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?
