Question

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. Click the icon to view the table of summated ratings and cost per person. a. Construct a scatter plot. Choose the correct graph below. A. B. A Cost ($) 90- A Cost ($) 90- A Cost ($) 90- A Cost ($) 90- . 0 0 0- 0 0- 0 90 90 0 90 0 90 Rating Rating Rating Rating b. Assuming a linear relationship, use the least-squares method to compute the regression coefficients bo and 61: and b1 bo (Round to two decimal places as needed.)

continued table..

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Answer 1

Ʃx =	1478
Ʃy =	1115
Ʃxy =	68207
Ʃx² =	89142
Ʃy² =	54149
Sample size, n =	25
x̅ = Ʃx/n = 1478/25 =	59.12
y̅ = Ʃy/n = 1115/25 =	44.6
SSxx = Ʃx² - (Ʃx)²/n = 89142 - (1478)²/25 =	1762.64
SSyy = Ʃy² - (Ʃy)²/n = 54149 - (1115)²/25 =	4420
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 68207 - (1478)(1115)/25 =	2288.2

a) Scatter plot: Answer B.

Scatterplot 90 80 70 60 50 Y 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 X

b)

y-intercept, b0 = y̅ - (SSxy/SSxx)* x̅ = 44.6 - (2288.2/1762.64)*59.12 = -32.147597 = -32.15

Slope, b1 = SSxy/SSxx = 2288.2/1762.64 = 1.2981664 = 1.30

Regression equation :

ŷ = -32.1476 + (1.2982) x

c)

Answer D.

d)

Predicted value of y at x = 60

ŷ = -32.1476 + (1.2982) * 60 = 45.74

e)

Answer B.