Question

a restaurant sells pizza for the prices in the data table. what is the linear regression equation of the data?
number of toppings
price of pizza
(in dollars)
0
12
1
13.5
2
15
3
16.5
4
18
5
19.5
6
21
$y = 1.5x + 12$
$y = 12x + 1.5$
a
c
$y = - 8y + 0.67$
$y = 0.67x - 8$

Explanation:

Step1: Recall the linear regression equation form

The linear regression equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step2: Find the y - intercept

When \(x = 0\) (number of toppings = 0), \(y=12\). So \(b = 12\).

Step3: Calculate the slope

Use the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Take two points \((x_1,y_1)=(0,12)\) and \((x_2,y_2)=(1,13.5)\). Then \(m=\frac{13.5 - 12}{1-0}=1.5\).

Answer:

A. \(y = 1.5x+12\)