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Question: A.     Construct a correlation matrix showing the correlations between the fo…

by | Sep 9, 2023 | Aswered Questions


a.     Construct
a correlation matrix showing the correlations between the following
variables: (Note, leave out Surface Condition Code)

Average Speed
–All:             

Wind Speed:  

                                   
Air temp:       

                                   
Rel
Humid;                

Visibility:      

                                   
Surface
Temperature:                        

Total
Vehicles:          
           

        Which variable has the
highest correlation with Average Speed?

b.Develop a multiple regression model
using Average Speed as the dependent variable and the following
variables as independent variables:

           

Wind Speed:  

                                   
Air temp:       

                                   
Rel
Humid;                

Visibility:      

                                   
Surface
Temperature:                        

Total Vehicles:

           
       Show the regression
equation.

c. After examining the results from
parts a. and b., can you identify any potential multicollinearity
issues? Explain.

d. Determine whether the overall
regression model is statistically significant at an alpha level =
0.05. State the appropriate null and alternative hypothesis and use
the p-value approach to conduct the hypothesis test.

e.Identify which of the independent
variables are not statistically significant at the 0.05 alpha
level. Use the p-value approach to make this determination.

f.Calculate the predicted average
speed for a five-minute time segment under the following
conditions:

Wind Speed = 44 mph

                                   
Air temp = 36 degrees

                                   
Rel Humid =
59                     

Visibility = 7.15
miles           

                                   
Surface Temperature =
51.98            

Total Vehicles = 48

<

  

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Average Speed- All Wind Spd Air Temp Rel Hum Visibility Surface Condition Code Surface Temp Total Vehicles All
68.62 21 42 64 15.07 Wet 44.312 29.00
70.04 26 40 82 6.14 Wet 43.1276 24.00
67.95 21 39 88 1.45 Wet 42.818 20.00
68.86 19 37 87 1.9 Wet 42.6272 22.00
69.88 18 37 88 2.49 Wet 42.3815 25.00
68.45 17 38 89 2.84 Wet 42.08 22.00
65.52 16 36 91 5.41 Wet 41.774 21.00
65.14 18 35 92 4.97 Wet 41.468 22.00
67.04 17 35 95 5.64 Wet 41.162 25.00
68.33 21 36 96 11.31 Wet 40.862 21.00
70.23 22 34 98 6.36 Wet 40.406 22.00
66.80 25 35 98 6.29 Wet 39.794 25.00
66.29 24 33 99 6.07 Wet 39.407 24.00
69.69 25 33 100 5.17 Wet 38.957 13.00
64.83 19 33 100 6.87 Wet 39.038 12.00
62.44 19 33 100 7.14 Wet 39.038 16.00
65.54 17 33 100 6.96 Wet 39.002 24.00
65.00 14 33 98 13.35 Wet 38.732 13.00
64.53 12 33 98 19.85 Wet 39.038 17.00
67.06 10 33 98 25.02 Wet 39.11 17.00
66.69 11 35 97 21.62 Wet 39.038 13.00
63.53 12 33 98 21.58 Wet 39.038 19.00
67.68 13 35 94 25.12 Wet 38.732 22.00
66.30 14 35 94 23.56 Wet 38.504 23.00
65.08 11 33 94 24.96 Wet 37.814 12.00
63.75 10 33 95 19.49 Wet 37.814 16.00
69.09 7 33 96 19.74 Wet 37.814 11.00
65.76 8 33 96 12.41 Wet 38.096 17.00
66.29 8 33 96 15.7 Wet 38.318 14.00
67.36 9 33 94 17.9 Wet 38.372 11.00
67.25 10 35 92 12.77 Wet 38.264 16.00
69.58 10 34 90 16.09 Wet 38.12 12.00
65.50 10 35 91 5.9 Wet 37.733 12.00
64.12 11 33 92 5.2 Wet 37.844 17.00
66.35 10 33 93 12.28 Wet 37.958 17.00
64.00 12 35 92 20.54 Wet 37.808 11.00
66.80 14 33 93 6.51 Wet 37.427 15.00
67.94 18 34 94 3.75 Wet 37.166 17.00
70.17 15 32 97 2.17 Wet 36.776 6.00
64.17 16 34 91 2.74 Wet 36.635 6.00
67.00 17 32 93 1.57 Wet 35.978 13.00
67.57 19 32 93 1.17 Wet 34.7135 7.00
68.17 18 32 94 0.95 Wet 33.854 12.00
63.27 20 33 95 0.73 Wet 33.827 11.00
67.31 18 33 96 0.66 Wet 33.701 13.00
62.83 20 33 97 0.57 Wet 33.494 12.00
66.86 18 33 98 0.54 Wet 33.242 7.00
64.57 16 33 99 0.5 Wet 33.143 14.00
66.50 17 33 100 0.37 Wet 33.143 8.00
58.64 21 33 100 0.47 Wet 32.936 14.00
55.00 19 32 100 0.3 Wet 32.936 15.00
50.88 21 32 100 0.21 Wet 33.044 8.00
62.20 21 32 100 0.14 Wet 32.936 5.00
55.07 22 31 100 0.22 Wet 32.936 14.00
47.75 24 31 100 0.48 Wet 32.99 8.00
46.67 26 31 100 0.32 Wet 33.044 6.00
44.00 25 31 100 0.32 Wet 33.044 5.00
30.50 24 31 100 0.25 Wet 33.017 2.00
38.29 30 31 100 0.11 Wet 33.188 7.00
43.75 29 31 100 0.13 Wet 32.792 8.00
34.57 28 31 100 0.18 Wet 32.8145 7.00
35.00 28 31 100 0.2 Wet 32.936 6.00
34.50 26 31 100 0.23 Wet 32.882 6.00
35.86 26 31 100 0.24 Wet 32.936 7.00
34.25 26 31 100 0.23 Wet 32.936 4.00
37.00 30 30 100 0.18 Wet 32.882 3.00
26.33 32 30 100 0.17 Wet 32.792 6.00
36.14 32 30 100 0.21 Wet 32.792 7.00
31.78 30 30 100 0.28 Wet 32.882 9.00
40.50 28 30 100 0.46 Wet 32.792 6.00
35.60 28 30 100 0.47 Wet 32.8145 5.00
30.50 29 30 100 0.45 Wet 32.792 6.00
37.50 29 29 100 0.3 Wet 32.792 8.00
32.00 31 29 99 0.15 Wet 32.837 4.00
38.00 32 28 100 0.1 Wet 32.792 9.00
37.71 34 28 99 0.09 Wet 32.792 14.00
42.00 32 28 99 0.1 Wet 32.837 2.00
43.50 32 28 98 0.12 Wet 32.936 6.00
25.00 34 27 98 0.09 Wet 32.738 15.00
8.25 47 26 91 0.34 Wet 32.63 4.00
5.10 47 26 91 0.4 Wet 32.63 9.00
23.00 46 33 65 7.95 Wet 43.529 10.00
18.25 45 33 67 6.96 Wet 44.294 5.00
17.41 44 33 63 6.69 Wet 41.924 12.00
26.33 42 33 66 7.21 Wet 36.896 3.00
66.3 17 29 98 2.28 Wet 32.486 10.0
61.9 14 29 97 1.47 Wet 32.630 20.0
68.3 13 29 97 1.23 Wet 32.630 23.0
63.3 14 29 97 1.07 Wet 32.630 23.0
61.3 14 29 95 1 Wet 32.630 18.0
65.3 17 29 96 1.04 Wet 32.630 20.0
61.6 16 29 96 0.8 Wet 32.783 16.0
64.4 13 30 96 0.81 Wet 32.936 23.0
67.2 14 30 96 0.71 Wet 32.936 9.0
65.6 13 30 97 0.7 Wet 32.909 14.0
65.2 13 30 97 0.73 Wet 33.650 18.0
67.4 14 30 96 0.72 Wet 34.304 19.0
65.0 14 30 96 0.79 Wet 34.871 21.0
61.3 13 30 97 0.8 Wet 35.006 13.0
67.6 14 30 97 0.84 Wet 35.078 36.0
64.4 12 30 97 0.72 Wet 35.780 20.0
67.9 12 30 97 0.64 Wet 35.528 20.0
67.1 12 30 97 0.37 Wet 34.079 31.0
61.8 10 30 98 0.32 Wet 33.386 32.0
62.6 11 31 97 0.57 Wet 33.242 32.0
65.0 11 30 97 0.37 Wet 33.998 30.0
60.6 7 31 99 0.44 Wet 33.092 31.0
65.3 10 31 98 0.48 Wet 33.044 30.0
64.6 15 31 98 0.5 Wet 33.044 26.0
66.1 14 31 95 0.56 Wet 34.730 28.0
63.6 13 31 96 0.48 Wet 36.806 26.0
64.9 12 30 95 0.53 Wet 36.797 29.0
64.3 15 31 94 0.65 Wet 37.352 34.0
67.7 14 31 95 0.61 Wet 39.481 39.0
67.3 13 31 95 0.55 Wet 40.856 32.0
67.0 14 31 95 0.85 Wet 40.334 31.0