During the recession that began in 2008, not only did some people stopmaking hou
ID: 3381604 • Letter: D
Question
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.
Explanation / Answer
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
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.