Scatter Plot for Cat Food Brand and Cost of Cat Food

Question 6: House cat owners invest a lot of time and expense to find just the right cat food for their finicky, spoiled and pampered pets. Some house cat owners believe that the reaction of the house cat, in terms of how much time passes between the serving of the food and the point at which the finicky, spoiled and pampered house cat actually starts dining, can be a good indicator of how the food was accepted by the house cat. Recently, my wife conducted an experiment with our female house cat (very, very finicky - different than male who eats anything/everything). She wanted to see if expensive foods would be accepted more quickly by the female than inexpensive foods. Cat Food Brand Cost of Cat Food ($) - X Time to Accept (Minutes) - Y

Fake Fish $1.00 18
Plain Fish $2.00 15
Fancy Fish $3.00 11
Gourmet Fish $5.00 9
Eau de Fische $6.00 5

a. Do a Scatter Plot of this data and label the axes.

b. Assume you've computed r using the formula on page 435, and r = - 0.60 (NOTE: DO NOT compute r yourself, instead use the assumed value of r = - 0.60 for parts b. and c. of this problem). What amount of variation (percent) in the Time to Sccept is explained by the variation in the cost of the cat food, and what amount of variation (percent) is not explained.
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c. Compute the Corrected Coefficient of Determination, r 2 , for the linear regression equation
model, using the r-value shown in part b. and assuming n = 5: {r 2 = r 2 - [1 - r 2 ][(k - 1)/(n - k)]}.

d. Assume that my wife has me derive the following linear regression model for the Cost of Cat Food - Time to Accept data described above, what do Y' and X refer to in the context of this equation.

Y' = 21 - 2.80X (NOTE: Use this equation, do not derive your own)

e. My wife decides to try a new brand of cat food, La Creame de la Mar, which costs $4.00. Using the above regression model in part d., what is the predicted time to accept for this brand.

f. If the actual time to accept for this brand is 2 minutes, explain why (in terms of increasing the explained variation, relative to the total variation) multiple regression might be a better choice to model this problem, and describe two additional and relevant predictor variables that could be used.