During the recession that began in 2008 not only did some pe

During the recession that began in 2008, not only did some people stopmaking house payments, but they also stopped making payments for localgovernment services such as trash collection and water and sewer services.The following data have been collected by an accountant who is performingan audit of account balances for a major city billing department. Thepopulation from which the data were collected represents those accounts forwhich the customer had indicated the balance was incorrect. The dependentvariable, y, is the actual account balance as verified by the accountant. Theindependent variable, x, is the computer-generated account balance.

X - 233 10 24 56 78 102 90 200 344 120 18

Y - 245 12 22 56 90 103 85 190 320 120 23

a. Compute the least squares regression equation.

b. If the computer-generated account balance was 100, what would youexpect to be the actual account balance as verified by the accountant?

c. The computer-generated balance for Timothy Jones is listed as 100 inthe computer-generated account record. Calculate a 90% intervalestimate for Mr. Jones’s actual account balance.

d. Calculate also a 90% interval estimate for the average of allcustomers’ actual account balances in which a computer-generatedaccount balance is the same as that of Mr. Jones (part c). Interpretyour results.

Solution

During the recession that began in 2008, not only did some people stopmaking house payments, but they also stopped making payments for localgovernment services such as trash collection and water and sewer services.The following data have been collected by an accountant who is performingan audit of account balances for a major city billing department. Thepopulation from which the data were collected represents those accounts forwhich the customer had indicated the balance was incorrect. The dependentvariable, y, is the actual account balance as verified by the accountant. Theindependent variable, x, is the computer-generated account balance.

Regression Analysis

r²

0.993

n

11

r

0.996

k

1

Std. Error

8.867

Dep. Var.

y

ANOVA table

Source

SS

df

MS

F

p-value

Regression

96,739.3005

1  

96,739.3005

1230.42

6.15E-11

Residual

707.6086

9  

78.6232

Total

97,446.9091

10  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=9)

p-value

90% lower

90% upper

Intercept

5.3730

4.1148

1.306

.2240

-2.1699

12.9158

x

0.9466

0.0270

35.077

6.15E-11

0.8971

0.9961

Predicted values for: y

90% Confidence Interval

90% Prediction Interval

x

Predicted

lower

upper

lower

upper

Leverage

100

100.032

95.068

104.995

83.036

117.027

0.093

a. Compute the least squares regression equation.

Y=5.373+0.9466*x

b. If the computer-generated account balance was 100, what would youexpect to be the actual account balance as verified by the accountant?

When x=100,

Y=5.373+0.9466*100

=100.032

c. The computer-generated balance for Timothy Jones is listed as 100 inthe computer-generated account record. Calculate a 90% intervalestimate for Mr. Jones’s actual account balance.

90% Prediction interval for x=100,     (83.036, 117.027)

d. Calculate also a 90% interval estimate for the average of all customers’ actual account balances in which a computer-generated account balance is the same as that of Mr. Jones (part c). Interpret your results.

90% confidence interval for x=100,     ( 95.068, 104.995)

The interval estimate average of all customers’ actual account balances in which a computer-generated account balance is not same as that of Mr. Jones. Predicting a particular value is more variance than the average of values. Prediction interval is wider than the confidence interval.

Regression Analysis
	r²	0.993	n	11
	r	0.996	k	1
	Std. Error	8.867	Dep. Var.	y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	96,739.3005	1	96,739.3005	1230.42	6.15E-11
Residual	707.6086	9	78.6232
Total	97,446.9091	10
Regression output				confidence interval
variables	coefficients	std. error	t (df=9)	p-value	90% lower	90% upper
Intercept	5.3730	4.1148	1.306	.2240	-2.1699	12.9158
x	0.9466	0.0270	35.077	6.15E-11	0.8971	0.9961
Predicted values for: y
		90% Confidence Interval	90% Prediction Interval
x	Predicted	lower	upper	lower	upper	Leverage
100	100.032	95.068	104.995	83.036	117.027	0.093