Problem 7: 19 points] (see dataset) A study was performed on wear of a bearing )
ID: 3322102 • Letter: P
Question
Problem 7: 19 points] (see dataset) A study was performed on wear of a bearing ) and its relationship to c the load. The obtained data is provided in the dataset file a) Find the least square regression equat ion. b) Interpret the slope coefficients in the above regression equation. c) Determine which independent variables have significant linear relation with the wear of the bearing d) Find and interpret the coefficient of determination. ) Use the model to predict wear when x1 -25 and x2- 1000. Determine a 90% prediction interval for the wear of a bearing when x1-25 and x2-1000.Explanation / Answer
a)
y=383.80-3.64x1-0.11x2
b)
x1 (oil viscosity): For every increase of 1 in oil viscosity, wear of a bearing would go down by 3.64, keeping all other things constant
x2 (load): For every increase of 1 in load, wear of a bearing would go down by 0.11, keeping all other things constant
c)
x1 because the p-value is less than 0.05
d)
r^2 is 0.9849 which means that 98.49% of the variation in dependent variable is accounted for by the variation in independent variable
e)
y=383.80-3.64*25-0.11*1000
y=182.8
SUMMARY OUTPUT Regression Statistics Multiple R 0.99 R Square 0.98 Adjusted R Square 0.97 Standard Error 12.35 Observations 6 ANOVA df SS MS F Significance F Regression 2 29787.48 14893.74 97.59 0.00 Residual 3 457.86 152.62 Total 5 30245.33 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 383.80 36.22 10.60 0.00 268.54 499.06 x1 -3.64 0.57 -6.42 0.01 -5.44 -1.84 x2 -0.11 0.04 -2.57 0.08 -0.25 0.03