# Calculate the residual for the 3rd observation.

1.True or False. When the correlation coefficient is zero, it means that the two variables are not related in any way.

(a)True

(b)False

2.True or False. The residual plot should show an approximate linear relationship if the linear regression model is appropriate.

(a)True

(b)False

3.Consider the following scatterplot for a hypothetical set of exam scores.

Fill in the blank. The observation marked “Point A” is called __ .

(a)an outlier with respect to the regression line

(b)an influential point

(c)a residual

4.Fill in the blank. The point (,) __ falls on the least squares regression line.

(a)never

(b)sometimes

(c)always

5.A correlation coefficient MUST fall between and .

1. The correlation coefficient and the slope of the regression line ALWAYS have the same sign.

(a) True

(b) False

Questions 7 through 9 refer to the following scenario.

In the following three exercises, you will be comparing outliers.

Construct a scatterplot for the following data.
Observation Number

1

2

3

4

5

6

7

8

9

10

X

5

6

5

8

7

9

6

6

8

2

Y

1

2

2

4

3

5

3

2

5

8

Now construct a scatterplot for these data.
Observation Number

1

2

3

4

5

6

7

8

9

10

X

1

5

6

5

3

3

7

8

9

9

Y

8

6

4

5

7

8

2

2

1

9

9.Identify the points that are outliers for each one. Which of these outliers would be more influential in determining the regression line?

Questions 10 through 14 refer to the following scenario.

In the hope of preventing ecological damage from oil spills, a biochemical company is developing an enzyme to break up oil into less harmful chemicals. The table below shows the time it took for the enzyme to break up oil samples at different temperatures. The researcher plans to use these data in a regression analysis from predicting the time to break up from the oil temperature.

Observation Number

1

2

3

4

5

6

Oil Temperature (°C)

3

10

15

21

33

37

Time to Break up (seconds)

165

98

65

62

26

9

10.Draw the scatterplot. Be sure to label your axes.

11.Give the least squares regression line for regressing time to break up on oil temperature.

12.The average annual water temperature in Alaskan waters is 4°C. How long would the enzyme take to break up oil under these circumstances?

13.The company claims that even when water temperatures are as low as –5°C, the enzyme will break up oil in less than 3 minutes. Briefly comment on the validity of this claim.

14.Calculate the residual for the 3rd observation.