An engineer is studying the effect of cutting speed on the rate of metal removal in a machining operation. However, the rate of metal removal is also related to the hardness of the test specimen. Five observations are taken at each cutting speed. The amount of metal removed (y) and the hardness of the specimen (x) are shown in the following table. Analyze the data using an analysis of covariance. Use α = 0.05.

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Cutting Speed (rpm) 1000 1200 1400 y y y 68 120 112 165 118 175 90 140 94 140 82 132 98 150 65 120 73 124 77 125 74 125 92 141 88 136 85 133 80 130