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		Shipment time (days)
1	626		5
2	801		11
3	733		4
4	640		3
5	756		13
6	790		8
7	718		8
8	652		3
9	792		12
10	629		4
11	696		9
12	718		10
13	754		3
14	648		4
15	666		3
16	831		10
17	691		13
18	822		9
19	793		3
20	784		11

Show your work and explain:

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

y ________
x̄ ________
sx _______

sy _______

r ________

2. State the decision rule for 0.01 significance level: H0: ρ ≤ 0; H1: ρ > 0. (Round your answer to 3 decimal places.)

Reject H0 if t > _______

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

Value of the test statistic __________

4. Can we conclude that there is a positive correlation between distance and time? Use the 0.01 significance level.

_________H0. We_________ conclude that there is a positive correlation between distance and time.

5. Coefficient of determination __________

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

7. Standard error ________

8. Would you recommend using the regression equation to predict shipping time? No Yes

Answer 1

EXCEL (Data Analysis) output:

SUMMARY OUTPUT Regression Statistics Multiple R 0.518088261 R Square 0.268415446 Adjusted R Square 0.22777186 Standard Error 3.289273883 Observations 20 ANOVA Significance F 0.019281769 Regression Residual Total 1 18 19 MS F 71.45219178 71.45219 6.604128 194.7478082 10.81932 2 66.2 Intercept Shipping Distnace Coefficients -13.40376382 0.028478355 Standard Error Stat P-value 8 .089914056 -1.65685 0.114877 0.011081719 2.56985 0.019282 Lower 95% Upper 95% -30.40004254 3.592514897 0.005196526 0.051760183 Descriptive statistics count mean sample standard deviation sample variance Shipping Distnace 20 727.00 68.10 4,636.95 Shipment time 20 7.30 3.74 14.01

j=7.3 i = 727 = 68.095 s, = 3.743 r=0.518 (2) Reject H, ift> 2.552.

(0.518) V20-2 V1-0.5182 2.1977 0.8554 = 2.569 Value of the test statistic: t = 2.569. Reject H. We can conclude that there is a positive correlation between distance and time. Coefficient of determination: R2 = 0.268. 26.8% of the variation in shipping time is explained by shipping distance.

Standard error: SE = 3.289 No.