(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 5 Solutions
Essentials Of Business Analytics
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- A restaurant uses comment cards to get feedback from its customers about newly added items to the menu. It recently introduced homemade organic veggie burgers. Customers who tried the new burger were asked if they would order it again. The data is summarized in the table and bar graph. A. Convert this table into a relative frequency Round answers to the nearest tenth. B. Based upon the bar chart and the relative frequency table, would you recommend that the restaurant owner keeps the organic veggie burger on the menu? Explain yourarrow_forwardIn 2019 a major appliance factory can produce 600 ovens daily . To make sure the temperature controls are calibrated properly, an oven is set to 350 degrees Fahrenheit . Once the display shows 350 is reached , the temperature of the oven is tested and recorded. A factory worker selects 50 ovens to test throughout the day. The recorded temperatures are evaluated (Please use the drop down menus to answer each question.) a. In this scenario, what value represents the population under study? 2019, 50,350, 600, or temperature b. In this scenario, what value represents the sample used for the study? 2019, 50,350, 600, or temperature c. What data type is the worker gathering ? 2019, 50,350, 600, or temperature d. What level of measurement does this type of data have? 2019, 50,350, 600, or temperaturearrow_forwardEach day, the office staff at Oasis Quick Shop prepares a frequency distribution and an ogive of sales transactions by dollar value of the transactions. Saturday's cumulative frequency ogive follows. The percentage of sales transactions on Saturday that were at least $100 each was a. 100 b. 10 c. 80 d. 20 e. 15arrow_forward
- The scores that golfers shot on 18 holes at a local course were tabulated. The results are shown in the following frequency distribution.arrow_forwardUse the table below to answer questions 1-3. Suppose we want to estimate the annual high temperatures of the hottest major cities in the United States. Below is data from 12 cities with the average annual temperature taken from 1971 to 2000 (https://www.statista.com/statistics/226809/us-cities-with-the-highest-annual-temperatures/). City Temperature (Fahrenheit) Phoenix, Arizona 87.2 Miami, Florida 84.3 Orlando, Florida 82.8 Riverside, California 80.9 Austin, Texas 79.8 Houston, Texas 79.7 San Antonio, Texas 80.3 Las Vegas, Nevada 80.1 Jacksonville, Florida 79.3 New Orleans, Louisiana 78.2 Tampa, Florida 81.7 Los Angeles, California 75.2 Flag question: Question 1 Question 1 State the population for this study. The population is____________ Question 2 State the sample for this study. The sample is_______________ Question 3 What are the variables for the study and classify each as…arrow_forwardA car dealership keeps track of how much it spends on advertising each month and of its monthly revenue. From this information, the list of advertising expenditures and probable associated revenues are shown in the table below.arrow_forward
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