Probability & Statistics Honors

Unit Test #4

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1.

In the mid-1990s, data concerning the size (carets) and price (dollars) for small diamonds were used to establish the following model:

price ^ =259.63+3721.02 size

The residual for a particular diamond was $410.1586. If the size of that diamond was 0.18 carets, what was the actual price?

(4)

The predicted price for that diamond was $ 259.63+3721.02 0.18 410.1536; since residual=observedpredicted , 410.1586=observed410.1536 observed=410.1586+410.1536 =820.3122 dollars.

 

An Image

2.

Researchers at Brigham Young University collected many body measurements from participants in a study. A graph of some of the data is shown above.

Identify and classify any unusual points in the plot.

(3)

The point near 125,130 has leverage; the point near 149,135 is influential.

 

3.

An analyst obtained data from a random sample of household electric bills, and found the following relationship between the amount of the bill (dollars) and the average temperature (°F) for the month:

bill ^ =185.221.5674 temperature

Use this model to predict the bill in a month where the average temperature was 65°F.

(3)

185.221.5674 65 =83.339 dollars.

 

A paper in the American Journal of Physical Anthropology provided some measurements of several skeletons—the length of the metacarpal bones in the palm (cm), and the height (cm). A portion of the collected data is given below.

Palm

45

51

39

41

48

49

46

43

47

Height

171

178

157

163

172

183

173

175

173

Use this information for all other questions on this test.

 

4.

Construct a model useful for predicting the height of a skeleton from the length of the metacarpal bones.

(4)

height ^ =94.428+1.7 palm

 

5.

Interpret the slope of your equation from [4].

(4)

For each additional centimeter of metacarpal length in the palm, the model predicts an average increase of 1.7 cm in height.

 

6.

Interpret the y-intercept of your equation from [4].

(4)

When the length of the metacarpals in the palm are zero cm, the model predicts an average height of 94.428 cm.

 

7.

Calculate and interpret the coefficient of determination for these data.

(4)

r 2 =0.7327; about 73.27% of the variation in height can be explained by a linear relationship with metacarpal length of bones in the palm.

 

8.

Predict the height of a skeleton with 44 cm metacarpal bones.

(3)

94.428+1.7 44 169.2116 cm

 

9.

Would it be appropriate to use this model to predict the metacarpal length for a skeleton that is 185 cm tall?

(3)

No—this model can only be used to predict height.

 

10.

Construct a residual plot for these data.

(5)

An Image

 


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