Question

1. The data in BUSI1013 Credit Card Balance.xlsx is collected for building a regression model to predict credit card balance of retail banking customers in a Canadian bank. Use this data to perform a simple regression analysis between Account balance and Income (in thousands). (12 points)
2. Develop a scatter diagram using Account Balance as the dependent variable y and Income as the independent variable x.
3. Develop the estimated regression equation.
4. Use the estimated regression equation to predict the Account Balance of a customer with Income of $58 thousands.
5. Use the critical-value approach to perform an F test for the significance of the linear relationship between account balance and Income at the 0.05 level of significance.
6. What percentage of the variability of Account Balance can be explained by its linear relationship with Income?
7. Use the p-value approach to perform a t test for the significance of the linear relationship between Account Balance and Income at the 0.05 level of significance.

Account Balance	Income	Years of Education	Size of Household
8976	63	12	2
8308	37	14	2
10028	52	16	2
11256	64	15	4
9869	47	17	2
10194	74	15	2
8706	49	12	2
9557	58	14	2
10565	70	16	3
9434	69	11	3
9687	25	18	3
9490	57	15	1
8806	46	14	3
9561	48	16	2
11757	80	15	3
9406	66	14	2
11150	46	15	3
7671	28	12	2
8803	53	13	1
9571	52	15	2
9566	77	12	3
7885	32	14	3
9773	55	11	1
9121	52	15	2
9298	43	14	3
10285	65	15	2
7801	38	12	1
9323	52	14	2
8643	36	16	3
12466	85	15	2
9447	64	14	2
10727	86	15	2
9243	57	15	3
9311	68	12	2
11033	74	14	3
11721	82	16	2
8727	24	15	3
8438	37	15	3
8317	55	12	2
8617	50	14	1
9052	39	16	3
10889	73	15	3
7766	26	14	1
9189	47	15	2

Answer 1

The data in BUSI1013 Credit Card Balance.xlsx is collected for building a regression model to predict credit card balance of retail banking customers in a Canadian bank. Use this data to perform a simple regression analysis between Account balance and Income (in thousands). (12 points)

Develop a scatter diagram using Account Balance as the dependent variable y and Income as the independent variable x.

Develop the estimated regression equation.

Account Balance = 6,804.237+ 49.999* Income

Use the estimated regression equation to predict the Account Balance of a customer with Income of $58 thousands.

When x=58,

Predicted Account Balance = 6,804.237+ 49.999* 58

=9704.18

Use the critical-value approach to perform an F test for the significance of the linear relationship between account balance and Income at the 0.05 level of significance.

Critical F(1, 42) with 0.05 level=4.07

Calculated F=52.38 is > critical F 4.07. Ho is rejected.

There is a significant linear relationship between account balance and Income.

What percentage of the variability of Account Balance can be explained by its linear relationship with Income?

R square =0.555.

55.5% of variance is explained.

Use the p-value approach to perform a t test for the significance of the linear relationship between Account Balance and Income at the 0.05 level of significance.

Calculated t=7.237, P=0.0000 which is < 0.05 level of significance.

There is a significant linear relationship between account balance and Income.

Regression Analysis
	r²	0.555	n	44
	r	0.745	k	1
	Std. Error of Estimate	753.265	Dep. Var.	Account Balance
Regression output						confidence interval
variables		coefficients	std. error	t (df=42)	p-value	95% lower	95% upper
Intercept	a =	6,804.237
Income	b =	49.999	6.908	7.237	0.0000	36.057	63.940
ANOVA table
Source	SS	df	MS	F	p-value
Regression	29,720,290.933	1	29,720,290.933	52.38	0.0000
Residual	23,831,169.862	42	567,408.806
Total	53,551,460.795	43
Predicted values for: Account Balance
		95% Confidence Interval		95% Prediction Interval
Income	Predicted	lower	upper	lower	upper	Leverage
58	9,704.15	9,470.04	9,938.27	8,166.08	11,242.23	0.024