Quick2U, a delivery company, would like to standardize its delivery charge model for shipments (Charge in $) such that customers will better understand their delivery costs. Three predictor variables are used: (1) distance (in miles), (2) shipment weight (in lbs), and (3) number of boxes. A sample of 30 recent deliveries is collected: a portion of the data is shown in the accompanying table. Charge Distance Weight Boxes 92.50 29 183 1 157.60 96 135 3
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
1. Quick2U, a delivery company, would like to standardize its delivery charge model for shipments (Charge in $) such that customers will better understand their delivery costs. Three predictor variables are used: (1) distance (in miles), (2) shipment weight (in lbs), and (3) number of boxes. A sample of 30 recent deliveries is collected: a portion of the data is shown in the accompanying table.
Charge Distance Weight Boxes
92.50 29 183 1
157.60 96 135 3
34.20 13 37 1
74.40 26 79 8
122.30 88 92 2
113.90 70 85 5
64.80 62 37 1
119.60 61 68 8
51.80 14 61 6
67.90 26 80 4
56.90 50 15 4
71.40 59 10 1
114.20 93 39 3
110.30 59 70 5
84.60 69 39 5
121.70 86 86 4
102.10 53 96 3
86.90 34 92 2
74.80 49 75 1
153.20 93 90 8
146.80 89 96 6
162.50 511 41 6
87.60 93 18 1
25.80 3 1 2 6
54.40 49 37 1
123.90 76 84 8
85.20 48 80 4
81.80 58 22 4
76.60 51 12 6
143.00 47 117 7
A-1. estimate the model charge = B0 + B1distance + B2 weight + B3 boxes + e. (negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)
Charge =...........+.........distance +.........weight +......boxes
A-2. Examine the joint significance of the predictor variables at the 1% level. First, specify the competing hypotheses.
a) H0: B1 = B2 = B3 = 0; HA least one Bj > 0
b) H0: B1 = B2 = B3 = 0; HA a leat one Bj < 0
c) H0: B1 = B2 = B3 = 0; HA a leat one Bj # 0
A-3. Find the P-value
a) P-value < 0.01
b) 0.01< p-value < 0.025
c) 0.025 < p-value <0.05
d) 0.05 < p-value < 0.10
e) P-value > 0.10
A-4. What is the conclusion to the test?
..............H0, we...........conclude the predictor variables are jointly significant in explaining the delivery charges
A-5. examine the individual significance of the predictor variables at the 1% level. First, specify the competing hypotheses
a) H0: B1 = 0 ; HA : B1 > 0
b) H0: B1 = 0 ; HA : B1 > 0
c) H0: B1 = 0 ; HA : B1 > 0
A-6. for each predictor variable, state the P-value and determine whether the predictor variable is significant in explaining delivery charges.
Predictor variables P-value Significant in explain
Delivery charges
Distance .................. ..............
Weight .................. ..............
Boxes ............... .................
B. is there any evidence of the multicollinearity?
a) Yes, since the predictor variables are statistically significant with logical signs
b) Yes, since the predictor variables are not statistically significant with logical signs
c) No. since the predictor variables are statistically significant with logical signs
d) No, since the predictor variables are not statistically significant with logical signs
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or each predictor variable, state the P-value and determine whether the predictor variable is significant in explaining delivery charges.
Predictor variables P-value Significant in explain
Delivery charges
Distance .................. ..............
Weight .................. ..............
Boxes ............... .................
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