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		678	3		11	814	11
2		758	14		12	782	5
3		733	14		13	753	7
4		802	15		14	831	3
5		832	15		15	723	6
6		684	6		16	746	7
7		683	9		17	632	5
8		768	4		18	740	13
9		776	10		19	778	6
10		840	13		20	822	7

Click here for the Excel Data File

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.

4. 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 0.10 significance level: H₀: ρ ≤ 0; H₁: ρ > 0. (Round your answer to 3 decimal places.)

2. 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.)

3. b-4. Can we conclude that there is a positive correlation between distance and time? Use the 0.10 significance level.

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

5. c-2. Fill in the blank below. (Round your answer to 1 decimal place.)

________% of the variation in shipping time is explained by shipping distance.

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

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

• Yes

• No

Answer 1

	n=	20.0000
	X̅=ΣX/n	758.750
	Y̅=ΣY/n	8.650
	sx=(√(Σx2-(Σx)2/n)/(n-1))=	57.950
	sy=(√(Σy2-(Σy)2/n)/(n-1))=	4.133
	Cov=sxy=(ΣXY-(ΣXΣY)/n)/(n-1)=	81.4342
	r=Cov/(Sx*Sy)=	0.3400

b-1)

x¯	758.75
y⎯⎯y¯	8.65
Sx	57.950
Sy	4.133
r	0.340

b-2)

0.1 level,right tail test and n-2= 18 df, critical t=			1.3304
Decision rule: reject Ho if test statistic t>1.330

b-3)

test stat t=

r*(√(n-2)/(1-r2))=

1.534

b-4)

Yes since test statistic is greater than critical value

c-1)

  coefficient of determination r² =0.116

c-2)

11.6 %  of the variation in shipping time is explained by shipping distance.

d)

	s2 =SSE/(n-2)=	15.9461
std error σ              =	=se =√s2=	3.993

e)

Yes