By: Amanda Letoski & Joe Dorzinsky

Linear Regression is used to quantify the relationship between two variables by fitting a line through the data

Simple means only on predictor variable (x).

The Linear Model y = βo + β1x +ε

Y = The Value of dependent (response) variableβo =y-intercept of the populationβ1 =Slope of the population regression lineX=The value of independent (explantory) variableΕ=Error term (residual)

Regression analysis involves lines that show how the response variable changes with changes in the explanatory variable

Quick Stab Collection Agency (QSCA) specializes in small accounts and avoids risky collections, such as those in which the debtor tends to be chronically late in payments or is knows to be hostile QSCA buys the rights to collect debts from the

originalowner at a substantial discount

It also takes the risk of not collecting the debt at all Profitability at QSCA depend critically on the

number of days to collect the payment and on the size of the bill, as well as on the discount rate offered

A random sample of accounts closed out during the months of January through June is available

Our job was to prepare a brief presentation to QSCA management advising them on the meaning and implications on the relationship, if any, between the size of the bill and the number of days to collect

Relationship between number of days to collect the bill and the amount of the bill over due

1) X = number of days to collect the bill & Y = the amount of the bill over due

2) The relationship test based on the correlation between the two variables shows that there is a negative relationship.

3) The Regression Coefficient intercept shows that the bill will be $181 dollars if it is 0 days over due. The Regression Coefficient of the X value, days, shows that for every 1 day increase in the days over due, the amount of the associated bill will be $14 less

4) The regression model used to represent the relationship between the number of days to collect the bill & the amount of bill over due is not significant. The R squared value = 0.17%, which means that there is that much variability in the amount of the bill over due explained by the number of days to collect the bill. The Standard Error = $78.17 is the amount of the mistake the amount of the bill over due can be wrong (plus or minus)

5) Null: B1 = 0, no relationship between the number of day to collect the bill & the amount the bill is over due Alt: B1 does not equal 0, There is a relationship

between the number of days to collect the bill & the amount of the bill over due

6) We would not reject the null because there is no linear relationship between the number of days to collect and the amount of the bill

The model for the linear relationship would be: Y = - 0.1372x + 181.1

Being that the slope & the r squared values are closer to 0, this shows that there is no linear relationship between the two variables

Relationship between the number of days to collect the Residential Accounts & amount of the Residential Bills

1) X = number of days to collect the Residential bill & Y = the amount of the Residential bill over due

2) The relationship test based on the correlation between the two variables shows that there is a positive relationship.

3) The Regression Coefficient intercept shows that the bill will be $74 dollars if it is 0 days over due. The Regression Coefficient of the X value, days, shows that for every 1 additional day overdue the Residential bill is, it will increase by $5.63

4) The regression model used to represent the relationship between the number of Residential days to collect the bill & the amount of Residential bill over due is significant. The R squared value = 93.1%, which means that there is that much variability in the amount the Residential bill is over due explained by the number of days to collect the Residential bill. The Standard Error = $78.17 is the amount of the mistake the amount of the bill over due can be wrong (plus or minus)

5) Null: B1 = 0, no relationship between the number of day to collect the bill & the amount the Residential bill is over due Alt: B1 does not equal 0, There is a relationship between

the number of days to collect the bill & the amount of the Residential bill is over due

6) We would reject the null because there is a strong linear relationship between the number of days to collect and the amount of the Residential bill

The model for the linear relationship would be: Y = 5.63x – 0.7401

For a Residential customer, a smaller bill is associated with less days to collect the payment

Relationship between the number of days to collect the Commercial Accounts & amount of the Commercial Bills

1) X = number of days to collect the Commercial bill & Y = the amount the Commercial bill is over due

2) The relationship test based on the correlation between the two variables shows that there is a negative relationship.

3) The Regression Coefficient intercept shows that the bill will be $571 dollars if it is 0 days over due. The Regression Coefficient of the X value, days, shows that for every 1 additional day overdue the Commercial bill is, it will decrease by $5.01

4) The regression model used to represent the relationship between the number of Commercial days to collect the bill & the amount the Commercial bill is over due is significant. The R squared value = 95.6%, which means that there is that much variability in the amount the Residential bill is over due explained by the number of days to collect the Residential bill. The Standard Error = $16.49 is the amount of the mistake the amount of the bill over due can be wrong (plus or minus)

5) Null: B1 = 0, no relationship between the number of day to collect the bill & the amount the Commercial bill is over due Alt: B1 does not equal 0, There is a relationship between

the number of days to collect the bill & the amount of the Commercial bill over due

6) We would reject the null because there is strong linear relationship between the number of days to collect and the amount of the Commercial bill

The model for the linear relationship would be: Y = - 5.01x + 517.27

For a Commercial customer, a smaller bill is associated with more days to collect the payment

There is a strong linear relationship between the amount of the bill and the amount of days to collect the bill that is over due. This is true for both the Residential customers & Commercial customers

The Residential customers linear relationship showed that the larger the amount of the bill, QSCA had more days to collect the bill (positive slope)

The Commercial customers linear relationship showed that the smaller the amount of the bill, QSCA had more days to collect the bill (negative slope)

Any Questions?