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

Answer:

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

Step-by-step 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 = $4 \times1000 = \bold{\ 4000}$

So, correct answer is:

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