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		61.07
110		66.01
120		79.28
130		75.04
140		80.30
150		97.95
160		98.17
170		110.07
180		121.28
190		118.21

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 = 0.9763).

1. what is the mean temperature?
130
155
140
145

2. what is the mean yield?
89.6555
90.7380
91.6321
91.6321
       
3. what is the standard deviation of temperature?
900.1573
30.2765
21.4653
101.5487
       
4. what is the standard deviation of yield?
460.7586
601.5487
21.4653
30.2765
       
5. The slope of the fitted regression line is closest to:
-9.6310
191.1070
82.1912
0.6922
207.8088
   
6. The intercept of the fitted regression line is closest to:
191.1070
82.1912
207.8088
-9.6310
   
7. The yield predicted by the regression model for a temperature of 150 degrees is closest to:
-1443.9578
80.355
90.738
94.199
97.66
       
8. The residual error for a temperature of 150 degrees is closest to:
-97.95
99
-3.7510
1
3.7510
97.95
   
9. 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:
0.35274
1/0.35274
would not change
None of the above
       
10. 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:

0.35274
1/0.35274
would not change
None of the above

Answer 1

Answer 1: 145

Based on the above table, Mean of Temperature (X) is:

Answer 2: 90.7380

Based on the above table, Mean of Yield (Y) is:

Answer 3: 30.2765

Based on the above table, Sum of squares of Temperature (X) is:

Standard deviation of Temperature (X) = sqrt(SS_xx/n-1) = sqrt(8250/(10-1))

Standard deviation of Temperature (X) = 30.2765

Answer 4: 21.4653

Based on the above table, Sum of squares of yield (Y) is:

Standard deviation of yield (Y) = sqrt(SS_yy/n-1) = sqrt(4146.82736/(10-1))

Standard deviation of yield (Y) = 21.4653

Answer 5: 0.6922

Based on the above table, the slope m of fitter regression line can be calculated as follows:

Answer 6: -9.6319

Based on the above table, the intercept can be calculated as follows:

Value of x-bar, y-bar and m is obtained from Answer 1, 2, and 5

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