MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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The efficiency for a steel specimen immersed in a phosphating tank is the weight of the phosphate coating divided by the metal loss (both in mg/ft2). An article gave the accompanying data on tank temperature (x) and efficiency ratio (y).
| Temp. | 173 | 175 | 176 | 177 | 177 | 178 | 179 | 180 |
|---|---|---|---|---|---|---|---|---|
| Ratio | 0.92 | 1.29 | 1.44 | 1.11 | 1.15 | 1.12 | 0.96 | 1.82 |
| Temp. | 183 | 183 | 183 | 183 | 183 | 184 | 184 | 185 |
|---|---|---|---|---|---|---|---|---|
| Ratio | 1.47 | 1.68 | 1.67 | 2.07 | 2.09 | 0.82 | 1.33 | 0.96 |
| Temp. | 185 | 185 | 185 | 187 | 187 | 188 | 189 | 191 |
|---|---|---|---|---|---|---|---|---|
| Ratio | 1.83 | 1.96 | 2.62 | 1.55 | 2.42 | 3.04 | 1.97 | 3.18 |
(a)
Determine the equation of the estimated regression line. (Round all numerical values to four decimal places.)
y =
(b)
Calculate a point estimate for true average efficiency ratio when tank temperature is 185. (Round your answer to four decimal places.)
(c)
Calculate the values of the residuals from the least squares line for the four observations for which temperature is 185. (Round your answers to two decimal places.)
(185, 0.96)(185, 1.83)(185, 1.96)(185, 2.62)
Why do they not all have the same sign?
These residuals do not all have the same sign because in the cases of the first two pairs of observations, the observed efficiency ratios were smaller than the predicted value. In the cases of the last two pairs of observations, the observed efficiency ratios were larger than the predicted value.These residuals do not all have the same sign because in the case of the second pair of observations, the observed efficiency ratio was equal to the predicted value. In the cases of the other pairs of observations, the observed efficiency ratios were larger than the predicted value. These residuals do not all have the same sign because in the case of the third pair of observations, the observed efficiency ratio was equal to the predicted value. In the cases of the other pairs of observations, the observed efficiency ratios were smaller than the predicted value.These residuals do not all have the same sign because in the cases of the first two pairs of observations, the observed efficiency ratios were larger than the predicted value. In the cases of the last two pairs of observations, the observed efficiency ratios were smaller than the predicted value.
(d)
What proportion of the observed variation in efficiency ratio can be attributed to the simple linear regression relationship between the two variables? (Round your answer to three decimal places.)
Transcribed Image Text:The efficiency for a steel specimen immersed in a phosphating tank is the weight of the phosphate coating divided by the metal loss (both in mg/ft2). An article gave the accompanying data on tank temperature (x) and efficiency ratio (y).
Temp. 173
Ratio
y =
Temp. 183
Ratio
Ratio
175
176
0.92 1.29 1.44 1.11 1.15
Temp. 185 185
183 183
USE SALT
177
1.47 1.68 1.67 2.07
1.83 1.96 2.62
183
185 187
177
183
2.09
187
1.55 2.42
178
1.12
179
0.82
180
0.96 1.82
184 184 185
1.33 0.96
188 189 191
3.04 1.97 3.18
(a) Determine the equation of the estimated regression line. (Round all numerical values to four decimal places.)
(b) Calculate a point estimate for true average efficiency ratio when tank temperature is 185. (Round your answer to four decimal places.)
(c) Calculate the values of the residuals from the least squares line for the four observations for which temperature is 185. (Round your answers to two decimal places.)
(185, 0.96)
(185, 1.83)
(185, 1.96)
(185, 2.62)
Why do they not all have the same sign?
These residuals do not all have the same sign because in the cases of the first two pairs of observations, the observed efficiency ratios were smaller than the predicted value. In the cases of the last two pairs of observations, the observed efficiency
ratios were larger than the predicted value.
These residuals do not all have the same sign because in the case of the second pair of observations, the observed efficiency ratio was equal to the predicted value. In the cases of the other pairs of observations, the observed efficiency ratios were
larger than the predicted value.
These residuals do not all have the same sign because in the case of the third pair of observations, the observed efficiency ratio was equal to the predicted value. In the cases of the other pairs of observations, the observed efficiency ratios were
smaller than the predicted value.
These residuals do not all have the same sign because in the cases of the first two pairs of observations, the observed efficiency ratios were larger than the predicted value. In the cases of the last two pairs of observations, the observed efficiency ratios
were smaller than the predicted value.
(d) What proportion of the observed variation in efficiency ratio can be attributed to the simple linear regression relationship between the two variables? (Round your answer to three decimal places.)
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