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 0.86 1.39 1.46 0.99 1.15 1.14 0.98 1.84 y = Ratio 175 176 Temp. 183 183 183 183 183 Ratio 1.37 1.58 1.63 Temp. 185 185 185 1.85 1.96 2.66 USE SALT 177 177 2.19 2.05 187 187 1.59 2.44 178 179 180 184 184 185 0.80 1.39 0.84 188 189 191 2.90 1.79 3.10 (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, 0.84) (185, 1.85) (185, 1.96)
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 0.86 1.39 1.46 0.99 1.15 1.14 0.98 1.84 y = Ratio 175 176 Temp. 183 183 183 183 183 Ratio 1.37 1.58 1.63 Temp. 185 185 185 1.85 1.96 2.66 USE SALT 177 177 2.19 2.05 187 187 1.59 2.44 178 179 180 184 184 185 0.80 1.39 0.84 188 189 191 2.90 1.79 3.10 (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, 0.84) (185, 1.85) (185, 1.96)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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
y =
Ratio
175
Ratio
176
Temp. 183 183. 183
Ratio 1.37 1.58
0.86 1.39 1.46 0.99
Temp. 185 185 185
USE SALT
177
183
1.63 2.19
187
177
1.15
183
2.05
187
178
1.14
179
0.98
188
184 184 185
180
0.80 1.39 0.84
189
1.85 1.96 2.66 1.59 2.44 2.90 1.79
1.84
191
3.10
(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, 0.84)
(185, 1.85)
(185, 1.96)
(185, 2.66)
Transcribed Image Text:Why do they not all have the same sign?
O 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.
O 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.
O 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 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.
(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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