(a)
Draw the time-series plot for the given data.
Identify the pattern.
(a)
Explanation of Solution
Step-by-step procedure to construct time-series plot is given below.
- Enter the data in columns A and B. Select the data.
- Click on Insert tab and then click on line.
- Select line with markers
The output is given below:
From the above time-series plot, it is clear that plot shows upward trend. Also, there exists seasonal pattern.
(b)
Find a multiple regression equation that represents seasonal effect using dummy variables for the given data.
(b)
Answer to Problem 25P
The regression equation is,
Explanation of Solution
Dummy variables are defined as given below:
Also, all the dummy variables are 0 when the reading time corresponds to 5:00 p.m. to 6:00 p.m.
The given data is entered as given below:
Hourly Dummy Variables | |||||||||||||
Date | Hour | yt | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
July 15 | 6:00 a.m. - 7:00 a.m. | 25 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
July 15 | 7:00 a.m. - 8:00 a.m. | 28 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
July 15 | 8:00 a.m. - 9:00 a.m. | 35 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
July 15 | 9:00 a.m. - 10:00 a.m. | 50 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
July 15 | 10:00 a.m. - 11:00 a.m. | 60 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
July 15 | 11:00 a.m. - 12:00 p.m. | 60 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
July 15 | 12:00 p.m. - 1:00 p.m. | 40 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
July 15 | 1:00 p.m. - 2:00 p.m. | 35 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
July 15 | 2:00 p.m. - 3:00 p.m. | 30 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
July 15 | 3:00 p.m. - 4:00 p.m. | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
July 15 | 4:00 p.m. - 5:00 p.m. | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
July 15 | 5:00 p.m. - 6:00 p.m. | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
July 16 | 6:00 a.m. - 7:00 a.m. | 28 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
July 16 | 7:00 a.m. - 8:00 a.m. | 30 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
July 16 | 8:00 a.m. - 9:00 a.m. | 35 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
July 16 | 9:00 a.m. - 10:00 a.m. | 48 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
July 16 | 10:00 a.m. - 11:00 a.m. | 60 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
July 16 | 11:00 a.m. - 12:00 p.m. | 65 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
July 16 | 12:00 p.m. - 1:00 p.m. | 50 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
July 16 | 1:00 p.m. - 2:00 p.m. | 40 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
July 16 | 2:00 p.m. - 3:00 p.m. | 35 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
July 16 | 3:00 p.m. - 4:00 p.m. | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
July 16 | 4:00 p.m. - 5:00 p.m. | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
July 16 | 5:00 p.m. - 6:00 p.m. | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
July 17 | 6:00 a.m. - 7:00 a.m. | 35 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
July 17 | 7:00 a.m. - 8:00 a.m. | 42 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
July 17 | 8:00 a.m. - 9:00 a.m. | 45 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
July 17 | 9:00 a.m. - 10:00 a.m. | 70 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
July 17 | 10:00 a.m. - 11:00 a.m. | 72 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
July 17 | 11:00 a.m. - 12:00 p.m. | 75 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
July 17 | 12:00 p.m. - 1:00 p.m. | 60 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
July 17 | 1:00 p.m. - 2:00 p.m. | 45 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
July 17 | 2:00 p.m. - 3:00 p.m. | 40 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
July 17 | 3:00 p.m. - 4:00 p.m. | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
July 17 | 4:00 p.m. - 5:00 p.m. | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
July 17 | 5:00 p.m. - 6:00 p.m. | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Step-by-step procedure to obtain multiple linear regression line is given below.
- Enter the data in columns A to M.
- Click on Data tab and then Data Analysis.
- Select Regression and click ok.
- In Input Y
Range select, $B$2:$B$37 and Input X Range select $C$2:$M$37 - Click Ok.
The output is given below:
From the output the regression equation is,
Here, X Variable 1 represents Hour1, X Variable 2 represents Hour2, … X variable 11 represents Hour11.
(c)
Find the estimates of the levels of nitrogen for July 18 using the model developed in part (b).
(c)
Explanation of Solution
From part (b), the regression equation is,
Forecast for July 18 is obtained as given below:
Hourly forecast | Calculation | |
Hour1 | 29.34 | |
Hour2 | 33.34 | |
Hour3 | 38.34 | |
Hour4 | 56 | |
Hour5 | 64 | |
Hour6 | 66.67 | |
Hour7 | 50 | |
Hour8 | 40 | |
Hour9 | 35 | |
Hour10 | 25 | |
Hour11 | 23.34 | |
Hour12 | 21.67 | 21.67 |
(d)
Construct a multiple regression equation that represents seasonal effect using dummy variables and a t variable for the given data.
(d)
Answer to Problem 25P
The regression equation is,
Explanation of Solution
Create a variable t such that t = 1 for hour 1 on July 15, t = 2 for hour 2 on July 2, …, t = 36 for hour 12 on July 18.
The given data is entered as given below:
Hourly Dummy Variables | ||||||||||||||
Date | Hour | yt | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | t |
July 15 | 6:00 a.m. - 7:00 a.m. | 25 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
July 15 | 7:00 a.m. - 8:00 a.m. | 28 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 |
July 15 | 8:00 a.m. - 9:00 a.m. | 35 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 3 |
July 15 | 9:00 a.m. - 10:00 a.m. | 50 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4 |
July 15 | 10:00 a.m. - 11:00 a.m. | 60 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 5 |
July 15 | 11:00 a.m. - 12:00 p.m. | 60 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 6 |
July 15 | 12:00 p.m. - 1:00 p.m. | 40 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 7 |
July 15 | 1:00 p.m. - 2:00 p.m. | 35 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 8 |
July 15 | 2:00 p.m. - 3:00 p.m. | 30 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 9 |
July 15 | 3:00 p.m. - 4:00 p.m. | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 10 |
July 15 | 4:00 p.m. - 5:00 p.m. | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 11 |
July 15 | 5:00 p.m. - 6:00 p.m. | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 12 |
July 16 | 6:00 a.m. - 7:00 a.m. | 28 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 13 |
July 16 | 7:00 a.m. - 8:00 a.m. | 30 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 14 |
July 16 | 8:00 a.m. - 9:00 a.m. | 35 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 15 |
July 16 | 9:00 a.m. - 10:00 a.m. | 48 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 16 |
July 16 | 10:00 a.m. - 11:00 a.m. | 60 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 17 |
July 16 | 11:00 a.m. - 12:00 p.m. | 65 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 18 |
July 16 | 12:00 p.m. - 1:00 p.m. | 50 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 19 |
July 16 | 1:00 p.m. - 2:00 p.m. | 40 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 20 |
July 16 | 2:00 p.m. - 3:00 p.m. | 35 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 21 |
July 16 | 3:00 p.m. - 4:00 p.m. | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 22 |
July 16 | 4:00 p.m. - 5:00 p.m. | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 23 |
July 16 | 5:00 p.m. - 6:00 p.m. | 20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 24 |
July 17 | 6:00 a.m. - 7:00 a.m. | 35 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 25 |
July 17 | 7:00 a.m. - 8:00 a.m. | 42 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 26 |
July 17 | 8:00 a.m. - 9:00 a.m. | 45 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 27 |
July 17 | 9:00 a.m. - 10:00 a.m. | 70 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 28 |
July 17 | 10:00 a.m. - 11:00 a.m. | 72 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 29 |
July 17 | 11:00 a.m. - 12:00 p.m. | 75 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 30 |
July 17 | 12:00 p.m. - 1:00 p.m. | 60 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 31 |
July 17 | 1:00 p.m. - 2:00 p.m. | 45 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 32 |
July 17 | 2:00 p.m. - 3:00 p.m. | 40 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 33 |
July 17 | 3:00 p.m. - 4:00 p.m. | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 34 |
July 17 | 4:00 p.m. - 5:00 p.m. | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 35 |
July 17 | 5:00 p.m. - 6:00 p.m. | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 36 |
Step-by-step procedure to obtain multiple linear regression line is given below.
- Enter the data in columns A to N.
- Click on Data tab and then Data Analysis.
- Select Regression and click ok.
- In Input Y Range select, $B$2:$B$37 and Input X Range select $C$2:$N$37
- Click Ok.
The output is given below:
From the output the regression equation is,
Here, X Variable 1 represents Hour1, X Variable 2 represents Hour2,… X variable 11 represents Hour11 and X variable 12 represents t.
(e)
Calculate the estimates of the levels of nitrogen for July 18 using the model developed in part (d).
(e)
Explanation of Solution
From part (d), the regression equation is,
Forecast for July 18 is given below:
Hourly forecast | T | Calculation | |
1 | 37 | 39.93 | |
2 | 38 | 43.93 | |
3 | 39 | 48.93 | |
4 | 40 | 66.6 | |
5 | 41 | 74.71 | |
6 | 42 | 77.28 | |
7 | 43 | 60.61 | |
8 | 44 | 50.61 | |
9 | 45 | 45.62 | |
10 | 46 | 35.62 | |
11 | 47 | 33.95 | |
12 | 48 | 32.29 |
(f)
Justify which of the models (b) or (d) is effective.
(f)
Answer to Problem 25P
Model (d) is preferred.
Explanation of Solution
For the multiple regression equation developed in part (b), MSE is obtained as given below:
Date | Hour | yt | Forecast | Forecast Error | Squared Forecast Error |
15-Jul | 6:00 a.m. - 7:00 a.m. | 25 | 29.34 | -4.34 | 18.8356 |
15-Jul | 7:00 a.m. - 8:00 a.m. | 28 | 33.34 | -5.34 | 28.5156 |
15-Jul | 8:00 a.m. - 9:00 a.m. | 35 | 38.34 | -3.34 | 11.1556 |
15-Jul | 9:00 a.m. - 10:00 a.m. | 50 | 56 | -6 | 36 |
15-Jul | 10:00 a.m. - 11:00 a.m. | 60 | 64 | -4 | 16 |
15-Jul | 11:00 a.m. - 12:00 p.m. | 60 | 66.67 | -6.67 | 44.4889 |
15-Jul | 12:00 p.m. - 1:00 p.m. | 40 | 50 | -10 | 100 |
15-Jul | 1:00 p.m. - 2:00 p.m. | 35 | 40 | -5 | 25 |
15-Jul | 2:00 p.m. - 3:00 p.m. | 30 | 35 | -5 | 25 |
15-Jul | 3:00 p.m. - 4:00 p.m. | 25 | 25 | 0 | 0 |
15-Jul | 4:00 p.m. - 5:00 p.m. | 25 | 23.34 | 1.66 | 2.7556 |
15-Jul | 5:00 p.m. - 6:00 p.m. | 20 | 21.67 | -1.67 | 2.7889 |
16-Jul | 6:00 a.m. - 7:00 a.m. | 28 | 29.34 | -1.34 | 1.7956 |
16-Jul | 7:00 a.m. - 8:00 a.m. | 30 | 33.34 | -3.34 | 11.1556 |
16-Jul | 8:00 a.m. - 9:00 a.m. | 35 | 38.34 | -3.34 | 11.1556 |
16-Jul | 9:00 a.m. - 10:00 a.m. | 48 | 56 | -8 | 64 |
16-Jul | 10:00 a.m. - 11:00 a.m. | 60 | 64 | -4 | 16 |
16-Jul | 11:00 a.m. - 12:00 p.m. | 65 | 66.67 | -1.67 | 2.7889 |
16-Jul | 12:00 p.m. - 1:00 p.m. | 50 | 50 | 0 | 0 |
16-Jul | 1:00 p.m. - 2:00 p.m. | 40 | 40 | 0 | 0 |
16-Jul | 2:00 p.m. - 3:00 p.m. | 35 | 35 | 0 | 0 |
16-Jul | 3:00 p.m. - 4:00 p.m. | 25 | 25 | 0 | 0 |
16-Jul | 4:00 p.m. - 5:00 p.m. | 20 | 23.34 | -3.34 | 11.1556 |
16-Jul | 5:00 p.m. - 6:00 p.m. | 20 | 21.67 | -1.67 | 2.7889 |
17-Jul | 6:00 a.m. - 7:00 a.m. | 35 | 29.34 | 5.66 | 32.0356 |
17-Jul | 7:00 a.m. - 8:00 a.m. | 42 | 33.34 | 8.66 | 74.9956 |
17-Jul | 8:00 a.m. - 9:00 a.m. | 45 | 38.34 | 6.66 | 44.3556 |
17-Jul | 9:00 a.m. - 10:00 a.m. | 70 | 56 | 14 | 196 |
17-Jul | 10:00 a.m. - 11:00 a.m. | 72 | 64 | 8 | 64 |
17-Jul | 11:00 a.m. - 12:00 p.m. | 75 | 66.67 | 8.33 | 69.3889 |
17-Jul | 12:00 p.m. - 1:00 p.m. | 60 | 50 | 10 | 100 |
17-Jul | 1:00 p.m. - 2:00 p.m. | 45 | 40 | 5 | 25 |
17-Jul | 2:00 p.m. - 3:00 p.m. | 40 | 35 | 5 | 25 |
17-Jul | 3:00 p.m. - 4:00 p.m. | 25 | 25 | 0 | 0 |
17-Jul | 4:00 p.m. - 5:00 p.m. | 25 | 23.34 | 1.66 | 2.7556 |
17-Jul | 5:00 p.m. - 6:00 p.m. | 25 | 21.67 | 3.33 | 11.0889 |
1076.001 |
For the multiple regression equation developed in part (d), MSE is obtained as given below:
Date | Hour | t | yt | Forecast | Forecast Error | Squared Forecast Error |
15-Jul | 6:00 a.m. - 7:00 a.m. | 1 | 25 | 24.09 | 0.91 | 0.8281 |
15-Jul | 7:00 a.m. - 8:00 a.m. | 2 | 28 | 28.09 | -0.09 | 0.0081 |
15-Jul | 8:00 a.m. - 9:00 a.m. | 3 | 35 | 33.09 | 1.91 | 3.6481 |
15-Jul | 9:00 a.m. - 10:00 a.m. | 4 | 50 | 50.76 | -0.76 | 0.5776 |
15-Jul | 10:00 a.m. - 11:00 a.m. | 5 | 60 | 58.87 | 1.13 | 1.2769 |
15-Jul | 11:00 a.m. - 12:00 p.m. | 6 | 60 | 61.44 | -1.44 | 2.0736 |
15-Jul | 12:00 p.m. - 1:00 p.m. | 7 | 40 | 44.77 | -4.77 | 22.7529 |
15-Jul | 1:00 p.m. - 2:00 p.m. | 8 | 35 | 34.77 | 0.23 | 0.0529 |
15-Jul | 2:00 p.m. - 3:00 p.m. | 9 | 30 | 29.78 | 0.22 | 0.0484 |
15-Jul | 3:00 p.m. - 4:00 p.m. | 10 | 25 | 19.78 | 5.22 | 27.2484 |
15-Jul | 4:00 p.m. - 5:00 p.m. | 11 | 25 | 18.11 | 6.89 | 47.4721 |
15-Jul | 5:00 p.m. - 6:00 p.m. | 12 | 20 | 16.45 | 3.55 | 12.6025 |
16-Jul | 6:00 a.m. - 7:00 a.m. | 13 | 28 | 29.37 | -1.37 | 1.8769 |
16-Jul | 7:00 a.m. - 8:00 a.m. | 14 | 30 | 33.37 | -3.37 | 11.3569 |
16-Jul | 8:00 a.m. - 9:00 a.m. | 15 | 35 | 38.37 | -3.37 | 11.3569 |
16-Jul | 9:00 a.m. - 10:00 a.m. | 16 | 48 | 56.04 | -8.04 | 64.6416 |
16-Jul | 10:00 a.m. - 11:00 a.m. | 17 | 60 | 64.15 | -4.15 | 17.2225 |
16-Jul | 11:00 a.m. - 12:00 p.m. | 18 | 65 | 66.72 | -1.72 | 2.9584 |
16-Jul | 12:00 p.m. - 1:00 p.m. | 19 | 50 | 50.05 | -0.05 | 0.0025 |
16-Jul | 1:00 p.m. - 2:00 p.m. | 20 | 40 | 40.05 | -0.05 | 0.0025 |
16-Jul | 2:00 p.m. - 3:00 p.m. | 21 | 35 | 35.06 | -0.06 | 0.0036 |
16-Jul | 3:00 p.m. - 4:00 p.m. | 22 | 25 | 25.06 | -0.06 | 0.0036 |
16-Jul | 4:00 p.m. - 5:00 p.m. | 23 | 20 | 23.39 | -3.39 | 11.4921 |
16-Jul | 5:00 p.m. - 6:00 p.m. | 24 | 20 | 21.73 | -1.73 | 2.9929 |
17-Jul | 6:00 a.m. - 7:00 a.m. | 25 | 35 | 34.65 | 0.35 | 0.1225 |
17-Jul | 7:00 a.m. - 8:00 a.m. | 26 | 42 | 38.65 | 3.35 | 11.2225 |
17-Jul | 8:00 a.m. - 9:00 a.m. | 27 | 45 | 43.65 | 1.35 | 1.8225 |
17-Jul | 9:00 a.m. - 10:00 a.m. | 28 | 70 | 61.32 | 8.68 | 75.3424 |
17-Jul | 10:00 a.m. - 11:00 a.m. | 29 | 72 | 69.43 | 2.57 | 6.6049 |
17-Jul | 11:00 a.m. - 12:00 p.m. | 30 | 75 | 72 | 3 | 9 |
17-Jul | 12:00 p.m. - 1:00 p.m. | 31 | 60 | 55.33 | 4.67 | 21.8089 |
17-Jul | 1:00 p.m. - 2:00 p.m. | 32 | 45 | 45.33 | -0.33 | 0.1089 |
17-Jul | 2:00 p.m. - 3:00 p.m. | 33 | 40 | 40.34 | -0.34 | 0.1156 |
17-Jul | 3:00 p.m. - 4:00 p.m. | 34 | 25 | 30.34 | -5.34 | 28.5156 |
17-Jul | 4:00 p.m. - 5:00 p.m. | 35 | 25 | 28.67 | -3.67 | 13.4689 |
17-Jul | 5:00 p.m. - 6:00 p.m. | 36 | 25 | 27.01 | -2.01 | 4.0401 |
414.6728 |
MSE for model in (d) is smaller than MSE for the model in (b). Thus, model (d) is preferred.
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Chapter 8 Solutions
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