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 (c) 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. i Surimated Ratings and Cost Per Person ОА. Costs OB. Cost (5) 907 nated Rating Cost ($ per person) 6.8 50 65 Rating Rating b. Assuming a linear relationship, use the least-squares method to compute the regression coefficients bo and by 65 bo= and by=0 (Round to two decimal places as needed.) 48 Saal Na Enter your answer in the edit fields and then click Check Answer.

Answer 1

b) y_pred= -31.463 + 1.301x b0= -31.463 b1= 1.301 a) B) Scatter plot $1588562733491_blob.png$Calculation: independent variable or explanatory variable is X and dependent variable or study variable is Y.In order to compute the regression coefficients, the following table needs to be used: x y xy x^2 y^2 55.0 40.0 2200.0 3025.0 1600.0 68.0 50.0 3400.0 4624.0 2500.0 67.0 60.0 4020.0 4489.0 3600.0 65.0 59.0 3835.0 4225.0 3481.0 63.0 45.0 2835.0 3969.0 2025.0 57.0 39.0 2223.0 3249.0 1521.0 54.0 42.0 2268.0 2916.0 1764.0 65.0 40.0 2600.0 4225.0 1600.0 52.0 33.0 1716.0 2704.0 1089.0 47.0 31.0 1457.0 2209.0 961.0 54.0 43.0 2322.0 2916.0 1849.0 49.0 37.0 1813.0 2401.0 1369.0 74.0 85.0 6290.0 5476.0 7225.0 62.0 54.0 3348.0 3844.0 2916.0 53.0 38.0 2014.0 2809.0 1444.0 47.0 33.0 1551.0 2209.0 1089.0 55.0 33.0 1815.0 3025.0 1089.0 45.0 23.0 1035.0 2025.0 529.0 58.0 43.0 2494.0 3364.0 1849.0 54.0 45.0 2430.0 2916.0 2025.0 64.0 65.0 4160.0 4096.0 4225.0 62.0 62.0 3844.0 3844.0 3844.0 55.0 26.0 1430.0 3025.0 676.0 74.0 49.0 3626.0 5476.0 2401.0 68.0 47.0 3196.0 4624.0 2209.0 sum 1467.0 1122.0 67922.0 87685.0 54880.0 Based on the above table, the following is calculated: n xbar = Σ(xi)/n = 1467.0/25 = 58.68 i=1 n ybar = Σ(yi)/n = 1122.0/25 = 44.88 i=1 n n n SS_xy= Σ xiyi -( Σxi * Σyi)/n = 67922.0-(1467.0)(1122.0)/25 = 2083.04 i=1 i=1 i=1 n n SS_xx= Σ(xi^2) -( Σ(xi)^2)/n = 87685.0-1467.0^2/25 = 1601.44 i=1 i=1 n n SS_yy= Σ(yi^2) - ( Σ(yi)^2)/n = 54880.0-1122.0^2/25 = 4524.64 i=1 i=1 Therefore, based on the above calculations, the regression coefficients are obtained as follows: ^ b_1=SS_xy/SS_xx = 2083.04/1601.44 = 1.301 b_0=ybar-xbar*b_1 = 44.88-58.68*1.301 =-31.463 The terms b_0 and b_1 are the parameters of the model. The parameter b_0 is termed as intercept term and the parameter b_1 is termed as slope parameter. These parameters are usually called as regression coefficients. y_pred=b_0+b_1*x Therefore, we find that the regression equation is y_pred= -31.463 + 1.301x Graphically We show that y_predicted line or Regression line 

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