Question

Building on your previous work, again use the values below. Find or re-compute the coefficients and the ANOV A tabie. -2 Locate the variance of the u-hats, and locate the sum of squared X-mean values. Recall the calculation for the homoskedasticity-only variance and standard error of B1-hat and perform those calculations. Use symbolic numbers, not necessarily decimal values. e a column of squared X values (not X-mean). Sum it and find the average. Recall the ealculation for the homoskedasticity-only variance and standard eror of B0-hat and perform those calculations. Use symbolic numbers, not necessarily decimal values. Creat Using symbolic numbers, not necessarily decimal values, create the t-statistics for the coefficients. Find the decimal values as the last step so that you have them to get the p-values. Get the p-values using the student-t distribution. Using the excel t-table inverse command listed above, verify the 95% critical value used above, and create the 95% confidence intervals. Check your answers by running the regression in excel. Send in your work in some format, perhaps a picture or scan of the previous page, or you could use the template below. No need to send in the excel output. That is simply for you to check your work. Regression Statistics Multiple R R Square Adjusted R SquareXXXXX Standard Error Observations ANOVA df SS MS F Significance F Regression Residual Total coeffic. Std Err tStat P-val Low 95% Up 95% Intercept X Variable 1 RESIDUAL OUTPUT Observation Predicted Y Residuals

Answer 1

	x	y	x^2	xy	y^2
	-2	-3	4	6	9
	-1	1	1	-1	1
	0	0	0	0	0
	1	-1	1	-1	1
	2	3	4	6	9
Sum	0	0	10	10	20
Average	0	0	2	2	4

My =0,Mx =0

Now,SSx =10,SSxy =10 ,b=SSxy/SSx =10/10=1

a=My-bMx =0-1*0 =0

The regression equation is y=x

Yactual	Ypredicted	Error(Actual-Predicted)	Error^2
-3	-2	-1	1
1	-1	2	4
0	0	0	0
-1	1	-2	4
3	2	1	1
Sum			10

SSE=10

MSE = 10/3 =3.333

Standard error of slope = sqrt(MSE/SSx) =sqrt(3.33/10 )= 0.5774

t-value of slope =Slope/Standard error = 1/0.5774 =1.732 ,p= 0.1869 (Using Excel formula,=T.DIST.2T(1.732,3)

Similarly for beta₀

s=

V =V5.2 = 1.826

Standard error of regression,s = 1.826

Standard error of slope =

= 1.826 /-+-= 0.8165 510 Sxx

t-value of intercept =intercept/Standard error =0

p-value= 1

Excel Regression Output

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.707106781
R Square	0.5
Adjusted R Square	0.333
Standard Error	1.826
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	10	10	3	0.181690114
Residual	3	10	3.333333
Total	4	20
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	0	0.8165	0	1	-2.598456527	2.598457
x	1	0.5774	1.732051	0.18169	-0.837386231	2.837386