Question

Tim Cooper plans to invest money in a mutual fund that is tied to one of the major market indices either the S&P 500 or the Dow Jones Industrial Average. To obtain even more diversification, Tim has thought about investing in both of these. To determine whether investing in two funds would help, Tim decided, to take 10 weeks of data and compare the two markets. The closing price for each index is shown in the table below. 1 2 3 4 5 6 7 8 9 10 DJIA 27260 27133 26990 26998 27101 27234 2734427400 27405 27406 S&P 2967 2956 2989 2995 3002 3010 3011 3020 3033 3034 Develop a regression model that would predict the DJIA based on the S&P index. Based on this model: a. What would you expect the DJIA to be when the S&P is 2975? [Select] b. What would expect the DJIA to be when the S&P is 3050? [ Select] c. What is the MAD of this model? (Select] d. What is the MAPE of this model? (Select ]

Answer 1

Weeks	DJIA	S&P	Forecast	Error	|Error|	APE
1	27260	2967	27092.5	167.5	167.51	0.61%
2	27133	2956	27049.8	83.2	83.18	0.31%
3	26990	2989	27177.8	-187.8	187.83	0.70%
4	26998	2995	27201.1	-203.1	203.11	0.75%
5	27101	3002	27228.3	-127.3	127.26	0.47%
6	27234	3010	27259.3	-25.3	25.30	0.09%
7	27344	3011	27263.2	80.8	80.82	0.30%
8	27400	3020	27298.1	101.9	101.91	0.37%
9	27405	3033	27348.5	56.5	56.48	0.21%
10	27406	3034	27352.4	53.6	53.60	0.20%
				Avg -->	108.70	0.4001%
Model:					MAD	MAPE
DJIA	15582.82	+	3.88	*S&P
Given S&P	2975	3050
Forecast for DJIA	27123.5	27414.5

Calculations:

в Ε F H Weeks DJIA S&P 27260 27133 26990 7 5 26998 27101 27234 27344 27400 27405 27406 2967 2956 2989 2995 3002 3010 3011 3020 3033 3034 Forecast Error Error APE =$C$15+$E$15*D3 =C3-E3 =ABS(F3) =G3/C3 =$C$15+$E$15*D4 =C4-E4 =ABS(F4) =G4/C4 =$C$15+$E$15*D5 =C5-E5 =ABS(F5) =G5/C5 =$C$15+$E$15*D6 =C6-E6 =ABS(F6) =G6/C6 =$C$15+$E$15*D7 =C7-E7 ABS(F7) =G7/07 =$C$15+$E$15*D8 =C8-E8 =ABS(F8) =G8/08 =$C$15+$E$15*D9 =C9-E9 =ABS(F9) =G9/09 =$C$15+$E$15*D10 =C10-E10 =ABS(F10) =G10/C10 =$C$15+$E$15*011 =C11-E11 =ABS(F11) =G11/C11 =$C$15+$E$15*D12 =C12-E12 =ABS(F12) =G12/C12 Avg --> AVERAGE(G3:G12) =AVERAGE(H3:H12) MAD MAPE =SLOPE(C3:C12,D3:012) *S&P Model: DJIA =INTERCEPT(C3:C12,D3:012) Given S&P 2975 Forecast for DJIA =C15+E15*C17 3050 =C15+E15*D17

Answers:

a) 27123.5 (your alternative may be rounded off to 27124)

b) 27414.5 (your alternative may be rounded off to 27415)

c) MAD = 108.70

d) MAPE = 0.4001% or, 0.004 (depends on which format is used in the alternative)