Homework # 6 - MATH 2227
The problems on this homework must be done alone. The honor code is in effect.
First name: Last name:
1. Data set A has a correlation coefficient of 0.7. Data set B has a correlation coefficient of -0.9. Which data set has a stronger linear correlation?
a. A
b. B
c. They both have the same linear correlation.
d. It's impossible to tell from the given information.
2. A data set has a correlation coefficient of -0.9. When we plug x = 3, we get \(\hat{y} = 10.\) If we plug in x = 5, we will find that
a. \(\hat{y} > 10.\)
b. \(\hat{y} < 10.\)
c. \(\hat{y} = 10.\)
According to the U.S. EPA, the average real-world fuel economy of new cars in the sedan/hatchback category for five model years is given by the following table:
Let x represent time in years since 2015 and let y represent the average fuel economy for sedans/hatchbacks in miles/gallon.
3. According to the above table, find y when x = 3.
a. 29.0
b. 30.2
c. 30.8
d. 30.9
d. 32.0
4. Compute the correlation coefficient r.
a. -.855
b. .855
c. .920
b. .966
c. 1
5. What percentage of the response variable y can be explained by the variable x?
a. 85.5\(\%\)
b. 93.4\(\%\)
c. 96.6\(\%\)
d. 98.1\(\%\)
d. 100\(\%\)
6. Find the regression line (remember in 2015, x = 0).
a. \(\hat{y} = 29.24 + .67 x\)
b. \(\hat{y} = 29.04 + .67 x\)
c. \(\hat{y} = 29.24 + .71 x\)
d. \(\hat{y} = 29.04 + .71 x\)
7. Use your line to predict the average fuel economy in 2022.
a. 33.7 miles/gallon
b. 33.9 miles/gallon
c. 34.0 miles/gallon
d. 34.1 miles/gallon
d. 34.2 miles/gallon