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 b_{1}.
c) Identify SSE, and s.
d) Identify the t statistic for testing H_{o}: β_{1} = 0.
e) Identify the p-value for testing the independent variable.
f) Identify the 95% confidence interval for β_{1}.