Question

For the dataset describing year, US Return, and Overseas Return

1. Find the least-squares regression equation of overseas returns on U.S. returns.

2. In 1997, the return on U.S. stocks was 33.4%. Use the regression line to predict the return on overseas stocks. (You may either calculate this by hand or use SAS output.) The actual overseas return was 2.1%. Are you confident that predictions using the regression line will be quite accurate? Why?

DATA

1971  29.6  14.6
1972  36.3  18.9
1973 -14.9 -14.8
1974 -23.2 -26.4
1975  35.4  37.2
1976   2.5  23.6
1977  18.1  -7.4
1978  32.6   6.4
1979   4.8  18.2
1980  22.6  32.3
1981  -2.3  -5.0
1982  -1.9  21.5
1983  23.7  22.4
1984   7.4   6.1
1985  56.2  31.6
1986  69.4  18.6
1987  24.6   5.1
1988  28.5  16.8
1989  10.6  31.5
1990 -23.0  -3.1
1991  12.8  30.4
1992 -12.1   7.6
1993  32.9  10.1
1994   6.2   1.3
1995  11.2  37.6
1996   6.4  23.0
1997   2.1  33.4

Answer 1

Solution:

In SAS use key words DATA to create dataset

Input statement to describe variables

Procedure regression to fit linear regression of Overseas_Return on US_Return.

SAS Code;

data stock;
infile cards;
input year US_Return Overseas_Return;
cards;
1971 29.6 14.6
1972 36.3 18.9
1973 -14.9 -14.8
1974 -23.2 -26.4
1975 35.4 37.2
1976 2.5 23.6
1977 18.1 -7.4
1978 32.6 6.4
1979 4.8 18.2
1980 22.6 32.3
1981 -2.3 -5.0
1982 -1.9 21.5
1983 23.7 22.4
1984 7.4 6.1
1985 56.2 31.6
1986 69.4 18.6
1987 24.6 5.1
1988 28.5 16.8
1989 10.6 31.5
1990 -23.0 -3.1
1991 12.8 30.4
1992 -12.1 7.6
1993 32.9 10.1
1994 6.2 1.3
1995 11.2 37.6
1996 6.4 23.0
1997 2.1 33.4
;
run;

proc reg data=stock;
model Overseas_Return=US_Return/ r cli clm;;
run;

Output;

The REG Procedure

Model: MODEL1

Dependent Variable: Overseas_Return

Number of Observations Read	27
Number of Observations Used	27

Analysis of Variance
Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	1	1517.67778	1517.67778	6.86	0.0147
Error	25	5527.78222	221.11129
Corrected Total	26	7045.46000

Root MSE	14.86981	R-Square	0.2154
Dependent Mean	14.50000	Adj R-Sq	0.1840
Coeff Var	102.55042

Parameter Estimates
Variable	DF	Parameter Estimate	Standard Error	t Value	Pr > |t|
Intercept	1	9.39847	3.46136	2.72	0.0118
US_Return	1	0.34739	0.13260	2.62	0.0147

The REG Procedure

Model: MODEL1

Dependent Variable: Overseas_Return

Output Statistics
Obs	Dependent Variable	Predicted Value	Std Error Mean Predict	95% CL Mean		95% CL Predict		Residual	Std Error Residual	Student Residual	Cook's D
1	14.6	19.6813	3.4786	12.5170	26.8456	-11.7705	51.1331	-5.0813	14.457	-0.351	0.004
2	18.9	22.0088	4.0502	13.6674	30.3503	-9.7318	53.7495	-3.1088	14.308	-0.217	0.002
3	-14.8	4.2223	4.8558	-5.7784	14.2230	-27.9942	36.4388	-19.0223	14.055	-1.353	0.109
4	-26.4	1.3389	5.7814	-10.5681	13.2460	-31.5193	34.1972	-27.7389	13.700	-2.025	0.365
5	37.2	21.6962	3.9666	13.5268	29.8656	-9.9996	53.3920	15.5038	14.331	1.082	0.045
6	23.6	10.2669	3.2863	3.4986	17.0353	-21.0970	41.6309	13.3331	14.502	0.919	0.022
7	-7.4	15.6863	2.8973	9.7192	21.6534	-15.5146	46.8871	-23.0863	14.585	-1.583	0.049
8	6.4	20.7235	3.7192	13.0637	28.3832	-10.8448	52.2918	-14.3235	14.397	-0.995	0.033
9	18.2	11.0660	3.1476	4.5833	17.5486	-20.2376	42.3695	7.1340	14.533	0.491	0.006
10	32.3	17.2496	3.0481	10.9719	23.5272	-14.0122	48.5113	15.0504	14.554	1.034	0.023
11	-5.0	8.5995	3.6417	1.0993	16.0996	-22.9305	40.1294	-13.5995	14.417	-0.943	0.028
12	21.5	8.7384	3.6091	1.3053	16.1715	-22.7757	40.2525	12.7616	14.425	0.885	0.024
13	22.4	17.6317	3.1013	11.2444	24.0190	-13.6523	48.9156	4.7683	14.543	0.328	0.002
14	6.1	11.9692	3.0203	5.7487	18.1897	-19.2811	43.2195	-5.8692	14.560	-0.403	0.003
15	31.6	28.9220	6.2042	16.1442	41.6997	-4.2617	62.1057	2.6780	13.514	0.198	0.004
16	18.6	33.5076	7.7991	17.4451	49.5700	-1.0741	68.0892	-14.9076	12.660	-1.177	0.263
17	5.1	17.9443	3.1492	11.4584	24.4303	-13.3599	49.2486	-12.8443	14.533	-0.884	0.018
18	16.8	19.2992	3.3978	12.3013	26.2970	-12.1151	50.7135	-2.4992	14.476	-0.173	0.001
19	31.5	13.0808	2.9125	7.0824	19.0793	-18.1260	44.2877	18.4192	14.582	1.263	0.032
20	-3.1	1.4084	5.7584	-10.4512	13.2681	-31.4327	34.2495	-4.5084	13.710	-0.329	0.010
21	30.4	13.8451	2.8726	7.9289	19.7613	-17.3461	45.0363	16.5549	14.590	1.135	0.025
22	7.6	5.1950	4.5611	-4.1987	14.5888	-26.8383	37.2283	2.4050	14.153	0.170	0.001
23	10.1	20.8277	3.7447	13.1154	28.5400	-10.7534	52.4088	-10.7277	14.391	-0.745	0.019
24	1.3	11.5523	3.0749	5.2194	17.8852	-19.7206	42.8252	-10.2523	14.548	-0.705	0.011
25	37.6	13.2893	2.8988	7.3191	19.2594	-17.9122	44.4907	24.3107	14.585	1.667	0.055
26	23.0	11.6218	3.0653	5.3086	17.9349	-19.6471	42.8907	11.3782	14.550	0.782	0.014
27	33.4	10.1280	3.3127	3.3053	16.9507	-21.2477	41.5037	23.2720	14.496	1.605	0.067

Sum of Residuals	0
Sum of Squared Residuals	5527.78222
Predicted Residual SS (PRESS)	6548.38833

Solution-1;

he least-squares regression equation of overseas returns on U.S. returns

is

Overseas_Return=9.39847+0.34739*US_Return

Solution-2:

the regression line to predict the return on overseas stocks. (You may either calculate this by hand or use SAS output.) The actual overseas return was 2.1%. Are you confident that predictions using the regression line will be quite accurate

Obs	Dependent	Predicted	Std	95% CL Mean		95% CL Predict		Residual	Std Error	Student	Cook's D
	Variable	Value	Error						Residual	Residual
			Mean
			Predict
27	33.4	10.128	3.3127	3.3053	16.9507	-21.2477	41.5037	23.272	14.496	1.605	0.067

Predicted return on overseas stocks. is 10.128

we are confident that predictions are not accurate sicne R sq is less

R sq=0.2154

=21.54%

21.54% variation in Overseas_Return is explained by model

but From Global F test

p<0.05

Model is signifcant and we can use this model to predict Overseas_Return