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		770	10		11	612	12
2		781	12		12	830	6
3		753	10		13	800	8
4		617	9		14	741	5
5		757	7		15	792	6
6		818	11		16	850	5
7		673	15		17	714	9
8		603	6		18	781	8
9		684	4		19	816	10
10		639	9		20	776	11

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 0.02 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 0.02 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.)

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

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

• Yes

• No

Answer 1

We input the data set in R programming software and use the mean(.), sd(.), cor(.), lm(.), summary(.) and plot(.) functions to answer the given questions and carry out the regression analysis and the test for significant positive correlation. Here, x = Distance, y = Shipping Time. The screenshot of the commands and the output is given below.


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? No, there does not appear that there is a relationship, because the points are scattered.

(b-1) .

(b-2) Reject H0 if t (test statistic) < -2.552 (critical value). This is the decision rule.

(b-3) Test statistic = t value of x in the output = -0.648.

(b-4) Can we conclude that there is a positive correlation between distance and time? No, since the test statistic value is greater than the critical value.

(c-1) R² = 0.023.
(c-2) R² = 2.3%.
Standard error of estimate = Residual standard error in the output = 2.878.
Would you recommend using the regression equation to predict shipping time? No, since the value of R² is very, very small.