Question

An accountant for a large department store has the business objective of developing a model to predict the amount of time it takes to process invoices. Data are collected from the past 32 working days, and the number of invoices processed and completion time (in hours) are shown below. (Hint: First determine which are the independent and dependent variables.) Use Excel:

Invoices	Time
103	1.5
173	2.0
149	2.1
193	2.5
169	2.5
29	0.5
188	2.3
19	0.3
201	2.7
58	1.0
110	1.5
83	1.2
60	0.8
25	0.4
60	1.8
190	2.9
233	3.4
289	4.1
45	1.2
70	1.8
241	3.8
163	2.8
120	2.5
201	3.3
135	2.0
80	1.7
77	1.7
222	3.1
181	2.8
30	1.0
61	1.9
120	2.6

• Assuming a linear relationship, create a regression model to compute the regression coefficients b₀ and b₁.
• Interpret the meaning of the Y intercept, b₀, and the slope, b₁. What does the slope tell you about the relationship between number of invoices processed and completion time?
• Use the prediction line developed to predict the mean amount of time it would take to process 150 invoices. Would you use the regression model to predict the amount of time it would take to process 350 invoices? Why?
• What is the coefficient of determination, r² ? Interpret its meaning.
• Plot the residuals against the number of invoices processed and also against time. Based on these plots, does the model seem appropriate?

Answer 1