Question

3. Nineteenth century economist W. Stanley Jevons was concerned about the loss of value in coins due to their loss in weight while in circulation. He collected, cleaned, and weighed 274 gold sovereigns, then grouped them roughly according to age (in decades) Age Number Average Weight (g) Standard Dev 7.9725 7.9503 7.9276 7.8962 7.8730 123 78 32 17 24 0.01409 0.02272 0.03426 0.04057 0.05353

Answer 1

Given data

Age*Avg Wt Avg Wt Number g 123 Age SD 2 3 4 5 7.9725 0.01409 78 7.9503 0.02272 7.9276 0.03426 7.8962 0.04057 7.873 0.05353 32 17 24 7.9725 15.9006 23.7828 31.5848 39.365

Age*Avg Wt Number SD 7.9725 15.9006 23.7828 31.5848 39.365 123 0.01409 78 0.02272 32 0.03426 17 0.04057 24 0.05353

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.996725
R Square	0.993461
Adjusted R Square	0.986921
Standard Error	1.418909
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	2	611.7252	305.8626	151.9208	0.006539335
Residual	2	4.026607	2.013304
Total	4	615.7518
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	1.148089	5.292775	0.216916	0.84839	-21.62488374	23.92106131
Number	-0.02825	0.035546	-0.79484	0.510047	-0.18119561	0.124688974
SD	730.1972	104.0586	7.017175	0.01971	282.4692941	1177.92503

f)

Under this new model 95% confidence interval of the slopes are

slope of number=[-0.811,0.1246]

slope of SD =[282.4692,1177.92503]