Question

Consider this scatter plot.

(a) How would you characterize the relationship between money spent on advertising and items sold? Explain.

(b) Sally uses the function y = 1.6x + 21.5 to model the situation. What score does the model predict should be spent in advertising to sell 30 items?

(c) What does the number 21.5 in Part (b) mean in the context of the situation?

Answer 1

Part a) Is a positive correlation

Part b)
`\$69.5`

Part c) see the explanation

Explanation:

Let

x ----> the number of items sold

y ----> the money spent on advertising

Part a) How would you characterize the relationship between money spent on advertising and items sold?

we know that

Positive correlation is a relationship between two variables in which both variables move in the same direction

so

As the value of x increases, the value of y increases

therefore

Is a positive correlation

Part b) Sally uses the function y = 1.6x + 21.5 to model the situation. What score does the model predict should be spent in advertising to sell 30 items?

we have

`y=1.6x+21.5`

For x=30 items

substitute the value of x in the linear equation and solve for y

`y=1.6(30)+21.5=\$69.5`

Part c) What does the number 21.5 in Part (b) mean in the context of the situation?

we have

`y=1.6x+21.5`

This is a linear equation in slope intercept form

where

The slope is

`m=\$1.6\ per\ item\ sold`

The y-intercept or initial value is

`b=\$21.5`

therefore

In the context of the situation the number 21.5 means the initial amount spent at the begin (when the number of items sold was zero)