Question

he data on sheet #2 represents data various economic factors.  We want to use a subset of the remaining variables to predict Interest Rates on US Treasury Bonds (Interest).  Construct a table of correlations and chose the two variables that have the strongest correlation to Interest and build a multiple regression model from those variables.  Write your regression equation, value, and the meaning of each variable used.  State the overall hypothesis test for your model

CRUDE	FOREIGN	DJIA	GNP	PURCHASE	CONSUMER	INTEREST
10.9	31	974.9000244	1718	1.756999969	234.3999939	7.61
12	35	894.5999756	1918	1.649000049	263.7999878	7.42
12.5	42	820.2000122	2164	1.531999946	308.2999878	8.41
17.7	54	844.4000244	2418	1.379999995	347.5	9.439999
28.1	83	891.4000244	2732	1.215000033	349.3999939	11.46
35.6	109	932.9000244	3053	1.09800005	366.6000061	13.91
31.8	125	884.4000244	3166	1.034999967	381.1000061	13
29	137	1190.300049	3406	1	430.3999939	11.11
28.6	165	1178.5	3772	0.961000025	511.7999878	12.44
26.8	185	1328.199951	4015	0.927999973	592.4000244	10.62
14.6	209	1792.800049	4240	0.912999988	646.0999756	7.68
17.9	244	2276	4527	0.879999995	685.5	8.38

Answer 1

For the given data , the correlation table is shown below:

	CRUDE	FOREIGN	DJIA	GNP	PURCHASE	CONSUMER	INTEREST
CRUDE	1
FOREIGN	0.304276	1
DJIA	-0.14611	0.861947	1
GNP	0.374804	0.991314	0.806587	1
PURCHASE	-0.61967	-0.91289	-0.60792	-0.95052	1
CONSUMER	0.152951	0.973337	0.883626	0.969579	-0.85455	1
INTEREST	0.969381	0.152756	-0.30097	0.227549	-0.48812	0.003861	1

The two variables that have the strongest correlation to Interest are CRUDE & PURCHASE.

Therefore the multiple regression analysis summary using this variable is given below:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.979934
R Square	0.960271
Adjusted R Square	0.951442
Standard Error	0.501724
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	2	54.75873	27.37936	108.7661	4.97E-07
Residual	9	2.265542	0.251727
Total	11	57.02427
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	2.259987	1.126809	2.005653	0.075858	-0.28903	4.809005	-0.28903	4.809005
CRUDE	0.282557	0.022094	12.78899	4.47E-07	0.232577	0.332537	0.232577	0.332537
PURCHASE	1.348011	0.624444	2.158737	0.059189	-0.06458	2.760602	-0.06458	2.760602

The regression equation is,

The increase a CRUDE by a unit will increase the Interest by 0.282557 units ,when other variable remain constant.

The increase a PURCHASE by a unit will increase the Interest by 1.348011 units ,when other variable remain constant.

For overall hypothesis test,

The p-value of F is quite small which is 0.000000497 . so we have sufficient evidence to reject the null hypothesis .

Hence the at lest of the the slope parameter is not equal to zero.