A magazine publishes restaurant ratings for various locations around the world.

Question

A magazine publishes restaurant ratings for various locations around the world. The magazine rates the restaurant for food, décor, service & the cost per person. Develop a regression model to predict the price per person, based on a variable that represents the sum of the three ratings. The magazine has compiled a table of this summated ratings variable & the cost per person for 25 restaurants in a major city.

Complete parts A & B.

A. Assuming a linear cost relationship, use the least-squares method to compute the regression coefficients b0 & b1 (round to two decimal places as needed)

b0 = _____ and b1 = _____

B. Predict the cost per person for a restaurant with a summated rating of 70 using the regression coefficients b0 & b1 found in part (a).

i = $____ per person (round to the nearest cent as needed)

Summed Rating Price ($ per person) 54 41 67 51 70 58 69 57 64 42 61 39 52 43 65 40 52 33 47 35 50 40 50 39 75 86 65 55 54 36 48 36 54 33 48 22 55 42 54 44 65 66 63 60 53 28 71 46 69 48

Explanation / Answer

A)

Using technology, we get              

b0 = intercept =    -26.94481567 = -26.94 [ANSWER]
                      
b1 = slope =    1.216013825 = 1.22 [ANSWER]

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B)      
              
Thus, the regression line is              
              
y^ =    1.216013825x   -   26.94481567
              
Thus, if x =    70          
              
Then              
              
y^ =    58.17615207 = 58.18 [ANSWER]          

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