Question

sales	155	187	266
quarter	1	2	3

using the following data:

A. what proportion of the variability in sales can be explained by the model?

B. predict the sales in the fourth quarter.

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9713947
R Square	0.9436077
Adjusted R Square	0.8872154
Standard Error	19.18767
Observations	3
ANOVA
	df	SS	MS	F	Significance F
Regression	1	6160.5	6160.5	16.73291	0.152637
Residual	1	368.1667	368.1667
Total	2	6528.667
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	91.666667	29.30965	3.127525	0.197014	-280.748	464.0811
X Variable 1	55.5	13.56773	4.090588	0.152637	-116.894	227.8944

A) proportion of the variability:- In simple linear regression, r2 is often called the coefficient of determination, because it is equal to the proportion of variability in Y (the outcome variable) that is explained by (or determined by) the linear relationship between X and Y.

r^2 = 0.9436077

B) using regression euqation predict the sales in the fourth quarter.

x=4 put in regression equation

y=91.666667+55.5*x

y=91.666667+55.5*4

y=313.6667

313.6667 sales in the fourth quarter.