Question

The table below lists weights​ (carats) and prices​ (dollars) of randomly selected diamonds. Find the​ (a) explained​ variation, (b) unexplained​ variation, and​ (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear​ correlation, so it is reasonable to use the regression equation when making predictions. For the prediction​ interval, use a​ 95% confidence level with a diamond that weighs 0.8 carats.

Weight: 0.3, 0.4, 0.5, 0.5, 1.0, 0.7

Price: ​$516, ​$1175, ​$1333, ​$1416, ​$5673, ​$2280

Answer 1

Regression Statistics
Multiple R	0.966959
R Square	0.93501
Adjusted R Square	0.918763
Standard Error	528.8261
Observations	6

ANOVA
	df	SS	MS	F	Significance F
Regression	1	16093785	16093785	57.54829	0.001619
Residual	4	1118628	279657.1
Total	5	17212414

a) Explained Variation = SS_Regression = 16093785

b) Unexplained Variation = SS_Residual = 1118628

c) prediction Interval for X = 0.8 carats

PI = = (2038.32, 5437.18)