Descriptive Statistics And Regression Analysis For Credit Card Charges

Table 1: Descriptive Statistics for Income and Amount Charged of Consumers

Table 1: Descriptive Statistics for Income and Amount Charged of Consumers

Statistics	Income ($1000s)	Amount Charged ($)
Mean Save Time On Research and Writing Hire a Pro to Write You a 100% Plagiarism-Free Paper. Get My Paper	43.48	3963.86
Standard Error	2.06	132.02
Median	42	4090
Mode	54	3890
Standard Deviation	14.55	933.55
Sample Variance	211.72	871508.74
Kurtosis	-1.25	-0.74
Skewness	0.10	-0.13
Range	46	3814
Minimum	21	1864
Maximum	67	5678
Sum	2174	198193
Count	50	50

From table 1 we find that the average (sd) income of the consumers is $43.48 ($14.55) thousands. The minimum and maximum income of the consumers is $21 and $67 (000s) respectively. The median income value is $42 (000s).

The average (sd) amount charged on credit cards is $3963.86 ($933.55). The minimum and maximum amount charged for credit cards is $1864 and $5678 respectively. The median amount charged on credit cards is $4090.

Table 2: Frequency distribution of Household Size

House Hold Size	Frequency
1	5
2	15
3	8
4	9
5	5
6	5
7	3

The maximum frequency (15) is for household size of 2. The minimum frequency (3) is for a household size of 7.  

Table 3: Regression Statistics with annual income as independent variable
Multiple R	0.6308
R Square	0.3979
Adjusted R Square	0.3853
Standard Error	731.9025
Observations	50

Table 4: Regression coefficients with annual income as independent variable

	Coefficients	Standard Error	t Stat	P-value
Intercept	2204.241	329.134	6.697	0.000
Income ($1000s)	40.470	7.186	5.632	0.000

The regression equation for annual income as independent variable can be written as

• Credit card charges = 2204.241 + 40.470*Income(000s)

The coefficient of both the intercept and slope of the regression equation are statistically significant (p-value < 0.001). In addition 39.79% of the variability in Credit charges can be predicted with Income. 

Table 5: Regression Statistics with Household size as independent variable
Multiple R	0.7529
R Square	0.5668
Adjusted R Square	0.5578
Standard Error	620.8163
Observations	50

Table 6: Regression coefficients with Household size as independent variable

	Coefficients	Standard Error	t Stat	P-value
Intercept	2581.644	195.270	13.221	0.000
Household Size	404.157	51.000	7.925	0.000

The regression equation with Household size as independent variable can be written as

• Credit card charges = 2581.644 + 404.157*Household Size

The coefficient of both the intercept and slope of the regression equation are statistically significant (p-value < 0.001). In addition 56.68% of the variability in Credit charges can be predicted with Household size.

 The model with household size is a better model since higher (56.68%) variability in credit card can be predicted.  

Table 7: Regression Statistics with income and Household size as independent variable
Multiple R	0.9085
R Square	0.8254
Adjusted R Square	0.8179
Standard Error	398.3249
Observations	50

Table 8: Regression coefficients with income and Household size as independent variable

	Coefficients	Standard Error	t Stat	P-value
Intercept	1305.034	197.771	6.599	0.000
Income ($1000s)	33.122	3.970	8.343	0.000
Household Size	356.340	33.220	10.727	0.000

The regression equation with income and Household size as independent variable can be written as

• Credit card charges = 1305.034 + 33.122*Income (000s) + 356.340*Household Size

The coefficient of both the intercept and slope of the regression equation are statistically significant (p-value < 0.001). In addition 82.54% of the variability in Credit charges can be predicted with both income and Household size as independent variables.

The credit card charges for 3 person household with annual income equal to $40,000 is

• Credit card charges = 1305.034 + 33.122*Income (000s) + 356.340*Household Size
• Credit card charges = 1305.034 + 33.122*40 + 356.340*3
• Credit card charges = $3698.934 ≈ $3699

For the study of the credit card charges variables like, frequency of use, amount spent can also be used.

Table 9: Descriptive statistics of the variables.

Descriptive Statistics	Mean	Standard deviation	Minimum	Maximum
Year Enrolled	2013	0.81	2012	2014
HI001 FINAL EXAM	31.72	6.75	0	45
HI001 ASSIGNMENT 01	17.21	1.99	8	22
HI001 ASSIGNMENT 02	15.46	2.31	8	21
HI002 FINAL EXAM	26.50	5.91	0	40
HI002 ASSIGNMENT 01	17.82	3.44	4	22
HI002 ASSIGNMENT 02	12.42	1.99	4	16
HI003 FINAL EXAM	25.99	8.27	4	43
HI003 ASSIGNMENT 01	18.19	3.91	10	30
HI003 ASSIGNMENT 02	13.54	1.76	8	20

Part a)

Table 10: Correlation between HI001 Final Exam and HI002 Final Exam

		HI001 Final Exam	HI002 Final Exam
HI001 Final Exam		1
HI002 Final Exam	r	0.049	1
Sig	0.630

The correlation between HI001 Final Exam and HI002 Final exam is very weak, positive and Linear (r = 0.049). In addition the correlation is not statistically significant, p-value = 0.630 > 0.05, level of significance.

Table 11: Correlation between HI001 Final Exam and HI003 Final Exam

		HI001 Final Exam	HI003 Final Exam
HI001 Final Exam		1
HI003 Final Exam	r	0.122	1
Sig	0.232

The correlation between HI001 Final Exam and HI003 Final exam is weak, positive and Linear (r = 0.122). In addition the correlation is not statistically significant, p-value = 0.232 > 0.05, level of significance.

Table 12: Correlation between HI002 Final Exam and HI003 Final Exam

		HI002 Final Exam	HI003 Final Exam
HI002 Final Exam		1
HI003 Final Exam	r	0.116	1
Sig	0.257

The correlation between HI002 Final Exam and HI002 Final exam is very weak, positive and Linear (r = 0.116). In addition the correlation is not statistically significant, p-value = 0.257 > 0.05, level of significance.

Table 2: Frequency Distribution of Household Size

Table 13: Correlation between HI001 Assignment 01 and HI003 Assignment 01

		HI001 Assignment 01	HI003 Assignment 01
HI001 Assignment 01		1
HI003 Assignment 01	r	0.004	1
Sig	0.968

 The correlation between HI001 Assignment 01 and HI003 Assignment 01 is very weak, positive and Linear (r = 0.004). In addition the correlation is not statistically significant, p-value = 0.968 > 0.05, level of significance. 

Table 14: Correlation between HI002 Assignment 01 and HI003 Assignment 01

		HI002 Assignment 01	HI003 Assignment 01
HI002 Assignment 01		1
HI003 Assignment 01	r	0.232	1
Sig	0.022

The correlation between HI002 Assignment 01 and HI003 Assignment 01 is weak, positive and Linear (r = 0.232). In addition the correlation is statistically significant, p-value = 0.022 < 0.05, level of significance. 

Table 15: Correlation between HI001 Assignment 01 and HI002 Assignment 01

		HI001 Assignment 01	HI002 Assignment 01
HI001 Assignment 01		1
HI002 Assignment 01	r	0.131	1
Sig	0.198

The correlation between HI001 Assignment 01 and HI002 Assignment 01 is weak, positive and Linear (r = 0.131). In addition the correlation is not statistically significant, p-value = 0.198 > 0.05, level of significance. 

Table 16: Correlation between HI001 Assignment 02 and HI003 Assignment 02

		HI001 Assignment 02	HI003 Assignment 02
HI001 Assignment 02		1
HI003 Assignment 02	r	0.101	1
Sig	0.325

The correlation between HI001 Assignment 02 and HI003 Assignment 02 is weak, positive and Linear (r = 0.101). In addition the correlation is not statistically significant, p-value = 0.325 > 0.05, level of significance.

Table 17: Correlation between HI002 Assignment 02 and HI003 Assignment 02

		HI002 Assignment 02	HI003 Assignment 02
HI002 Assignment 02		1
HI003 Assignment 02	r	0.107	1
Sig	0.296

The correlation between HI002 Assignment 02 and HI003 Assignment 02 is weak, positive and Linear (r = 0.107). In addition the correlation is not statistically significant, p-value = 0.296 > 0.05, level of significance.

Table 18: Correlation between HI001 Assignment 02 and HI002 Assignment 02

		HI001 Assignment 02	HI002 Assignment 02
HI001 Assignment 02		1
HI002 Assignment 02	r	0.038	1
Sig	0.712

The correlation between HI001 Assignment 02 and HI002 Assignment 02 is very weak, positive and Linear (r = 0.08). In addition the correlation is not statistically significant, p-value = 0.712 > 0.05, level of significance.

Table 19: Correlation between HI001 Assignment 01 and HI001 Assignment 02

		HI001 Assignment 01	HI001 Assignment 02
HI001 Assignment 01		1
HI001 Assignment 02	r	0.659	1
Sig	0.000

The correlation between HI001 Assignment 01 and HI001 Assignment 02 is moderate, positive and Linear (r = 0.659). In addition the correlation is statistically significant, p-value < 0.001, less than 0.05, level of significance.

Table 20: Depression Scores for Medical Center 1

Depression Scores	Florida	New York	North Carolina
2	2	0	0
3	3	0	4
4	1	1	1
5	3	1	1
6	3	2	1
7	4	4	3
8	3	7	5
9	1	1	1
10	0	1	1
11	0	1	2
12	0	1	1
13	0	1	0

It presents the analysis of individuals and depression scores at medical center 1. From the above it is seen that there are no individuals with depression score 2 from New York and North Carolina. Individuals from Florida visiting medical center 1 do not have depression score more than 10. The maximum number of individuals from New York has a depression score of 8. Maximum number of individuals from Florida has a depression score of 7. 

Table 21: Depression Scores for Medical Center 2

Depression Scores	Florida	New York	North Carolina
8	0	0	1
9	1	2	0
10	1	0	1
11	1	2	2
12	3	1	3
13	3	1	2
14	1	4	3
15	2	2	2
16	2	1	1
17	4	2	2
18	0	1	2
19	0	1	1
20	1	1	0
21	1	0	0
22	0	0	0
23	0	1	0
24	0	1	0

It Presents the analysis of individuals and depression scores at medical center 2. From the above it is seen that there are 4 individuals from Florida with a depression score of 17.  From the above it is seen that there are 4 individuals from New York with a depression score of 14. One individual each with depression score of 23 and 24 are from New York. 

 Thus it can be seen from the above that the depression scores are higher for medical center 2 i.e., individuals with higher depression scores are present at medical center 2. 

Null Hypothesis: The average depression scores of individuals from the three geographical locations is equal

Alternate Hypothesis: The average depression scores of individuals from the three geographical locations is not equal

Table 22: ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	61.03	2	30.517	5.241	0.008	3.159
Within Groups	331.90	57	5.823
Total	392.93	59

Table 23: SUMMARY
Groups	Count	Sum	Average	Variance
Florida	20	111	5.55	4.58
New York	20	160	8	4.84
North Carolina	20	141	7.05	8.05

From the above table 22, it is seen that F(2,57) = 5.241 is more than the F-crit value = 3.159. Moreover, p-value = 0.008 < 0.05, level of Significance. Thus we reject null hypothesis. There are statistically significant differences in the average depression scores of the three geographical locations at Medical Center 1.

For Medical Center 2

Null Hypothesis: The average depression scores of individuals from the three geographical locations is equal

Alternate Hypothesis: The average depression scores of individuals from the three geographical locations is not equal

Table 24: ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	17.033	2	8.516667	0.714	0.494	3.159
Within Groups	679.70	57	11.92456
Total	696.733	59

Table 25: SUMMARY
Groups	Count	Sum	Average	Variance
Florida	20	290	14.50	10.05
New York	20	305	15.25	17.04
North Carolina	20	279	13.95	8.68

From the above table 23, it is seen that F(2,57) = 0.741 is less than the F-crit value = 3.159. Moreover, p-value = 0.494 > 0.05, level of Significance. Thus we do not reject null hypothesis. There are statistically no significant differences in the average depression scores of the three geographical locations at Medical Center 2. 

For medical Center 1 it can be inferred that the average depression score (8±4.84) of people of New York is higher than the average depression score (5.55±4.58) of people of Florida.

For medical center 1 it can be inferred that the average depression score of 14.50±10.05 for individuals of Florida is equal to 15.25±17.04 for New York, which is equal to 13.95±8.68 for people of North Carolina.