Question

1. From the table below giving the quantity demanded of a commodity (Y), its price (X10, and consumer income (X2) from 1996 to 2015,

1. Find the least-squares regression equation of Y on X1 and X2 USING EXCEL’S DATA ANALYSIS TOOL.
2. Test at the 5 percent for the statistical significance of the slope parameters,
3. Find the adjusted and the adjusted coefficients of determination, and
4. Test at 5 percent level for the overall statistical significance of the regression.

Show all your results to three decimal places.

Year	Y	X1	X2
1996	72	$10	$2000
1997	81	9	2100
1998	90	10	2210
1999	99	9	2305
2000	108	8	2407
2001	126	7	2500
2002	117	7	2610
2003	117	9	2698
2004	135	6	2801
2005	135	6	2921
2006	144	6	3000
2007	180	4	3099
2008	162	5	3201
2009	171	4	3308
2010	153	5	3397
2011	180	4	3501
2012	171	5	3689
2013	180	4	3800
2014	198	4	3896
2015	189	4	3989

Answer 1

Excel Regression results are as under:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.984
R Square	0.968
Adjusted R Square	0.964
Standard Error	7.205
Observations	20.000
ANOVA
	df	SS	MS	F	Significance F
Regression	2	26884.298	13442.149	258.942	0.000
Residual	17	882.502	51.912
Total	19	27766.800
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	114.074	29.931	3.811	0.001	50.924	177.223
X1	-9.470	1.820	-5.205	0.000	-13.309	-5.631
X2	0.029	0.006	4.506	0.000	0.015	0.042

a)

Y=114.074-9.470X₁+0.029X₂

b)

Let us test for slope parameter of X₁

Significance level: 95%

We can see calculated p value is 0.001.

It is less than 0.05

So, we can reject Null hypothesis. We can say that there is significant relationship between X₁ and Y

Let us test for slope parameter of X₂

Significance level: 95%

We can see calculated p value is 0.000.

It is less than 0.05

So, we can reject Null hypothesis. We can say that there is significant relationship between X₂ and Y

3)

Please refer to the excel results

R²=0.968

Adjusted R²=0.964

4)

Significance level: 95%

We can see calculated p value is 0.000.

It is less than 0.05

So, we can reject Null hypothesis. We can say that overall regression model is significant.