Assessment 2

1. A company manager says that the average balance on their credit cards is $500. Do you think that this
assertion is justified? Use a one-sample t-test to draw your conclusion.

Answer: Yes.
a. Null Hypothesis : Average balance on credit card is 500.
Alternate Hypothesis : Average balance on credit card is not 500.

b. Result : Refer Excel File (Sheet1)

Conclusion : Fail to Reject Null Hypothesis

2. Is there a difference between men and women as far as average balance is concerned? Use a two-sample
t-test to draw your conclusion.

Answer: No
a. Null Hypothesis : Average balance for men and women is same.
Alternate Hypothesis : Average balance for men and women is not same.

b. Result : Refer Excel File (Sheet2)

Conclusion : Fail to Reject Null Hypothesis

3. Is there a difference between students and non-students as far as average balance is concerned? Use a
two-sample t-test to draw your conclusion.

Answer: Yes
a. Null Hypothesis : Average balance for students and non-students is same.
Alternate Hypothesis : Average balance for students and non-students is not same.

b. Result : Refer Excel File (Sheet3)

Conclusion : Reject Null Hypothesis

4. It is generally assumed that if there are more credit cards then the balance on the cards will be more. Based
on this dataset, do you think this is true? Calculate a correlation coefficient and show a scatter plot to
support your answer.

Answer: No (Refer Excel File – Sheet4)

a. Correlation Coefficient : 0.086456
 b. Scatter Plot :

Balance
2500

2000

1500

1000

500

0
0 2 4 6 8 10

5. Examine whether the following demographic variables influence balance: (a) age, (b) years of education, (c)
marital status. For age and years of education, use scatter plots to depict their relationship with balance and
calculate the correlation coefficient. For the relationship between marital status and balance, use a two-
sample t-test to draw your conclusion

Answer:
a. Correlation Coefficient : 0.001835
Scatter Plot :

Balance
2500

2000

1500

1000

500

0
0 20 40 60 80 100 120

Inference : Age does not influence balance. Refer Excel File (Sheet5-a)

b. Correlation Coefficient : -0.00806

 Scatter Plot :

Balance
2500

2000

1500

1000

500

0
0 5 10 15 20 25

Inference : Years of education does not influence balance. Refer Excel File (Sheet5-b)

c. Null Hypothesis : Marital Status does not influence balance.

Alternate Hypothesis : Marital Status influence balance.
Result : Refer Excel File (Sheet5-c).
Conclusion : Fail to Reject Null Hypothesis.

6. “Ethnicity of the cardholder does not matter as far a balance is concerned.” Carry out an analysis of variance
(ANOVA) and discuss whether this statement is supported by the data or not.

Answer:
a. Null Hypothesis : Means for all the Ethnicity are same
Alternate Hypothesis : Means for all the Ethnicity are different

b. ANOVA Test : Refer Excel File (Sheet6)

c. Inference : Fail to Reject Null Hypothesis.

7. A general principle that credit card companies often follow is to assign a higher credit limit to people with a
higher credit rating. Does the data show that this principle is being followed?

Answer: Yes (Refer Excel File – Sheet7)

a. Correlation Coefficient : 0.99688
 b. Scatter Plot :

Rating
1200

1000

800

600

400

200

0
0 2000 4000 6000 8000 10000 12000 14000 16000

8. Run a simple linear regression of balance on the credit limit. (Here credit limit is the X and the balance is the
Y). Report the coefficients and the R-squared. Show a scatter plot.

Answer: Refer Excel File – Sheet8

a. Coefficients : 0.171637278(Credit Limit), -292.7904955
b. R-squared : 0.74252218
c. Scatter Plot :

Balance y = 0.1716x - 292.79

R² = 0.7425
2500
2000
1500
1000
500
0
-500 0 5000 10000 15000

d. Inference : For every unit increase in Credit Limit, balance increases by 0.171637278

9. Run a simple linear regression of balance (Y) on credit rating (X). Report the coefficients and R-squared.
Show a scatter plot

Answer: Refer Excel File – Sheet9

a. Coefficients : 2.566240327(Rating), -390.8463418
b. R-squared : 0.745848418
c. Scatter Plot :
 y = 2.5662x - 390.85
Balance R² = 0.7458

2500

2000

1500

1000

500

0
0 200 400 600 800 1000 1200
-500

d. Inference : For every unit increase in Credit Rating, balance increases by 2.566240327

10. Consider your findings in questions 8-9. Discuss business mechanisms to increase or decrease the balance
on credit cards. Try to quantify your answers.In this context, focus on possible specific strategies using
variables in Q8 and Q9 that the business could adopt to increase the balance on credit cards

Answer:
Mechanism to increase or decrease balance on credit cards based on below variables:

a. Rating:
i. Increase : For every unit increase in rating, balance increases by 2.566240327
ii. Decrease : For every unit decrease in rating, balance decreases by 2.566240327

b. Limit:
i. Increase : For every unit increase in limit, balance increases by 0.171637278
ii. Decrease : For every unit decrease in limit, balance decreases by 0.171637278

11. The credit limit is provided as a consolidated amount for all the credit cards the cardholder has. Run a
multiple linear regression of Balance (Y) on Limit and Cards as two X variables. Report the coefficients.
Discuss the effect on the balance of (a) increasing the credit limit on the same number of cards and (b)
increasing the number of cards without altering the total credit limit.

Answer:
a. Ran Multiple Liner Regression : Refer Excel File – Sheet11
b. Coefficients : 0.171479037(Limit), 26.03375427(Cards), -369.0359554
c. Effect on the balance of:
i. Increasing the credit limit on the same number of cards:

For every unit increase in the credit limit, balance increases by 0.171479037

ii. Increasing the number of cards without altering the total credit limit:

For every unit increase in the number of cards, balance increases by 26.03375427
12. Run a simple linear regression equation with Income as X and Balance as Y. Report the coefficients. Is the
coefficient of Income significantly different from zero? What does this say about the effect of income on
balance?

Answer:
a. Ran Simple Linear Regression : Refer Excel File – Sheet12
b. Coefficients : 6.04836341(Income), 246.514751
c. Is the coefficient of Income significantly different from zero? : Yes
d. What does this say about the effect of income on balance? : For every unit increase in income,
balance increases by 6.04836341

13. Based on the equation derived in question 12, what is the estimated balance for a person with an income of
USD 100k per year?

Answer:
a. Regression Equation : y = 6.0484x + 246.51 (Refer Excel File – Sheet12)
b. Estimate Balance : y = 6.0484(100) + 246.51
= 604.84 + 246.51
= 851.35
= USD 851.35k

14. Based on the dataset, explore the relationship between credit card balance (Y) and (a) Income (b) Age (c)
Education (c) Limit, and (d) Rating as X variables? Estimate a multiple linear regression model and report
the statistical significance of each of these variables.

Answer: Regression Output: Refer Excel File – Sheet14

a. Income : For every unit increase in income, without any change in other variables, balance
decreases by 7.608832003
b. Age : For every unit increase in age, without any change in other variables, balance
decreases by 0.860030445
c. Education : For every unit increase in education, without any change in other variables, balance
increases by 1.967791521
d. Limit : For every unit increase in limit, without any change in other variables, balance
increases by 0.07901642
e. Rating : For every unit increase in rating, without any change in other variables, balance
increases by 2.773843725