An individual wanted to determine the relation that might exist between speed and miles per gallon of an automobile. Let X be the average speed of a car on the highway measured in miles per hour and let Y represent the miles per gallon of the automobile. The following data is collected:
|
X
|
50
|
55
|
55
|
60
|
60
|
62
|
65
|
65
|
|
Y
|
28
|
26
|
25
|
22
|
20
|
20
|
17
|
15
|
a. In the space below, draw a scatterplot of the bivariate data set.
b. What is the value for r? Interpret this value, would you say that the correlation is positive or negative? Strong or Weak? How do you know?
c. From the regression equation given above, what value is the slope of the line? Interpret this slope, what does it tell us about the relationship between average speed and miles per gallon?
d. Predict the miles per gallon of a car traveling 63 miles per hour.
e. Predict the average speed of a car whose fuel mileage is 23 miles per gallon.
f. Find r squared. What does this statistic tell us about between average speed and miles per gallon?