In the early 1990s researchers at The Ohio State University studied consumer ratings of six fast-food restaurants: Borden Burger, Hardee's, Burger King, McDonald's, Wendy's, and White castle.  Each of 406 randomly selected individuals gave each restaurant a rating of 1, 2, 3, 4, 5, or 6 on taste, convenience, familiarity, price and preference.  In all cases, 1 was the best rating and 6 the worst rating. The mean ratings given by the 406 individuals are given below:

                             Mean     Mean     Mean     Mean     Mean

     Restaurant     Taste     Conv.    Famil.    Price      Pref.

     Borden Burger 3.5659  2.7005  2.5282  2.9372       4.2552

     Hardee's        3.3290  3.3483  2.7345  2.7513  4.0911

     Burger King    2.4231  2.7377  2.3368  3.0761  3.0052

     McDonald's    2.0895  1.9380  1.4619  2.4884  2.2429

     Wendy's         1.9661  2.8920  2.3376  4.0814  2.5351

     White Castle  3.8061  3.7242  2.6515  1.7080  4.7812      

Question

a) Perform a simple linear regression analysis of this data where 'mean preference' is the dependent variable and 'mean taste' is the independent variable.

b) Identify the least squares point estimates b_o and b₁.

c)  Identify SSE, and s.

d) Identify the t statistic for testing H_o: β₁ = 0.

e) Identify the p-value for testing the independent variable.

f) Identify the 95% confidence interval for β₁.