Question

A. Jensen Tire & Auto is in the process of deciding whether to purchase a maintenance contract for its new computer wheel alignment and balancing machine. Managers feel that maintenance expense should be related to usage, and they collected the following information on weekly usage (hours) and annual maintenance expense (in hundreds of dollars): Weekly Usage (hours) Annual Maintenance Expense ($100) 13 17.0 20 30.0 28 37.0 32 47.0 17 30.5 24 32.5 40 51.5 38 40.0 A3. Using the OLS results and find the residual, i.e., ei, that corresponds with 32 hours of weekly usage of this machine: a. 37.2004 b. 42.2348 c. 5.7652 d. 2.1963

Answer 1

y: Annual Maintenance Expense ($100)

x: Weekly Usage (hours)

=a +bx

' 'a' indicates the value of Y when X=0. It is called Y-intercept

'b' indicates the slope of the regression line and gives a measure of change of 'Y' for a unit change in 'X'

x: WeeklyUsage(hours)	y: AnnualMaintenanceExpense	xy	x2
13	17.0	221	169
20	30.0	600	400
28	37.0	1036	784
32	47.0	1504	1024
17	30.5	518.5	289
24	32.5	780	576
40	51.5	2060	1600
38	40.0	1520	1444
=212	=285.5	=8239.5	=6286

= 8.959394 + 1.008608x

Residual : Actual y - predicted y: y-

x:WeeklyUsage(hours)	y:AnnualMaintenanceExpense	=8.959394+1.008608x	Residual=y-
13	17.0	22.071298	-5.071298
20	30.0	29.131554	0.868446
28	37.0	37.200418	-0.200418
32	47.0	41.23485	5.76515
17	30.5	26.10573	4.39427
24	32.5	33.165986	-0.665986
40	51.5	49.303714	2.196286
38	40.0	47.286498	-7.286498

Residual for 32 = 5.765155.7652

residual, i.e., that corresponds with 32 hours of weekly usage of this machine:

c. 5.7652