Question

1.

Johnson Filtration, Inc., provides maintenance service for water-filtration systems throughout southern Florida. Customers contact Johnson with requests for maintenance service on their water-filtration systems. To estimate the service time and the service cost, Johnson’s managers want to predict the repair time necessary for each maintenance request.

Management collected data over the last 10 service calls, and ran a multiple regression analysis on this sample. As a result, they developed the following estimated regression equation to predict y = the repair time (in hours) given the number of months since the last maintenance service, the type of repair (electrical or mechanical), and the specific repairperson who performed the service:

= 1.86 + 0.28 Months + 1.11 Type − 0.61 Person, where

Months = number of months since the last maintenance
Type is 1 for electrical and 0 for mechanical repair

Interpret the coefficient of variable Months in the equation:

(HINT: 1 hour = 60 minutes)

Select one:

a. For every additional 0.28 months since the last maintenance service, the length of repair time required is increased by 1.86 hours

b. For each additional month since the last maintenance service, the length of repair time required is increased by 17 minutes

c. For each additional month since the last maintenance service, the length of repair time required is increased by 128 minutes

d. For every additional 0.28 months since the last maintenance service, the length of repair time required is increased by one hour

2. You have run a simple regression on a sample with 23 observations, and obtained the following information:

SSR = 254
SST = 442

Calculate the value of the standard error of estimate, s

Round your answer to three decimal places

3. Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained:

	= 12 + 1.8x
	n = 19
	sb1= 0.2683

Using α = 10%, the critical t value for testing the significance of the slope is ____
Show your answer with three decimal places.

Answer 1

Que.1

If month is increased by 1 then repair time is increased by 0.28 hours = 0.28* 60 = 16.8 =17 min

For each additional month since the last maintenance service, the length of repair time required is increased by 17 minutes.

Que.2

Variance of error = MSE = SSE / df

Where,

SSE =SST - SSR = 442 - 254 = 188

Here n = total no. of observations = 10

p = no. of independent variable = 3

df(error) = n -p -1 = 10 - 3- 1 = 6

MSE = 188 / 6 = 31.33

Hence standard error of residual =

Que.3

Degrees of freedom for t test = n-2 = 19 - 2 = 17

Hence critical value at 10% level of significance is t0.10/2, 17 = 1.740