Eco 309-Assignment 4 due by midnight on November 27, 2022
Total points 125. Submit through D2L in Word/Excel format, single or multiple files. Must show
all Excel work, answer all parts of the question, and write necessary explanations to earn full
points. Use Excel to solve this numerical problem (project).
Question 4. The local utility company hypothesizes that fuel consumption (natural gas) in their
town would be affected by temperature and chill index. The following data was collected for 10
weeks during the winter.
Week
Fuel Consumption
Y(MMcf)
Average Temp
X1 (0F)
Chill Index
X2
1
160
30.0
18
2
130
28.0
15
3
135
32.5
25
4
120
39.0
20
5
105
41.0
10
6
75
51.0
16
7
110
40.5
5
8
9
10
100
100
95
50.5
45.0
48.0
0
10
8
Conduct a Multiple Regression among Fuel consumption (Y), temperature (X1), and chill index
(X2). Solve using excel. What is the multiple regression equation- show all estimated coefficients
in the equation? Interpret the coefficients and predict the fuel consumption when temperature is
45 degrees, and the chill index is 8. Are the coefficients of the multiple regression model
statistically significant at alpha = 0.05 and 0.01? How do you know- discuss the test statistics
used to determine the significance of overall explanatory power? Discuss indicating the
individual test statistics and p-values and their meaning in terms of statistical significance of
individual coefficients. What are R2, adjusted R2 and se? Interpret R2 and Adjusted R2 and
compare these values. Discuss the ANOVA table and conclude about the overall statistical
significance of the model. Plot the errors and comment on the plot. What would be the estimated
error when observed value of Fuel consumption is 75 units when Average Temp is 510 and Chill
Index 16. By looking at the overall explanatory power and the statistical significance of the
individual slope coefficients, do you suspect Multicollinearity? Why or why not?
t
Sales(Y)
Ses(0.1) Error(0.1) Ses(0.6) Error(0.6)
100
2
110
100
10
100
10
3
140
101
39
106
34
4
140
104.9
35.1
126.4
13.6
5
120
108.41
11.59
134.56
-14.56
6
150 109.569
40.431 125.824
24.176
7
180 113.6121 66.3879 140.3296 39.6704
8
160 120.2509 39.74911 164.1318 -4.13184
9
160 124.2258 35.7742 161.6527 -1.65274
10
170 127.8032 42.19678 160.6611 9.338906
11
160 132.0229 27.9771 166.2644 -6.26444
12
200 134.8206 65.17939 162.5058 37.49422
13
240 141.3385 98.66145 185.0023 54.99769
14
220 151.2047 68.79531 218.0009 1.999076
15
200 158.0842 41.91578 219.2004 -19.2004
16
240 162.2758 77.7242 207.6801 32.31985
17
260 170.0482 89.95178 227.0721 32.92794
18
280 179.0434 100.9566 246.8288 33.17118
19
280 189.1391 90.86094 266.7315 13.26847
20
260 198.2252 61.77485 274.6926 -14.6926
21
204.4026 -204.403 265.877 -265.877
71321.04
12381.72
SumofSq
SumOfSq
3753.739
651.6696
MSE
MSE
61.26776
25.52782
RMSE
RMSE
1
250
200
150
100
50
0
1
2
3
4
5
1
2
3
4
5
120
100
80
60
40
20
0
0
1
2
3
4
5
300
250
200
150
100
50
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21
Ses(0.1)
Ses(0.6)
300
250
200
150
100
50
0
5
6
7
8
1
9 10 11 12 13 14 15 16 17 18 19 20 21
2
3
4
5
6
7
8
Error(0.1)
9
10
Error(0.6)
60
50
40
30
20
10
0
-10
-20
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
-30
1
2
3
4
5
6
7
8
9
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
-30
Ses(0.6)
10 11 12 13 14 15 16 17 18 19 20 21
Error(0.6)
9
10
11
12
13
14
15
16
17
18
19
t
Sales(Y)
Ses(0.1) Error(0.1) Ses(0.6) Error(0.6) Lt
Tt
HTP
100
100
5
2
110
100
10
100
10
107
6.6
105
3
140
101
39
106
34
124.16
15.048
113.6
4
140
104.9
35.1
126.4
13.6 139.5248 15.30144 139.208
5
120
108.41
11.59
134.56
-14.56 140.8957 4.157043 154.8262
6
150 109.569
40.431 125.824
24.176 147.0317 5.740151 145.0528
7
180 113.6121 66.3879 140.3296 39.6704 163.6631 14.45317 152.7718
8
160 120.2509 39.74911 164.1318 -4.13184 170.8698 8.655964 178.1163
9
160 124.2258 35.7742 161.6527 -1.65274 171.7154 2.407733 179.5257
10
170 127.8032 42.19678 160.6611 9.338906 172.4739 1.08832 174.1232
11
160 132.0229 27.9771 166.2644 -6.26444 168.1373 -3.25159 173.5622
12
200 134.8206 65.17939 162.5058 37.49422 178.9314 7.984973 164.8857
13
240 141.3385 98.66145 185.0023 54.99769 208.1499 24.97172 186.9164
14
220 151.2047 68.79531 218.0009 1.999076 227.8729 20.77282 233.1216
15
200 158.0842 41.91578 219.2004 -19.2004 229.1875 5.206174 248.6458
16
240 162.2758 77.7242 207.6801 32.31985 236.6362 7.000213 234.3936
17
260 170.0482 89.95178 227.0721 32.92794 250.1818 12.23657 243.6364
18
280 179.0434 100.9566 246.8288 33.17118 269.451 17.86268 262.4184
19
280 189.1391 90.86094 266.7315 13.26847 284.3882 15.52229 287.3137
20
260 198.2252 61.77485 274.6926 -14.6926 283.9463 2.750922 299.9105
21
204.4026 -204.403 265.877 -265.877
286.6972
71321.04
12381.72
SumofSq
SumOfSq
3753.739
651.6696
MSE
MSE
61.26776
25.52782
RMSE
RMSE
1
Error
5
26.4
0.792
-34.8262
4.947213
27.22818
-18.1163
-19.5257
-4.12317
-13.5622
35.11426
53.08358
-13.1216
-48.6458
5.606371
16.36361
17.5816
-7.31372
-39.9105
12455.8
SumOfSq
655.5687
MSE
25.60408
RMSE
Alpha
Beta
0.4 1-A
0.8 1-B
0.6
0.2
SALES(Y) VS HTP
Series1
Series2
350
300
250
200
150
100
50
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
HTP Error
60
40
20
0
0
-20
-40
-60
5
10
15
20
25
20
25
Year-q
2010-1
2010-2
2010-3
2010-4
2011-1
2011-2
2011-3
2011-4
2012-1
2012-2
2012-3
2012-4
2013-1
2013-2
2013-3
2013-4
2014-1
2014-2
2014-3
2014-4
2015-1
2015-2
2015-3
2015-4
2016-1
2016-2
Y
t
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Lt
84
110
100
95
102
145
140
122
125
160
150
135
150
210
180
175
210
250
240
225
235
290
275
265
118.0893
133.5609
144.2015
142.2813
147.7567
150.6047
154.4095
156.2094
168.1978
185.8185
190.9618
200.7256
223.8191
231.1018
247.9067
260.0047
263.2706
269.3707
281.255
298.3019
Tt
St
Hwm
Error
Alpha
0.863753
Beta
1.131105
Gamma
1.028278
0.976864
20.83929 0.863753
18.69221 1.094739 157.1429 -12.1429
400
15.47159 0.982346 156.5584 -16.5584
350
8.514859 0.881338 155.9789 -33.9789
300
7.299079 0.849539 130.2507 -5.25067
250
5.518635 1.068855 169.7456
-9.7456
200
4.833102 0.973624 153.3672 -3.36716
150
3.619831 0.867647 140.3465 -5.34651
6.967259 0.883353 135.7811 14.21885
100
11.22863 1.117879 187.2261 22.77395
50
8.794481 0.948802 191.8497 -11.8497
0
9.182211 0.870999 173.3179 1.682067
1
14.74674 0.927277 185.4228 24.57725
11.76113 1.088995 266.6878 -16.6878
13.77863 0.964245 230.429 9.571042
13.10637 0.866495 227.9277
-2.9277
9.170209 0.899549 253.2496 -18.2496
400
7.942144 1.079066 296.6868 -6.68678
9.518999 0.975057 267.3976 7.602377
350
12.53016 0.883988 251.9542 13.04579
300
279.6088
250
348.9291
4191.186
200
SumOfSq
150
220.5887
100
MSE
14.85223
50
RMSE
0
1
0.5
0.4
0.8
Y vs HWM
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Series1
Series2
HWM
30
20
10
0
1
-10
-20
-30
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21
-40
2
3
4
Error
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
ECO 309 Assignment 2
Question 1
A: The graph showing actual, Ses0.1, and Ses0.6 seems to be more accurate than the
individual graphs of each. Moving on, SES0.6 seems to be more accurate due to having a
lower RMSE and MSE. Furthermore, the et for 0.1 has no stationarity and does have systematic
underestimation. On the other hand, the et for 0.6 has stationarity due its horizontal trendline but
there is slight systematic underestimation.
Question 2
A: Yes, the htp is significantly better than the SES forecasts due to SES 0.1 having a great
amount of systematic underestimation and SES0.6 being quite similar to the actual (Y) values.
As for the HTP erroràstationarity, it has none, due to itàtrendline showing a downward slope.
Question 3
A: Yes, there is a seasonal pattern. Reasoning, we can clearly see fluctuations at regular
intervals. Starting from period 2, every 4 periods there is a peak and after each of these peaks
thereàa drop in the 2 periods following. As for the et we can see it moving in an upward trend
according to the trendline.

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