Probability & Statistics Honors

Unit Test #4

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1.

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

The residual for a particular month was -$44.7909. If the average temperature that month was 32.5°F, what was the amount of the electric bill?

(4)

When the average temperature is 32.5, the predicted bill is 134.2795. The residual is observedexpected, so 44.7909=observed134.2795 observed=134.279544.7909 =89.4886 dollars.

 

An Image

2.

Researchers in California 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 circled point near 75,110 has leverage and appears to be an outlier (making it influential); the circled point near 72,129 is an outlier.

 

3.

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

Use this model to predict the price of a 0.3 caret diamond.

(3)

price ^ =259.63+3721.02 0.3 856.676 dollars.

 

Statistics from a sample of Major League Baseball players were collected during the 1992 season. A portion of the collected data is given below.

Runs

74

32

87

16

102

6

0

39

4

65

58

41

21

46

88

Hits

129

51

169

26

163

25

3

64

8

144

144

55

56

106

188

Use this information for all other questions on this test.

 

4.

Construct a model useful for predicting the number of runs a player had from the number of hits.

(4)

The least squares regression model is runs ^ =0.9974+0.4989 hits .

 

5.

Interpret the slope of your equation from [4].

(4)

For each additional hit a player has, the model predicts an average increase of 0.4989 runs.

 

6.

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

(4)

When a player has zero hits, the model predicts an average of 0.9974 runs.

 

7.

Calculate and interpret the coefficient of determination for these data.

(4)

r 2 =0.92003; about 92% of the variation in the number of runs can be explained by a linear relationship with the number of hits.

 

8.

Predict the number of runs for a player with 75 hits.

(3)

runs ^ =0.9974+0.4989 75 38.41507

 

9.

Would it be appropriate to use this model to predict the number of hits for a player with 110 runs?

(3)

No. This model can only be used to predict runs from the number of hits.

 

10.

Construct a residual plot for these data.

(5)

An Image

 


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