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. Hence, repair time in hours is the dependent variable. Repair time is believed to be related to three factors, the number of months since the last maintenance service, the type of repair problem (mechanical or electrical), and the repairperson who performed the service. Data for a sample of 10 service calls are reported in the table below.

Repair Time in Hours	Months Since Last Service	Type of Repair	Repairperson
2.9	2	Electrical	Dave Newton
3.0	6	Mechanical	Dave Newton
4.8	8	Electrical	Bob Jones
1.8	3	Mechanical	Dave Newton
2.9	2	Electrical	Dave Newton
4.9	7	Electrical	Bob Jones
4.2	9	Mechanical	Bob Jones
4.8	8	Mechanical	Bob Jones
4.4	4	Electrical	Bob Jones
4.5	6	Electrical	Dave Newton

(a)Develop the estimated regression equation to predict the repair time (y), in hours, given the number of months since the last maintenance service (x₁), the type of repair (x₂), and the repairperson who performed the service (x₃). (Use

x₂ = 0

if the type of repair is mechanical and

x₂ = 1

if the type of repair is electrical. Use

x₃ = 0

if Bob Jones performed the service and

x₃ = 1

if Dave Newton performed the service. Round your numerical answers to three decimal places.) =

(b)At the 0.05 level of significance, test whether the estimated regression equation developed in part (a) represents a significant relationship between the independent variables and the dependent variable.State null and alternative hypotheses.H₀: One or more of the parameters is not equal to zero. H_a: ₁ = ₂ = ₃ = 0H₀: ₁ = ₂ = ₃ = 0 H_a: All the parameters are not equal to zero. H₀: ₁ = ₂ = ₃ = 0 H_a: One or more of the parameters is not equal to zero.H₀: ₀ = 0 H_a: ₀ 0Find the value of the test statistic. (Round your answer to two decimal places.)Find the p-value. (Round your answer to three decimal places.)p-value = State your conclusion.Reject H₀. There is sufficient evidence to conclude that there is a significant relationship.Do not reject H₀. There is sufficient evidence to conclude that there is a significant relationship. Reject H₀. There is insufficient evidence to conclude that there is a significant relationship.Do not reject H₀. There is insufficient evidence to conclude that there is a significant relationship.(c)Is the independent variable

x₃,

the repairperson who performed the service, statistically significant? Use = 0.05.State the null and alternative hypotheses.H₀: ₃ = 0 H_a: ₃ 0H₀: ₃ 0 H_a: ₃ < 0 H₀: ₃ = 0 H_a: ₃ > 0H₀: ₃ 0 H_a: ₃ > 0Find the value of the test statistic. (Round your answer to two decimal places.)Find the p-value. (Round your answer to three decimal places.)p-value = State your conclusion.Reject H₀. There is sufficient evidence to conclude that the repairperson is a significant factor.Do not reject H₀. There is insufficient evidence to conclude that the repairperson is a significant factor. Do not reject H₀. There is sufficient evidence to conclude that the repairperson is a significant factor.Reject H₀. There is insufficient evidence to conclude that the repairperson is a significant factor.What explanation can you give for the results observed?Since the p-value > , this indicates that once the effect of months since last service has been accounted for, the repairperson does not significantly add to the model.Since the p-value , this indicates that once the effect of months since last service has been accounted for, the repairperson does not significantly add to the model. Since the p-value , this indicates that once the effect of months since last service has been accounted for, the repairperson still significantly adds to the model.Since the p-value > , this indicates that once the effect of months since last service has been accounted for, the repairperson still significantly adds to the model.