Question

a restaurant sells pizza for the prices in the data table. calculate the linear regression equation of the data.
options:
y = 12x + 1.5
y = 0.67x - 8
y = 1.5x + 12
y = -8x + 0.67

Explanation:

Step1: Analyze the context

The problem is about calculating the linear regression equation for pizza prices. Linear regression is a statistical method, so we'll use the subfield of Statistics (under Mathematics) to solve this. First, we need to recall that a linear regression equation is in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y - intercept.

Step2: Evaluate the slope and intercept logic

For a real - world situation like pizza prices (where as the size or number of pizzas (x) increases, the price (y) should increase, so the slope \( m \) should be positive. Let's analyze the options:

• Option 1: \( y = 12x+1.5 \): The slope of 12 is very steep. If x increases by 1, y increases by 12, which is too large for a pizza price increase.
• Option 2: \( y = 0.67x - 8 \): A negative y - intercept (-8) doesn't make sense for a price (you can't have a negative price when x = 0, like the price of 0 pizzas can't be negative).
• Option 3: \( y=1.5x + 12 \): The slope of 1.5 is a reasonable rate of increase for pizza prices, and the y - intercept of 12 could represent a base price (like a delivery fee or base cost of a small pizza), and as x (number of pizzas or size) increases, the price increases by 1.5 per unit of x.
• Option 4: \( y=-8x + 0.67 \): The negative slope (-8) implies that as x increases, y decreases, which doesn't make sense for pizza prices (more pizzas or larger pizzas should cost more, not less).

Answer:

C. \( y = 1.5x + 12 \) (assuming the options are labeled A: \( y = 12x + 1.5 \), B: \( y = 0.67x-8 \), C: \( y = 1.5x + 12 \), D: \( y=-8x + 0.67 \))