Question:The manager of the purchasing department of a large organization wants to develop a model for predicting the time it takes to process invoices. Data are collected for 30 days, giving the number of invoices completed and the time taken (in hours).
Invoices Processed Time
149 2.1
60 1.8
188 2.3
19 0.3
201 2.7
58 1
77 1.7
222 3.1
181 2.8
30 1
110 1.5
83 1.2
60 0.8
25 0.4
173 2
169 2.5
190 2.9
233 3.4
289 4.1
45 1.2
193 2.5
70 1.8
241 3.8
103 1.5
163 2.8
120 2.5
201 3.3
135 2
80 1.7
29 0.5
(b) Describe what the scatterplot in (a) suggests about the relationship between number of invoices and time taken.
(c) Use Excel to find the least squares regression line for predicting Time based on Invoices Completed.
(d) Interpret, in context, the slope coefficient in the model.
(e) Give the value, and interpret the meaning, of the R Square.
(f) Give the value, and interpret the meaning, of the Standard Error ().
(g) Predict the time taken to process 150 invoices.
(h) Construct a residual plot of the residuals against the fitted values. Comment on what it shows.
(i) How strong is the evidence for a relationship between Time and Invoices Completed?