showing data not to be linear, expo.; finding log model

[higher]

1. The average length of a girl t months after birth is shown in the accompanying table.

+---------------+----+----+----+----+----+
| Age in months |  4 | 10 | 18 | 27 | 35 |
+---------------+----+----+----+----+----+
|  Length (cm)  | 62 | 72 | 81 | 89 | 95 |
+---------------+----+----+----+----+----+

A) Show why the data is neither linear or exponential by showing the change for the model.

For linear: Show what the slope is between all successive ordered pairs: (Calculate the four slopes).

For exponential: Show what the percent change is between ordered pairs: (Calculate the four percentage changes between the pairs).

B) Find a log function to fit the data:

c) What is the estimated length from the model for an average 3 year old? Use the conversion 1 cm : 0.394 inches.

d) Does this model adequately describe the length for very young girls (that is, near birth, as in newborns)? Explain (Use 1 cm = 0.394 inches in discussing the problem)

Assume in your discussion that in the U.S, the average length of a newborn baby girl is 19.7 inches. What does this mean in terms of the model?

 

[stapel]

The instructions are fairly straightforward. Where are you stuck?

A) Just follow the instructions. Find the slopes between the pairs of consecutive points. Then find the percentage increase or decrease in the same pairs.

Are the slopes between each pair of consecutive points at least roughly the same, or not? So is it linear, or not?

The points (ages) are evenly spaces, so exponential growth, by definition, would require a consistent percentage change. Are the changes at least roughly the same, or not? So is it exponential, or not?

B) Use whatever regression technique they gave you in class. (There are different ones, including the "plug the points into a calculator and do stuff in STAT mode".)

C) Plug the given age into the model you created in (B), and copy down the result.

D) What do you get when you plug "0" in for the age? Or "1", or maybe "0.5" (half a month, or about two weeks). Does this reflect what you've seen in real life?

E) How does (months, length) = (0, 19.7") = (0, 50cm) compare with your model's prediction?

If you get stuck, please reply showing everything you have tried, starting with the slopes and percentages you computed.

Thank you.

Eliz.

 

[higher]

this is my effort.could you please check again? thx..

A(4,62) B(10,72) C(18,81) D(27,89) E(35,95)

A) Show why the data is neither linear nor exponential by showing the change for the model: For linear-show what the slope is between all successive ordered pairs: (Calculate the 4 slopes)

slopes:
m of AB= 1.67
m of BC= 1.125
m of CD= 0.89
m of DE= 0.75

For exponential-show what the percent change is between ordered pairs:
(Calculate the 4 percentage changes between the pairs)

% of change:
% of change of AB: 16%
% of change of BC: 12.5%
% of change of CD: 9.88%
% of change of DE: 6.74%

Based on the calculation above where the slopes between each pair of consecutive points are not roughly the same. The points (ages) are evenly spaces, so exponential growth, by definition, would require a consistent percentage change. But in fact the changes in percent are not consistent. So, the data is neither linear nor exponential by showing the change for the model.

B) Find a log function to fit the data:

Input List: Y(X) = 39.410+15.0366ln x Model:??????

Can you help me explain what the model mean?
What should I do with the model? Draw a graph?

c) What is the estimated length from the model for an average 3 year old?
Use the conversion 1 cm= 0.394 inches.

In centimeter: 55.93 in inches: 22.036


d) Does this model adequately describe the length for very young girls
(that is, near birth, as in newborns)? Explain (Use 1 cm = 0.394 inches in discussing the problem)

Y(X) = 39.410+15.0366ln x
As an example when I plug “1”, or maybe “0.5” (half a month, or about two weeks)
Y (1) = 39.41
Y (0.5) =28.99


Based on the example above, the model is not very good for very young girls. This model doesn’t reflect as what I have seen in the real life.


Assume in your discussion that in the U.S, the average length of a newborn Baby girl is 19.7 inches. What does this mean in terms of the model?

(Months, length) = (0, 19.7”) = (0, 50cm)
If a girl is 19.7 according to the model, she has a negative model.

Is my answer above is right?
I am not really good in interpretation, could you please help me?
Thank you very much with your help.
I really appreciate it.