A chemical engineer is investigating the effect of process operating temperature
ID: 3182913 • Letter: A
Question
A chemical engineer is investigating the effect of process operating temperature on product yield.The study results in the following data:
Temperature Yield
100 62.95
110 68.07
120 73.94
130 83.95
140 82.70
150 96.68
160 109.66
170 109.76
180 108.30
190 125.30
You can use Minitab to answer the following questions. However, you should be able to calculate the slope and intercept of the least squares regression model by hand, which requires only the means and standard deviations of X and Y, and the correlation coefficient (here r = 0.9788).
1. what is the standard deviation of temperature?
2. what is the standard deviation of yield?
3. The yield predicted by the regression model for a temperature of 150 degrees is closest to:
4. The residual error for a temperature of 150 degrees is closest to:
5. If the yield were measured in ounces instead of grams (note that 1 gram is 0.35274 ounces), the slope would change by a factor of:
6. If the yield were measured in ounces instead of grams (note that 1 gram is 0.35274 ounces), the correlation coefficient would increase by a factor of:
Explanation / Answer
1. what is the standard deviation of temperature?
=30.27 (we used "STDEV.S" function in excel)
2. what is the standard deviation of yield?
=20.86 gm
3. The yield predicted by the regression model for a temperature of 150 degrees is closest to 151.461 gm
4. The residual error for a temperature of 150 degrees is closest to: -1.4617 gm (actual- predicted)
5. If the yield were measured in ounces instead of grams (note that 1 gram is 0.35274 ounces), the slope would change by a factor of 2.835 (=1/0.35274)
i.e. the new slope = 2.835 *old slope = 2.835*1.42= 4.02
6. If the yield were measured in ounces instead of grams (note that 1 gram is 0.35274 ounces), the correlation coefficient would not change at all.
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