4.2 Homework

1.   At the final exam in a statistics class, the professor asks each student to indicate how many hours he or she studied for the exam. After grading the exam, the professor computes the least-squares regression line for predicting the final exam score from the number of hours studied. The equation of the line is y=50+5x

(a) Antoine studied for 4 hours. What do you predict his exam score will be?

(b) Emma studied for 2  hours longer than Jeremy did. How much higher do you predict Emma’s score to be?

2.  Price of eggs and milk: The following table presents the average price in dollars for a dozen eggs and a gallon of milk for each month from March through December 

2005 . Use a TI-84  calculator to answer the following.

Compute the least-squares regression line for predicting the price of milk from the price of eggs. Round the slope and y-intercept to at least four decimal places.

If the price of eggs differs by $0.25 from one month to the next, by how much would you expect the price of milk to differ? Round your answer to at least two decimal places.

Predict the price of milk in a month when the price of eggs is $1.67. Round the answer to two decimal places.

3.   Butterfly wings: Do larger butterflies live longer? The wingspan (in millimeters) and the lifespan in the adult state (in days) were measured for 10 species of butterfly. Following are the results.

(a) Compute the least-squares regression line for predicting the lifespan from the wingspan. Round the slope and y -intercept to four decimal places as needed.

(b) Is it possible to interpret the y-intercept? Explain.

(c) If the wingspans of two butterflies differ by 3 millimeters, by how much would you predict their lifespans to differ? Round the answer to two decimal places as needed.

(d) Predict the lifespan for a butterfly whose wingspan is 29  millimeters. Round the answer to two decimal places as needed.

4.  Interpreting technology: The following display from the TI-84 Plus calculator presents the least-squares regression line for predicting the price of a certain stock 

y from the prime interest rate in percent x.

Write the equation of the least-squares regression line. Use the full accuracy shown in the calculator output (do not round your answers).

What is the correlation between the interest rate and the yield of the stock?

Predict the price when the prime interest rate is 6%. Round the answer to at least four decimal places.