Expose marine bacteria to x-rays for time periods from 1 to 15 minutes. Here are the number of surviving bacteria in hundreds on a culture plate after each exposure time.

Time count Time Count

1 355 9 56

2 211 10 38

3 197 11 36

4 166 12 32

5 142 13 21

6 106 14 19

7 104 15 15

8 60

a) What Is the shape of the growth.

b) Since it is a decay model, try to transform the data by taking the logarithm of counts. What happens?

c) What is the least squares regression line of your transformed data?

d) Use an inverse transformation and give the new predicted line

Mammal Heart Weight Length of cavity

Mouse .13 .55

Rat .64 1

Rabbit 5.8 2.2

Dog 102 4

Sheep 210 6.5

Ox 2030 12

Horse 3900 16

Use the power function (logs) to transform the data.

a) What is new least squares regression line?

b) Now do an inverse transformation so as to get in a∙bx form.

A 1969 study among Pima Indians of Arizona investigated the relationship between a mother’s diabetic status and the appearance of birth defects in her children. The results appear below:

Birth Defects

Nondiabetic Prediabetic Diabetic

None 754 362 38

1 or more 31 13 9

a) Find the marginal distributions in counts

b) Compute the conditional distributions (in %’s) of birth defects for each diabetic status.

State whether the following is an example of causation, confounding variables or common response.

a) Over the past 30 years in the US there has been a strong correlation between cigarette sales and the number of high school graduates.

b) A serious study once found that people with 2 cars live longer than people with only 1 car. Owning 3 cars is even better and so on. There is a substantial positive correlation between the # of cars x and the length of life y. What is this an example of , and what lurking variables, if any may exist