Question

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

Answer 1

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