Chapter 10
For Problems 1-3, use the following information for students in a certain class.
Average weight: 150 poundsSD for weight: 20 pounds
Average height: 68 inchesSD for height: 2.5 inches
Correlation (r): 0.6
1. a) Write the regression equation for weight on height (that is, the line that estimates weight when height is given).
b) Use the equation to estimate the average weight of students who are 64 inches tall.
c) If we randomly select a student and find she is 64 inches tall, what weight should we predict her to have?
2. a) Write the regression equation for height on weight (that is, the line that estimates height when weight is given).
b) Use the equation to estimate the average height of students who weigh 170 pounds.
c) If we randomly select a student and find he weighs 170 pounds, what height should we predict him to have?
3. a) Use the above information to sketch a rough scatter plot of height vs. weight. Plot the point of averages and sketch the SD line.
b) Use your answers from problem 2 to sketch the regression line for weight on height on your scatter plot from a).
c) Use your answers from problem 3 to sketch the regression line for height on weight on your scatter plot from a).
For Problems 4 and 5, use the following information from the first and second exam scores in a college math class.
Average 1st exam score: 60%SD of 1st exam: 10%
Average 2nd exam score: 70% SD of 2nd exam: 15%
Correlation (r): 0.5
4. Predict the second exam scores for students whose first exam scores were
a) 75%
b) 30%
c) 60%
5. Predict the percentile rank on the second exam for students whose percentile ranks on the first exam were
a) 84th
b) 42nd
c) 95th
For Problems 6 and 7, use the following information from a study on fuel efficiency in sedans.
Average age: 6 yearsSD of age: 2 years
Average fuel efficiency: 30 mpg (miles per gallon)SD on efficiency: 4 mpg
Correlation (r): -0.84
6.a) Predict the fuel efficiency of a 10-year old sedan.
b) Predict the age of a sedan which gets 20 miles to the gallon.
c) If a sedan was chosen at random and you were told nothing about its age, what would be your best prediction on its fuel efficiency?
7. a) Predict the age of a sedan which gets 40 miles to the gallon
b) Predict the fuel efficiency of a 1.8-year old sedan.
c) Why didn’t the answer from part b) match up with the 40 mpg in part a)?
For Problems 8 and 9, use the following information froman early-season track practice in which 100 runners were timed for two successive mile runs.
Average 1st mile time: 5:20SD on 1st mile: 0:08
Average 2nd mile time: 5:20SD on 2nd mile: 0:12
Correlation (r): 0.35
8. a) Predict the 2nd mile time for a runner who ran the 1st mile in 5:47.
b) Predict the 2nd mile time for a runner who ran the 1st mile in 5:15.
9.A coach notices that runners who ran the 1st mile slower than 5:20 were likely to run faster on the 2nd mile, while runners who ran the 1st mile faster than 5:20 tended to run their 2nd mile slower than their first. The coach concludes that the runners who ran the 1st mile slower than 5:20 weren’t pushing hard enough and orders them to run another mile. Is the coach’s conclusion valid? Why/why not?
10. A statistician has a backyard garden. Over the years, he notices that the average rainfall during the growing season and his yield of potatoes is positively associated. Historically, the average rainfall at his house has been 18.5” from March to September, with an SD of 0.75”. He gets 40 potatoes on average, with an SD of 5 potatoes (he plants the same number of potatoes each year). He calculates the correlation to be 0.52.
a) One September, he has recorded 20” of rain for the growing season. How many potatoes should he expect to get from his garden this year?
b) During a drier year, he recorded only 16.4” of rain for the growing season. How many potatoes should he expect to get from his garden this year?