Zagat restaurant guides publish ratings of restaurants for many large cities around the world (see www.zagat.com). The review for each restaurant gives a verbal summary as well as a 0- to 30-point rating of the quality of food, décor, service, and the cost of a dinner with one drink and tip. For Italian restaurants in London in 2007, the food ratings had a mean of 20.46 and standard deviation of 2.70. The cost of a dinner (in U.S. dollars) had a mean of $79.76 and standard deviation of $20.54. The equation that predicts the cost of a dinner using the rating of the quality of food is ŷ = 2.5 + 4.0x. The correlation between these two variables is 0.53.
a. Predict the cost of a dinner in a restaurant that gets the (i) lowest possible food quality rating of 0, (ii) highest possible food quality rating of 30.
b. Interpret the slope.
c. Interpret the correlation.
d. Show how the slope can be obtained from the correlation and other information given.