**Section **9.1

1. R value 0.834 and r value -0.925

-0.925 represents the stronger correlation, the correlation coefficient ranges from negative one to positive one, a correlation coefficient value of -1 means that there is strong negative correlation, the correlation coefficient +1 means that there is strong positive correlation, given that -0.925 is close to the value -1 than how 0.834 is close to value one then -0.925 represents the stronger correlation.

2. Correlation coefficients:

From the above discussion the correlation coefficient ranges from negative one to positive one, therefore a value less than -1 or greater than the value 1 cannot represent the correlation coefficient value. The value zero on the other hand indicates that the two variables considered are not correlated, therefore as the correlation coefficient approaches zero then the weaker the relationship between variables.

Exercises 14;

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*Section* 9.1

Identify the explanatory variable (independent variable) and the response variable (dependent variable):

Explanatory and response variable:

The explanatory variable can also be referred to as the independent variable; the response variable can also be referred to as the dependent variable.

Section 9.2:

Exercises 13:

The data below is provided:

Height, x

Stories, y

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Section 9.1

764

55

625

47

520

51

510

28

492

39

484

3/16

Section 9.1

34

450

33

430

31

410

40

The estimated model using excel is stated as:

Y = 7.5345+ 0.0619x

The following is the scatter diagram:

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Section 9.1

The following table summarizes the predicted values:

x

y predicted

a

500

38.4845

b

650

47.7695

c

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*Section *9.1

310

26.7235

d

725

52.412

Exercises 14:

The following data is provided:

Age, x

Vocabulary sixe, y

3

6/16

*Section *9.1

1100

4

1300

4

1500

5

2100

6

2600

2

460

7/16

Section 9.1

3

1200

The estimated model using excel is Y = -504.47 + 510.79 X

The following is the scatter diagram

The r squared value is 0.9657 and this indicates a very strong correlation between the variables, this value means that 96.575 of deviations in vocabulary are explained by age. Therefore this model can be used to predict.

The following table summarizes the predicted values:

coefficient

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Section 9.1

a

-504.47

x

510.79

9/16

Section 9.1

x

Y estimated

a

2

517.11

b

3

1027.9

c

10/16

__Section __9.1

6

2560.27

d

12

5625.01

Section 9.3:

Correlation of determination:

5. R = 0.350

R2 = 0.35 * 0.35 = 0.1225

The correlation of determination in this case is 0.1225, this value means that the independent variable explains 12.25% of deviations of the dependent variable, the unexplained **deviations** is therefore 87.75%.

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Section 9.1

6. R = -0.275

R2 = -0.275 *- 0.275 = 0.075625

The correlation of determination in this case is 0.075625, this value means that the independent variable explains 7.56% of deviations of the dependent variable, the unexplained deviations is therefore 92.44%.

Section 9.4:

Multiple regressions:

y=640 – 0.105×1 + 0.124×2

The table below summarizes the predicated values:

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**Section **9.1

coefficient

a

640

x1

0.105

13/16

Section 9.1

x2

0.124

x1

x2

14/16

Section 9.1

y predicted

a

13500

12000

3545.5

b

15000

13500

3889

c

14000

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Section 9.1

13500

3784

d

14500

13500

**3836**.5

From the *above* the predicted values for x1 and x2 values are indicated in the y predicted column.

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