Question

In: Statistics and Probability

MWH CUS AHEC t D1 D2 Jan-10 221,870 329,075 674.2 1 1 0 Feb-10 175,726 329,754...

	MWH	CUS	AHEC	t	D1	D2
Jan-10	221,870	329,075	674.2	1	1	0
Feb-10	175,726	329,754	532.9	2	0	0
Mar-10	158,684	330,374	480.3	3	0	0
Apr-10	179,014	330,751	541.2	4	0	0
May-10	158,494	331,128	478.6	5	0	0
Jun-10	245,588	331,050	741.8	6	0	1
Jul-10	285,503	332,673	858.2	7	0	1
Aug-10	283,385	332,918	851.2	8	0	1
Sep-10	250,406	333,162	751.6	9	0	0
Oct-10	211,725	333,284	635.3	10	0	0
Nov-10	156,017	333,518	467.8	11	0	0
Dec-10	182,422	334,508	545.3	12	1	0
Jan-11	213,135	335,497	635.3	13	1	0
Feb-11	194,887	335,813	580.3	14	0	0
Mar-11	133,260	336,405	396.1	15	0	0
Apr-11	154,670	336,637	459.5	16	0	0
May-11	171,713	336,869	509.7	17	0	0
Jun-11	310,874	336,918	922.7	18	0	1
Jul-11	318,138	337,519	942.6	19	0	1
Aug-11	304,805	338,063	901.6	20	0	1
Sep-11	276,765	338,606	817.4	21	0	0
Oct-11	207,074	338,987	610.9	22	0	0
Nov-11	159,807	339,361	470.9	23	0	0
Dec-11	188,262	340,009	553.7	24	1	0
Jan-12	227,781	340,656	668.7	25	1	0
Feb-12	159,576	341,266	467.6	26	0	0
Mar-12	168,212	341,912	492.0	27	0	0
Apr-12	169,883	342,461	496.1	28	0	0
May-12	217,582	342,850	634.6	29	0	0
Jun-12	285,227	343,216	831.0	30	0	1
Jul-12	320,056	343,877	930.7	31	0	1
Aug-12	313,702	344,271	911.2	32	0	1
Sep-12	251,051	344,418	728.9	33	0	0
Oct-12	177,654	345,105	514.8	34	0	0
Nov-12	163,067	345,305	472.2	35	0	0
Dec-12	194,556	345,567	563.0	36	1	0
Jan-13	247,126	345,667	714.9	37	1	0
Feb-13	184,078	346,239	531.7	38	0	0
Mar-13	167,302	346,554	482.8	39	0	0
Apr-13	144,089	346,943	415.3	40	0	0
May-13	206,792	347,271	595.5	41	0	0
Jun-13	308,944	347,866	888.1	42	0	1
Jul-13	316,351	347,982	909.1	43	0	1
Aug-13	308,119	348,610	883.9	44	0	1
Sep-13	255,635	349,077	732.3	45	0	0
Oct-13	168,472	349,352	482.2	46	0	0
Nov-13	166,379	349,497	476.1	47	0	0
Dec-13	205,975	349,629	589.1	48	1	0
Jan-14	230,231	349,921	658.0	49	1	0
Feb-14	164,773	350,111	470.6	50	0	0
Mar-14	148,026	350,967	421.8	51	0	0
Apr-14	148,877	351,667	423.3	52	0	0
May-14	202,760	352,097	575.9	53	0	0
Jun-14	298,366	352,340	846.8	54	0	1
Jul-14	356,241	352,727	1010.0	55	0	1
Aug-14	300,386	352,858	851.3	56	0	1
Sep-14	237,898	353,640	672.7	57	0	0
Oct-14	193,688	353,434	548.0	58	0	0
Nov-14	151,736	353,649	429.1	59	0	0
Dec-14	207,533	353,885	586.4	60	1	0
Jan-15	236,812	354,068	668.8	61	1	0
Feb-15	159,097	354,644	448.6	62	0	0
Mar-15	165,744	355,563	466.1	63	0	0
Apr-15	150,227	355,971	422.0	64	0	0
May-15	194,866	356,579	546.5	65	0	0
Jun-15	295,847	356,932	828.9	66	0	1
Jul-15	366,289	357,572	1024.4	67	0	1
Aug-15	342,595	357,750	957.6	68	0	1
Sep-15	292,113	358,421	815.0	69	0	0
Oct-15	208,374	358,514	581.2	70	0	0
Nov-15	138,642	358,803	386.4	71	0	0
Dec-15	220,531	358,819	614.6	72	1	0

MWH =	total MWH consumed by all Texas and New Mexico households served by EPE in month t		(MWH = megawatt hours)
CUS =	total number of residential customers in month t
AHEC =	kWh average household electricity consumtion in month t = (MWH/CUS)*1000	(kWh = kilowatt hours)
D1 =	1 if month t pertains to December or January; 0 otherwise
D2 =	1 if month t pertains to June, July or August; 0 otherwise

(i) Estimate the following time-series model

?????=?1+?2∙?+ ?3∙?1?+?4∙?2?

?????= average household electricity consumption (kWh) in month t in El Paso Electric’s combined Texas and New Mexico service territory.

?1?= 1 if month t pertains to December or January (winter heating peak); 0 otherwise

?2?= 1 if month t pertains to June, July or August (summer cooling peak); 0 otherwise

(ii) With a two-tailed test (and a = 0.05), test the hypothesis that in the population ?2=0 (iii) With a two-tailed test (and a = 0.05), test the hypothesis that in the population ?3=0

(iv) With a two-tailed test (and a = 0.05), test the hypothesis that in the population ?4=0

(v) Based on your results from part (ii), does there appear to be either a significant upward or downward time trend in average household electricity consumption in El Paso Electric’s combined Texas and New Mexico service territory?

(vi) Interpret the R2 statistic.

(vii) Provide a forecast for AHEC for each of the following months: (1) January 2016 (t = 73); (2) July 2016 (t = 79); and (3) October 2016 (t = 82).

(viii) Given actual values in the source references found in “EPE Sales Cus” (click on cells B-82 and B-83), calculate the forecast errors associate with each of the three forecasts in part (vii) and note if they were underestimates or overestimates

(ix) As it turned out, July 2016 was 35% hotter than normal (based on “cooling degree days”). Why might this explain the July 2016 forecast error from part (viii)?

Expert Solution

1 - 5 have been solved.

Input the data in excel as shown. Using the regression tool from data analysis tab, the regression output is generated.
Inputs for the regression tab are shown below.

The regression output is as shown below.

The regression equation is given as

y = 531.7904 +0.08307 t+87.844 D1+359.085 D2

(ii) With a two-tailed test (and a = 0.05), test the hypothesis that in the population ?2=0

From the regression table we have

Using the t-table, with df = 72-4 = 68, we get pvalue = 0.8777.

Since the pvalue is greater than 0.05, we fail to reject the null hypothesis and conclude that beta2 is not significant in predicting y.

(iii) With a two-tailed test (and a = 0.05), test the hypothesis that in the population ?3=0

Using the t-table, with df = 72-4 = 68, we get pvalue = 0.006117716

Since the pvalue is less than 0.05, we reject the null hypothesis and conclude that beta3 is significant in predicting y.

(iv) With a two-tailed test (and a = 0.05), test the hypothesis that in the population ?4=0

Using the t-table, with df = 72-4 = 68, we get pvalue = 0.000000008

Since the pvalue is less than 0.05, we reject the null hypothesis and conclude that beta4 is significant in predicting y.

(v) Based on your results from part (ii), does there appear to be either a significant upward or downward time trend in average household electricity consumption in El Paso Electric’s combined Texas and New Mexico service territory?
Slope of the regression line is positive. There is a signficant increase int he electricity in a seasonal pattern.

(vi) Interpret the R2 statistic.
The R2 = 0.7270, that is 72.70%
In simple words, it means 72% of the variation in the data is being explained by the independent variables.

orchestra answered 1 year ago

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