Chapter 3 Review
1. A random sample of size 23 was taken of the houses sold in Colorado Springs, Colorado for one month. This scatterplot shows the selling price (in thousands of dollars) versus the area or square footage of the house.
a. Identify the explanatory and response variables.
b. Describe the association between the variables.
c. Estimate the correlation coefficient.
2. Researchers are interested in determining if a larger fat content in cereals results in a higher caloric value as well. Here are the fat and calorie content for one serving of seven different cereals:
Fat (g) / 5 / 3 / 3 / 1 / 0 / 2 / 1Calories / 130 / 150 / 140 / 90 / 110 / 140 / 130
a. Find the equation of the least-squares regression line. Define any variables you use.
b. Interpret the slope and y-intercept in context of the situation.
c. What is the predicted number of calories in one serving of a cereal that contains 4 grams of fat?
d. Calculate the residual for the cereal that contains 5 grams of fat per serving.
e. Find and interpret r2 in context.
3. Below is the regression analysis for diameter (in inches) versus age (in years) for 25 oak trees.
a. Find the equation of the regression line.
b. Interpret the slope of the regression line in the context of this problem.
c. Find and interpret the value of the correlation coefficient.
d. Find and interpret the correlation.
e. Find and interpret the value of s.
4. Data on fuel consumption (in gallons per hour) and average speed (in miles per hour) for a sample of 27 commercial aircraft yielded the regression line y = -5465.5 + 15.50 x as well as the residual plot below.
What does the residual plot tell you?