DATAfile: Showtime A statistical program is recommended. The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow. (a) (b) () (d) Weekly Gross Revenue ($1,000s) Television Newspaper Advertising | Advertising ($1,000s) ($1,000s) 96 90 95 92 95 94 94 94 Develop an estimated regression equation with the amount of television advertising as the independent variable. (Round your numerical values to two decimal places. Let X, represent the amount of television advertising in $1,000s and y represent the weekly gross revenue in $1,000s.) 7 =| 88.64 + 1.60x, O Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables. (Round your numerical values to two decimal places. Let x, represent the amount of television advertising in $1,000s, x, represent the amount of newspaper advertising in $1,000s, and y represent the weekly gross revenue in $1,000s.) y=| 8323+ 2.29)(1 + 1.3034:2 v Is the estimated regression equation coefficient for television advertising expenditures the same in part (a) and in part (b)? No s ,itis[160 | inpart(a)and| 229 | & in part (b). Interpret the coefficient in each case. (O In part (a) it represents the change in revenue due to a one-unit increase in television advertising expenditure with newspaper advertising held constant. In part (b) it represents the change in revenue due to a one-unit increase in newspaper advertising with television advertising held constant. O1n part (a) it represents the change in revenue due to a one-unit increase in newspaper advertising expenditure with television advertising held constant. In part (b) it represents the change in revenue due to a one-unit increase in television advertising with newspaper advertising held constant. O part (a) it represents the change in revenue due to a one-unit increase in television advertising expenditure. In part (b) it represents the change in revenue due to a one-unit increase in television advertising with newspaper advertising held constant. (O In part (a) it represents the change in revenue due to a one-unit increase in television advertising with newspaper advertising held constant. In part (b) it represents the change in revenue due to a one-unit increase in television advertising expenditure. O1n part (a) it represents the change in revenue due to a one-unit increase in television advertising expenditure. In part (b) it represents the change in revenue due to a one-unit increase in newspaper advertising with television advertising held constant. Predict weekly gross revenue (in dollars) for a week when $3,900 is spent on television advertising and $1,100 is spent on newspaper advertising. (Round your answer to the nearest cent.) $(03461 | X Management proposed the following regression model to predict sales at a fast-food outlet. y=,60+lx1 +,62)(2+,63x3 + e where 1 = number of competitors within one mile X5 = population within one mile (1,000s) . {1 if drive-up window present 3 0 otherwise y = sales ($1,000s). The following estimated regression equation was developed after 20 outlets were surveyed. y =10.1 4.2)c1 + 6.8)(2 + 15.9)(3 (a) What is the expected amount of sales (in dollars) attributable to the drive-up window? $[15000 | (b) Predict sales (in dollars) for a store with four competitors within one mile, a population of 8,000 within one mile, and a drive- up window. $[54454 | (c) Predict sales (in dollars) for a store with one competitor within one mile, a population of 3,000 within one mile, and no drive- up window. $[26300 | 123 Tutorial Submit Answer p A statistical program is recommended. 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. (a) Develop the estimated regression equation to predict the repair time (y), in hours, given the number of months since the last maintenance service (xl), the type of repair (Xz)' and the repairperson who performed the service (x3). (Use X, = 0 if the type of repair is electrical and Xy =1 if the type of repair is mechanical. Use x3=0 if Bob Jones performed the service and (b) Re_pair Time | Months Si!'lce in Hours Last Service X3 = 1 if Dave Newton performed the service. Round your numerical answers to three decimal places.) y =| 1.860 + 0.29le + 1.102x2 U.()'UQxS & 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. O H,: One or more of the parameters is not equal to zero. HyiBy=B,=8;=0 OHyB,=8,=5;=0 H_: One or more of the parameters is not equal to zero. O Hy: By =B, =83=0 Ha: All the parameters are not equal to zero. Q Hy: B,=0 Hi:fy#0 v Find the value of the test statistic. (Round your answer to two decimal places.) (1804 & Find the p-value. (Round your answer to three decimal places.) p-value = 0.002 4 State your conclusion. O Reject HO. There is insufficient evidence to conclude that there is a significant relationship. () Do not reject Hn' There is insufficient evidence to conclude that there is a significant relationship. o Reject HO. There is sufficient evidence to conclude that there is a significant relationship. () Do not reject Hu' There is sufficient evidence to conclude that there is a significant relationship. A statistical program is recommended. Johnsan 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. Rt?pair Time | Months Si!'lce in Hours Last Service (a) Ignore for now the months since the last maintenance service (xq) and the repairperson who performed the service. Develop the estimated simple linear regression equation to predict the repair time (y) given the type of repair (Xz)' Let Xy = 0 if the type of repair is electrical and Xy = 1 if the type of repair is mechanical. (Round your numerical values to three decimal places.) 7