Question

A regional express delivery service company recently conducted a study to investigate the relationship between the cost of shipping a package ($), the package weight (in pound) and the distance shipped (in miles). Twenty packages were randomly selected from among the large number received for shipment, and a detailed analysis of the shipping cost was conducted for each package.

Cost_of_Shipment	Package_Weight	Distance_Shipped
$3.30	4.10	95
$2.00	0.30	160
$11.00	5.10	240
$2.60	5.90	47
$1.90	4.50	53
$8.00	3.50	250
$15.50	7.00	260
$5.00	2.40	209
$1.00	0.60	100
$4.40	0.75	280
$6.00	6.20	115
$1.70	1.10	90
$14.50	6.50	240
$14.00	7.50	190
$9.20	6.60	160
$1.10	2.70	45
$12.10	8.10	160
$1.50	0.70	80
$8.00	4.40	202
$3.90	3.20	145
$4.40	0.75	280
$16.50	7.20	280
$15.50	7.00	250
$14.00	7.50	190
$3.30	4.10	95
$2.20	1.50	160
$11.00	5.10	240
$1	0.6	100
$4	0.75	280
$2	0.7	80
$8	4.4	202
$2	4.5	52
$8.00	3.2	240
$15.50	7.6	270
$5.00	2.5	211
$1.00	7	98
$8.00	4.4	202
$3.90	3.2	145
$4.40	0.75	280
$5.00	2.4	209

1. Use the F test to determine the overall significance of the regression relationship for the expanded model. What is the conclusion at the 0.01 level of significance?

2. Use the t test to determine the significance of each independent variable. What is the conclusion for each test at the 0.01 level of significance?  

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.931476
R Square	0.867647
Adjusted R Square	0.860493
Standard Error	1.847203
Observations	40
ANOVA
	df	SS	MS	F	Significance F
Regression	2	827.6411	413.8206	121.2782	5.65E-17
Residual	37	126.2499	3.412159
Total	39	953.891
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-5.08357	0.830332	-6.12233	4.29E-07	-6.76598	-3.40116	-6.76598	-3.40116
Package_Weight	1.347949	0.119289	11.29982	1.48E-13	1.106246	1.589653	1.106246	1.589653
Distance_Shipped	0.036372	0.00387	9.397333	2.43E-11	0.02853	0.044214	0.02853	0.044214

a)

Ho: overall model is not significant

ha: overall model is significant

F=121.28

p value=0.000<0.01

so, reject Ho

hence, overall regression model is significant

b)

for Package_Weight

t=11.29982287

p value =0.00<0.01, reject Ho

hence, variable Package_Weight is significant predictor

-------------

similarly , for Distance_Shipped

p value=0.00<α=0.01

hence, variable distance shipped , is significant predictor