Question

A restaurant sells pizza for the prices in the data table. Calculate the linear
regression equation of the data.*

Answer 1

Answer:

y = 1.5x + 12

Step-by-step explanation:

Let the equation that represents the number of toppings (x) and price of pizza (y) is,

y = mx + b

If we plot the points given in the table,

m = Slope of the line

b = y-intercept

Since, slope of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by,

m = $\frac{y_2-y_1}{x_2-x_1}$

Therefore, slope of a line passing through (0, 12) and (1, 13.5) will be,

m = $\frac{13.5-12}{1-0}$

m = 1.5

Here slope of the line represents the increase in price of a pizza with increase in each topping.

y-intercept of the line 'b' = 12 (For x = 0)

Now we put these values in the equation.

y = 1.5x + 12

Therefore, linear regression equation of the line is,

y = 1.5x + 12

Answer 2

The linear regression equation of the restaurant pizza sales is $\^y = 1.5\^x + 12$

To do this, we make use of a graphing calculator.

From the graphing calculator, we have:

• Sum of X = 21
• Sum of Y = 115.5
• Mean X = 3
• Mean Y = 16.5
• Sum of squares (SSX) = 28
• Sum of products (SP) = 42

A linear regression equation is represented as:

$\^y = b\^x + a$

Where:

$b =\frac{ SP}{SSX}$

So, we have:

$b = \frac{42}{28}$

$b = 1.5$

Also, we have:

$a = MY - bMX$

So, we have:

$a = 16.5 - (1.5 \times3)$

$a= 12$

Recall that:

$\^y = b\^x + a$

So, we have:

$\^y = 1.5\^x + 12$

Hence, the linear regression equation is $\^y = 1.5\^x + 12$

Read more about linear regression at:

https://brainly.com/question/25987747