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 | |||
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?
On the graph below, use the point tool to plot the point corresponding to the first Distance and its Shipping Time (Distance 1).
Repeat the process for the remainder of the sample (Distance 2, Distance 3, … ).
To enter exact coordinates, double-click on the point and enter the exact coordinates of x and y.
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¯ | |
S_{x} | |
S_{y} | |
r | |
b-2. State the decision rule for 0.05 significance level: H_{0}: ρ ≤ 0; H_{1}: ρ > 0. (Round your answer to 3 decimal places.)
Reject H0 is t >
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.)
b-4. Can we conclude that there is a positive correlation between distance and time? Use the 0.05 significance level.
c-1. Determine the coefficient of determination. (Round your answer to 3 decimal places.)
c-2. What percentage of the variation in shipping time is explained by shipping distance. (Round your answer to 1 decimal place.)
Determine the standard error of estimate. (Round your answer to 3 decimal places.)
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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