Question

A regression analysis was performed to determine the relationship between the costs of a product (y), the time to make the product (x 1), the number of different materials used (x2), and the amount spent on marketing the product (x 3). The estimated regression equation is ý = 83 - 2x1 + 6x 2 + 1.1X 3. What is the estimated cost if the time to make the product is 5 hours, the number of different materials used is 4, and the amount spent on marketing is $100?

a. 83
b. 185.4
c. 213
d. 205.4

Answer 1

Correct option: (b) 185.4.

Explanation:

The regression analysis is used to predict the value of the response variable (Y) based on one or more than one experimental variable(s) (X).

The general form of the regression equation is:

`\hat y=\alpha +\beta_(1)x_(1)+\beta_(2)x_(2)+\beta_(3)x_(3)+...+\beta_(n)x_(n)`

Here,

α = intercept

`\beta _(i)` = slope coefficient, (i = 1, 2, 3, ...n)

The regression equation of costs of a product (y) based on the time to make the product (x₁), the number of different materials used (x₂), and the amount spent on marketing the product (x₃) is:

`\hat y=83-2x_(1)+0.6x_(2)+1.1x_(3)`

The information provided is:

x₁ = 5 hours

x₂ = 4

x₃ = $100

Compute the value of y for the given values as follows:

`\hat y=83-2x_(1)+0.6x_(2)+1.1x_(3)`

`=83-(2* 5)+(0.6* 4)+(1.1* 100)\\=83-10+2.4+110\\=185.4`

Thus, the estimated cost of a product is $185.4.