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 below in the format of a data file. Column 1 has treatment (1 for cutting speed 1000, 2 for cutting speed 1200, 3 for cutting speed 1400), column 2 has x=hardness, column 3 has y=amount of metal removed.

1 125 77.4

1 120 68.4

1 140 90.4

1 150 97.9

1 136 87.6

2 133 85.4

2 140 94.4

2 125 74

2 120 64.8

2 165 112.1

3 130 79.6

3 175 117.6

3 132 82.3

3 141 91.9

3 124 72.9

analysis of these data and include the following.

1. A scatterplot of the ys versus the xs, using different symbols (or colours) to distinguish the points corresponding to different cutting speeds. Do the ys appear to be related to the xs? Include regression lines of y versus x for each cutting speed. Does it seem reasonable to believe that these three lines have the same slope?

2. An ANCOVA table.

3. An ANOVA table based on the ys, disregarding the xs, to determine whether there are differences in the (mean) amount of metal removed for different cutting speeds. Comment on differences with part (2).

You will be asked a few questions concerning the analysis.

Please use 3 decimal places for the answers below which are not integer-valued.

Part a)

The type II SS for cutting speed (treatment) is_________and its degree of freedom is_________

Part b)

The MSE for ancova is:_________and its degree of freedom is_________

Part c)

The appropriate F ratio for cutting speed is:

_________

Part d)

What is the estimate slope for x=hardness?

_________