A cake shop invited 50 customers to taste its 50 chocolate cakes. Each cake has different combination of % chocolate and % suger. Each customer then rate the cake he/she tasted (score range: 0-100, the higher score, the better taste). The information of the 50 customers and cakes they tasted are listed in the following data table.

a. Develop an estimated multiple regression equation. Use taste rating as dependent variable and % Chocolate, % suger, and Rater's gender (Code female as 0, Male as 1) as independent variables.

b. What is the r2 and adjusted r2?

c. Perform a test to indicate whether rater's gender is a significant factor in the taste rating. Use alpha=0.05. State your hypotheses, test statistic, and results.

d. Perform a test to indicate whether the multiple regression model is overall significant. Use alpha=0.05. State your hypotheses, test statistic, and results.

e. What is the taste rating of a cake with 34% of chocolate and 28% of suger, and tasted by a male?

Sample# % Chocolate in Cake % Sugar in Cake Taste Rating Rater's Gender Rater's Gender 29 19 61 0 Female 30 16 50 Male 3 18 26 Male 18 21 60 Male 19 25 73 Male LO OO V O UT A W NI 28 24 84 Female 48 17 95 Female 15 21 59 Female 14 11 50 Female 10 1 17 60 Male OHHOHOOO 11 22 16 67 Female 12 15 25 65 Male 13 10 25 50 Male 14 40 20 95 Female 24 11 60 Female 15 16 50 17 92 Male 17 39 14 87 Male 18 1 22 41 Female Female 19 9 15 43 20 4 16 29 Male 21 12 13 47 Male 6 12 35 Male 22 23 8 18 40 Male 24 24 10 67 Female 14 94 Male 25 34 26 2 25 39 Female 27 40 20 89 O Female 28 1 13 69 Male 24 15 69 Female 29 o o Female 30 9 16 51 31 33 11 70 Male 21 17 67 Male 32 Male 33 25 25 82 17 10 Male 34 52 35 34 21 53 Male 36 11 16 35 Male 37 7 14 40 Female 38 6 24 52 Male 45 93 Male 39 20 40 4 14 31 Male 50 Male 41 15 82 42 9 21 58 Male 43 35 25 93 Male 44 29 12 70 Female - O 45 36 21 96 Male 46 21 16 59 Male 47 30 21 86 Male Male 48 40 17 98 3 17 36 Male 49 50 1 24 45 Female