Question

HOW DO YOU FIND B0 AND B1?

A magazine publishes restaurant ratings for various locations around the world. The magazine rates the restaurants for food, decor, service, and the cost per person. Develop a regression model to predict the cost per person, based on a variable that represents the sum of the three ratings. The magazine has compiled the accompanying table of this summated ratings variable and the cost per person for 25 restaurants in a major city. Complete parts (a) through (e) below. B Click the icon to view the table of summated ratings and cost per person. A Cost ($) 90 OB. A Cost ($) 904 OC. A Cost ($) 90- OD. A Cost ($) 90- 011 90 90 90 90 Rating Rating Rating Rating b. Assuming a linear relationship, use the least-squares method to compute the regression coefficients bo and by bo = and b1 = 0 (Round to two decimal places as needed.) Enter your answer in the edit fields and then click Check Answer.

Answer 1

(a)

20 20 40 60 80 Rating 08 09 Cost

The answer is (A)

b)

From the data,

EX = 1481

$\sum Y = 1122$

$\sum X^2 = 89277$

> XY = 68559

$S_{XX} = \sum x^2 - (\sum x)^2/n = 89277 - 1481^2 / 25 = 1542.56$

$S_{XY} = \sum xy - (\sum x \sum y)/n = 68559 - (1481 * 1122)/ 25 = 2091.72$

Slope, b1 = Sxy / Sxx = 2091.72 / 1542.56 = 1.356006

$\bar{X} = \sum X / n = 1481/25 = 59.24$

$\bar{Y} = \sum Y / n = 1122/25 = 44.88$

Intercept, b0 = $\bar{Y}$ - b1 $\bar{X}$ = 44.88 - 1.356006 * 59.24 = -35.4498

b0 = -35.45

b1 = 1.36