A study has been undertaken to assess the degree of racial prejudice in a random

ID: 3228786 • Letter: A

Question

A study has been undertaken to assess the degree of racial prejudice in a randomly selected sample of 21 people. Two independent variables have been isolated.

AGE: is the person's age in years.

STATUS: is the person's "index of social and economic status". The norm for this index is 100. Someone very poor and with practically no social status might have an index score of, say, 10. A person with a high income and high social status might have a score of 192.

PREJ: is the degree of racial prejudice as measured by a test. (this is the dependent variable)

Use Excel to perform a Multiple Regression analysis

Answer the following questions.

a. How well does the data fit your regression model? Why?

b. Is there a relationship between the independent variables and the dependent variable? Why?

c. The Correlation of the independent variables is given by Excel:
                   age                status
age           1
status -0.42307707            1
Are there any potential problems with multicollinearity? Why?
Are you surprised at this? Carefully explain why.

d. What is the estimated regression equation?

e. What would be the estimated degree of prejudice for a person whose age is 47 and status is 100?

f. Is the coefficient of the age variable significant in determining prejudice?

g. Interpret the coefficient for the variable age? Are you surprised that it is negative? Explain why.

h. Do the residuals indicate anything unusual? Why?

PREJ AGE STATUS 80 23 135 86 30 170 48 38 82 40 30 77 66 19 72 64 23 122 94 17 159 32 70 68 48 51 129 32 31 67 88 21 129 76 22 126 52 33 53 40 31 75 76 22 123 14 65 43 62 26 153 40 38 79 72 22 116 60 29 91 76 52 133

Explanation / Answer

Part-a

R-square=0.7994 which means that age and status explained 79.94% of variability in degree of racial prejudice. Also ANOVA F-test was significant with p<0.05. Hence, data fit the regression model well.

Part-b

The coefficient of age is significant with p-value=0.004<0.05 and also coefficient of status is significant with p-value=0.00002<0.05. So there exists a relationship between the independent variables and the dependent variable.

Part-c

As there is high correlation between age and status so there is a problem of multicollinearity. We are not surprised as person's "index of social and economic status" depends on his age

Part-d

The estimated regression equation is

PREJ=36.96285734 -0.553241884*AGE + 0.387455323 STATUS

Part-e

The estimated degree of prejudice for a person whose age is 47 and status is 100

=36.96285734 -0.553241884*47+ 0.387455323 *100

=49.70602109

Part-f

The coefficient of age is significant with p-value=0.004<0.05

Part-g

Corresponding to one year increase in age there is on an average a decrease of 0.553241884 in degree of prejudice for a person, holding status fixed. We are surprised as with age this should increase.

Part-h

From following standardized residuals we observe that none of them is grater than 3 or less than -3, so residuals do not indicate anything unusual

Observation

Predicted PREJ

Residuals

Standard Residuals

76.54476263

3.45523737

0.359536137

86.23300575

-0.233005751

-0.024245509

47.71100224

0.288997759

0.03007178

50.1996607

-10.1996607

-1.061329863

54.34804481

11.65195519

1.21244896

71.50784343

-7.507843429

-0.781231716

89.16314169

4.83685831

0.503301268

24.58288742

7.417112577

0.771790681

58.72925793

-10.72925793

-1.116437319

45.77186558

-13.77186558

-1.433037102

75.32651446

12.67348554

1.318744718

73.61090661

2.389093394

0.24859809

39.24100729

12.75899271

1.327642201

48.87150817

-8.871508168

-0.923128408

72.44854064

3.551459364

0.369548556

17.66271377

-3.662713766

-0.381125178

81.85923279

-19.85923279

-2.066460585

46.54863627

-6.548636271

-0.681421024

69.73635337

2.263646626

0.235544675

56.17727711

3.822722894

0.397774993

59.72583734

16.27416266

1.693414647