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A study has been carried out on the wear of a particular bearing (y) and its...

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 8
4 19 115
2 23 155
a) Fit a multiple linear regression model to this data.
b) What is the determination coefficient ?

Math   Statistics-And-Probability   
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Answer #1

By using software,

Sum of X1 = 40
Sum of X2 = 371
Sum of Y = 92
Mean X1 = 6.6667
Mean X2 = 61.8333
Mean Y = 15.3333
Sum of squares (SSX1) = 63.3333
Sum of squares (SSX2) = 18882.8333
Sum of products (SPX1Y) = -80.3333
Sum of products (SPX2Y) = 1234.3333
Sum of products (SPX1X2) = -929.3333

a)

The regression equation is,

Y = 1.11305X1 + 0.01059X2 + 22.09896 .

b)

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