Question

(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:​

Answer 1

a) Positive Correlation

b) 69.5

c) Base advertisement fee

Explanation:

a) Relationship between money spent on advertising and items sold

If we spent greater amount of money on advertisement, thus, we create more awareness and thus, the number of item sold increases.

Similarly, if less money is spent on advertisement, the number of items sold will be less.

Thus, the money spent on advertisement varies directly with the number of items sold.

Thus, they have a positive relationship or a positive correlation.

b) Money spent in advertising to sell 30 items

We are given the function:

`y= 1.6x+ 21.5`

We put x = 30

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

Thus, the score predicted by model is 69.5 units.

c) Interpretation of 21.5

Comparing the equation to a general linear equation, we get

`y = mx + c`

where m is the slope and c is the y-intercept.

y-intercept tells us the value of function when x is zero.

Thus, for the given scenario it will tell about the basic advertisement fee to be paid if we want to sell 0 products.

Comparing we get,

c = 21.5

Interpretation:

Thus, 21.5 units is the basic amount of advertisement fee that needed to be paid( the number of items sold is 0)