Question

# Bardi Trucking Co., located in Cleveland, Ohio, makes deliveries in the Great Lakes region, the Southeast,...

Bardi Trucking Co., located in Cleveland, Ohio, makes deliveries in the Great Lakes region, the Southeast, and the Northeast. Jim Bardi, the president, is studying the relationship between the distance a shipment must travel and the length of time, in days, it takes the shipment to arrive at its destination. To investigate, Mr. Bardi selected a random sample of 20 shipments made last month. Shipping distance is the independent variable and shipping time is the dependent variable. The results are as follows:

 Shipment Distance (miles) Shipping Time (days) Shipment Distance (miles) Shipping Time (days) 1 791 4 11 721 5 2 727 12 12 662 3 3 775 14 13 821 7 4 711 9 14 790 8 5 625 12 15 758 10 6 810 9 16 774 15 7 762 14 17 848 12 8 642 3 18 804 15 9 654 3 19 722 12 10 650 10 20 676 3
1. Draw a scatter diagram. Based on these data, does it appear that there is a relationship between how many miles a shipment has to go and the time it takes to arrive at its destination?

1. On the graph below, use the point tool to plot the point corresponding to the first Distance and its Shipping Time (Distance 1).

2. Repeat the process for the remainder of the sample (Distance 2, Distance 3, … ).

3. To enter exact coordinates, double-click on the point and enter the exact coordinates of x and y.

1. b-1. Fill in the blanks. (Round your answers to 3 decimal places. Negative values should be indicated by minus sign.)

 x⎯⎯x¯ y⎯⎯y¯ Sx Sy r

1. b-2. State the decision rule for 0.05 significance level: H0: ρ ≤ 0; H1: ρ > 0. (Round your answer to 3 decimal places.)

Reject H0 is t >

1. b-3. Compute the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

2. b-4. Can we conclude that there is a positive correlation between distance and time? Use the 0.05 significance level.

3. c-1. Determine the coefficient of determination. (Round your answer to 3 decimal places.)

1. c-2. What percentage of the variation in shipping time is explained by shipping distance. (Round your answer to 1 decimal place.)

2. Determine the standard error of estimate. (Round your answer to 3 decimal places.)

3. Would you recommend using the regression equation to predict shipping time?

• Yes

• No

 S.No X Y (X-Xbar)^2 (Y-Ybar)^2 (X-Xbar)(Y-Ybar) 1 794 9 2606.103 1.1025 -53.6025 2 807 12 4102.402 3.8025 124.8975 3 636 5 11438.3 25.5025 540.0975 4 700 4 1844.703 36.6025 259.8475 5 664 8 6233.103 4.2025 161.8475 6 700 11 1844.703 0.9025 -40.8025 7 734 15 80.1025 24.5025 -44.3025 8 831 13 7752.802 8.7025 259.7475 9 697 10 2111.403 0.0025 2.2975 10 840 13 9418.702 8.7025 286.2975 11 821 14 6091.802 15.6025 308.2975 12 724 5 359.1025 25.5025 95.6975 13 815 10 5191.202 0.0025 -3.6025 14 776 6 1092.303 16.4025 -133.853 15 712 10 957.9025 0.0025 1.5475 16 684 11 3475.103 0.9025 -56.0025 17 772 15 843.9025 24.5025 143.7975 18 801 13 3369.802 8.7025 171.2475 19 722 12 438.9025 3.8025 -40.8525 20 629 5 12984.6 25.5025 575.4475 Total 14859 201 82236.95 234.95 2558.05 Average 742.95 10.05 3800.866 11.51806 197.0661 Sx Sy Sxy r = 0.582

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