Question

A regression analysis between sales (y in $1000) and advertising (x.in dollars) resulted in the following equation: ỹ= 30,000 + 4x

The above equation implies that an:________
a. increase of $l in advertising is associated with an increase of $4 in sales.
b. increase of $4 in advertising is associated with an increase of $4000 in sales.
c. increase of $1 in advertising is associated with an increase of $34,000 in sales.
d. increase of $1 in advertising is associated with an increase of $4000 in sales.

Answer 1

Correct answer is option d. increase of $1 in advertising is associated with an increase of $4000 in sales.

Explanation:

Given the equation of regression analysis is given as:

`y= 30,000 + 4x`

where
`x` is the cost on advertising in Dollars.

and
`y` is the sales in Thousand Dollars.

To find:

The correct increase in sales when there is increase in the advertising cost.

Solution:

Suppose there is an increase of
`\$1` in the advertising cost.

Let the initial cost be
`x` then the cost will be
`(x+1)`.

Initial sales

`y= 30,000 + 4x` ....... (1)

After increase of $1 in advertising cost, final cost:

`y'= 30,000 + 4(x+1)\\\Rightarrow y' = 30,000+4x+4\\\Rightarrow y' = 30,004+4x ..... (2)`

Subtracting (2) from (1) to find the increase in the sales:

`y'-y=30004+4x-30000-4x = 4`

The units of sales is Thousand Dollars ($1000).

So, increase in sales =
`4 *1000 = \bold{\$4000}`

So, correct answer is:

d. increase of $1 in advertising is associated with an increase of $4000 in sales.