spss统计辅导、统计学spss辅导、Data and Models Project

Directions: For the following functions, determine the line of best fit. Use your calculator and

look at the scatterplot to help you guess what type of function would be the best fit for each

example. Print this sheet and write your answers on it. Then scan the document and drop it into

the Dropbox on D2L. The project is due April 23 at 11:30 p.m. No late projects will be accepted.

1. What is the optimal amount of time for a scuba diver to be on the bottom of the ocean?

That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic.

The Navy defense's “optimal time” to be the time at each depth for the best balance between

length of work period and decompression time after surfacing. Let x = depth of dive in meters,

and let y = optimal time in hours. A random sample of divers gave the following data:

(a) Determine the least-squares line of best fit for the data (use linear regression).

(b) If the dive is 18 meters, what is the optimal time predicted by the equation in part (a)?

2. In 1990, a total of $557 billion was spent on food and drinks in the U.S. In 2003, the total

spent was $947 billion.

(a) Find the equation of the exponential function that models the total spent on food and

drinks in the U.S. As a function of the number of years since 1990.

(b) Use the model from part (a) to predict the amount spent in 2000.

Moody, S18 Project, 581.odt Page 1 of 3

x 14.1 24.3 30.2 38.3 51.3 20.5 22.7

y 2.58 2.08 1.58 1.03 0.75 2.38 2.2

Data and Models Project

3. In 1940, there were 6,102,000 farms in the United States. By 2004, the number of farms

was down to 2,113,000.

(a) Find the equation of the exponential function to model the number of farms after

1940.

(b) Use the model to predict the number of farms in 2010.

4. The following table gives the takeoff weights, in thousands of pounds, of various jet

liners and their wingspans, in feet.

(a) Use your calculator to find a power function that fits this data.

(b) The Boeing 777 has a wingspan of 200 feet. What is its maximum takeoff weight?

(c) If the maximum takeoff weigh of a plane is 450 thousand pounds, what is its wingspan?

Moody, S18 Project, 581.odt Page 2 of 3

Airplane W = Weight S = Wingspan

Boeing 707 330 145.7

Boeing 727 209.5 108

Boeing 737 117 93

Boeing 747 805 195.7

Boeing 757 300 156.1

DC8 350 148.5

DC9 121 93.5

DC10 572 165.4

Data and Models Project

5. The use of automobiles has sparked immune changes in human culture, both for good and

for bad. The following table shows the growth in the number of cars produced throughout the

world, in millions, in various years since 1950.

Determine the line of best fit. (It could be a linear, exponential, or power function.)

Moody, S18 Project, 581.odt Page 3 of 3

Year 0 10 20 25 30 35 40 45 50 55

Cars 8 13 23 25 29 32 36 36 41 46