As price increases, the number of rentals decreases.
c. An estimate of around 700 rentals. Since there is an inverse relationship between price and number of rentals and $6.99$ is higher than the highest price in the data set ($5.99$), the number of rentals is expected to be less than the 800 rentals at the $5.99$ price point.