Please verbally explain the procedures you took to obtain these answers 16.58 Da

Question

Please verbally explain the procedures you took to obtain these answers 16.58 Data file XR16058 lists the following data for a sample of automatic teller machine (ATM) customers: time (seconds) to complete their transaction, estimated age, and gender (1 = male, 0 = female) a. Determine the multiple regression equation and b. What is the estimated time required by a female C. Determine the 95% prediction interval for the time d. Determine the 95% confidence interval for the interpret the partial regression coefficients customer who is 45 years of age? required by the customer described in part (b). mean time required by customers similar to the one described in part (b). Determine the 95% confidence interval for the popu- lation partial regression coefficients, 1 and 2. Interpret the significance tests in the computer printout. e. Determine the 950 contidenc interval for the popu e. f.

Explanation / Answer

Part a)

Use stat graphics to determinate the regression models.

Instructuctions:

- Import te given data into de worksheet.

- Select - improve/ regression analysis/ multiple factors/ multiple regression.

- Select as dependent variable the "Time" and as independent variables the "age" and "gender" and select OK.

- The software will give you this answer:

R-squared = 43,6995 percent

R-squared (adjusted for d.f.) = 33,4631 percent

Standard Error of Est. = 8,72022

Mean absolute error = 6,0817

Durbin-Watson statistic = 2,14027 (P=0,6075)

Lag 1 residual autocorrelation = -0,122862

And the regression model is : Time = 69,4926 + 0,110122*Age - 12,1858*Gender.

Due to the age coefficients (0.110122) is positive, the time to complete a ATM transaction increase with the age. Another case is seen in the gender (-12.1858). The negative coefficient means that mens decrease in a ight level the time to get money of a ATM. Whereas the women increase the time.

Part b)

Substituting in the regression model obtained.

We have: Time = 69,4926 + 0,110122*Age - 12,1858*Gender. ; Where

Age: 45

Gender: female (0)

Time: 69,4926 + 0,110122*45 - 12,1858*0 = 74.44 s.

Part c)

Substituting these intervals for each factor.We obtain the prediction interlvals for the time required for the custumers in part b.

Time with 95% (age = 45) = 23.17 - 121.75

Part d )

To obtain the prediction interlvals for the mean time required by custumers. Apply the regression model, to obtain the  predicted time value and then calcule its mean. :

Part e)

f) The factor more significant is the gender because its value is of significance p less than 0.05

Time Time lower limit Time upper limit 76 26.3 122 70 52.14 118 76 26.75 121.6 42 54.8 114.51 66 58.22 109.11 57 56.7 111.51 53 55.56 113.51 67 19.15 133.6 81 27.13 121 76 19.1 132 70 50.4 121.71 75 33.97 110 73 26.75 121.6 72 49.48 118.11 Mean 39.74642857 119.1614286

Part e)

f) The factor more significant is the gender because its value is of significance p less than 0.05

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