Question

Jim is a transportation engineer and is interested in whether roadways that score high in one traffic engineering aspect also tend to score high in other aspects. To address this question, he completed a survey of 80 roadways that contain five measures of effectiveness with ratings for safety, capacity, speed, alignment, and flow.

a) Conduct a correlational analysis to investigate these relationships. What are your conclusions?

b) Jim determines that the speed of a facility affect/s the other roadway scores. Reevaluate Jim's hypothesis by controlling for speed. What effect does partialling out the effects of speed have on the relationships?

safety capacity speed alignment flow

48   56   48   35   47
44   50   47   41   51
38   41   49   59   46
48   59   59   49   52
44   44   52   37   47
43   57   42   52   54
49   53   56   32   49
52   65   57   54   54
55   63   56   58   53
50   60   49   52   54
45   47   44   51   49
61   56   57   63   50
49   57   50   51   50
44   45   46   31   47
39   50   51   28   52
50   51   51   43   54
49   51   50   50   49
37   52   44   45   53
49   55   51   47   53
47   48   46   44   54
55   56   55   42   54
49   60   62   58   53
45   58   65   59   54
39   40   36   44   46
54   56   51   55   52
58   58   51   44   53
52   52   62   47   53
50   56   38   47   51
62   57   52   25   53
55   55   59   57   49
50   52   52   47   53
44   35   44   46   45
55   55   39   24   48
46   45   44   54   47
48   51   47   50   50
52   52   38   53   47
52   49   50   59   49
50   49   39   40   48
48   50   52   52   43
50   45   46   36   47
50   46   44   44   52
43   40   43   27   45
40   44   54   50   47
57   67   53   41   58
57   52   56   67   58
61   62   51   60   56
46   52   52   60   56
42   44   48   41   56
60   58   66   50   57
47   47   58   51   56
50   59   51   43   57
63   65   56   63   62
59   52   42   42   56
50   52   59   57   56
49   59   62   51   61
51   52   56   44   58
47   62   67   54   66
52   62   58   47   62
60   48   55   45   63
45   45   59   47   60
59   53   51   39   57
57   51   68   59   59
46   60   64   54   57
51   61   46   44   59
47   53   49   41   55
50   63   52   48   64
57   69   70   51   57
50   57   51   37   56
65   69   62   60   55
50   58   54   49   56
56   63   54   49   58
54   65   57   38   56
42   53   47   45   56
53   53   62   49   59
61   54   57   63   61
47   56   50   58   55
46   55   48   55   57
57   54   58   58   57
56   60   51   47   58
50   52   50   46   56

Answer 1

From the given data set, first we will compute the total correlation coefficient

safety	capacity	speed	alignment	flow
x1	x2	x3	x4	x5
48	56	48	35	47
44	50	47	41	51
38	41	49	59	46
48	59	59	49	52
44	44	52	37	47
43	57	42	52	54
49	53	56	32	49
52	65	57	54	54
55	63	56	58	53
50	60	49	52	54
45	47	44	51	49
61	56	57	63	50
49	57	50	51	50
44	45	46	31	47
39	50	51	28	52
50	51	51	43	54
49	51	50	50	49
37	52	44	45	53
49	55	51	47	53
47	48	46	44	54
55	56	55	42	54
49	60	62	58	53
45	58	65	59	54
39	40	36	44	46
54	56	51	55	52
58	58	51	44	53
52	52	62	47	53
50	56	38	47	51
62	57	52	25	53
55	55	59	57	49
50	52	52	47	53
44	35	44	46	45
55	55	39	24	48
46	45	44	54	47
48	51	47	50	50
52	52	38	53	47
52	49	50	59	49
50	49	39	40	48
48	50	52	52	43
50	45	46	36	47
50	46	44	44	52
43	40	43	27	45
40	44	54	50	47
57	67	53	41	58
57	52	56	67	58
61	62	51	60	56
46	52	52	60	56
42	44	48	41	56
60	58	66	50	57
47	47	58	51	56
50	59	51	43	57
63	65	56	63	62
59	52	42	42	56
50	52	59	57	56
49	59	62	51	61
51	52	56	44	58
47	62	67	54	66
52	62	58	47	62
60	48	55	45	63
45	45	59	47	60
59	53	51	39	57
57	51	68	59	59
46	60	64	54	57
51	61	46	44	59
47	53	49	41	55
50	63	52	48	64
57	69	70	51	57
50	57	51	37	56
65	69	62	60	55
50	58	54	49	56
56	63	54	49	58
54	65	57	38	56
42	53	47	45	56
53	53	62	49	59
61	54	57	63	61
47	56	50	58	55
46	55	48	55	57
57	54	58	58	57
56	60	51	47	58
50	52	50	46	56

Since the calculation steps are very long, we will use the Excel to calculate the above total correlations

[How to do it in Excel: Go to data. Choose Data Analysis. Choose correlation. Select Data set]

The correlation coeffecient matrix is given below

	x1	x2	x3	x4	x5
x1	1.000
x2	0.552	1.000
x3	0.351	0.462	1.000
x4	0.218	0.244	0.400	1.000
x5	0.393	0.546	0.525	0.261	1.000

From the above, the following set of varibles have moderate correlation as they have values around 0.5

(x1, x2); (x2,x5) and (x3,x5)

Other combinations have low level of correlations that mean there is no strong relationship in the ratings

(b) According to Jim, speed is the deciding factor on the ratings. Therefore we need to find the relation of other variables with respect to x3 or in other words, how speed influenc other ratings.

From the above table it is clearly coming out there is only moderate relationship between x3 and x5 which is 0.525. So, only flow is affected by speed. Other facotrs are not so much affected by speed,