Question

A study has been carried out on the wear of a particular bearing (y) and its relationship with oil fluidity (x_1) and load (x_2). As a result of the study, the following data were obtained.
x_1 y x_2
12 10 3
9 11 30
7 14   60
6 16 80
4 19 115
2 23 155
a) Fit a multiple linear regression model to this data.
b) What is the determination coefficient ?

Answer 1

excel<data<data analysis<regression

ANOVA
	df	SS	MS	F	Significance F
Regression	2	121.3543	60.67715	1249.425	4.15E-05
Residual	3	0.145692	0.048564
Total	5	121.5
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-0.36423	2.037522	-0.17876	0.869515	-6.84854	6.12007	-6.84854	6.12007
X Variable 1	0.824615	0.179177	4.602233	0.019287	0.254393	1.394836	0.254393	1.394836
X Variable 2	0.140408	0.011472	12.23967	0.001174	0.103901	0.176916	0.103901	0.176916

a) the multiple regression model

y^ = -0.36423+0.824615x1+0.140408x2

b) coefficient of determination:

R^2 = 0.999

Regression Statistics
Multiple R	0.9994
R Square	0.998801
Adjusted R Square	0.998001
Standard Error	0.220373
Observations	6