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 accompanyingdata on tank temperature (x) and efficiency ratio (y).Temp.171173174175175176177178Ratio0.781.331.441.110.970.981.101.76Temp.181181181181181182182183Ratio1.471.581.692.232.250.861.511.00Temp.183183183185185186187189Ratio1.711.962.581.572.603.021.793.06(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 183. (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 183. (Round your answers to two decimal places.)(183, 1.00)(183, 1.71)(183, 1.96)(183, 2.58) Why do they not all have the same sign?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 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.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 thecases 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. Inthe 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 casesof the other 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 threedecimal places.)

The given information is that the variable x represents the tank temperature and the variable y…

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. 171 173 174 175 175 176 177 178 Ratio 0.78 1.33 1.44 1.11 0.97 0.98 1.10 1.76 Temp. 181 181 181 181 181 182 182 183 Ratio 1.47 1.58 1.69 2.23 2.25 0.86 1.51 1.00 Temp. 183 183 183 185 185 186 187 189 Ratio 1.71 1.96 2.58 1.57 2.60 3.02 1.79 3.06 (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 183. (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 183. (Round your answers to two decimal places.) (183, 1.00) (183, 1.71) (183, 1.96) (183, 2.58)

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. 171 173 174 175 175 176 177 178 Ratio 0.78 1.33 1.44 1.11 0.97 0.98 1.10 1.76 Temp. 181 181 181 181 181 182 182 183 Ratio 1.47 1.58 1.69 2.23 2.25 0.86 1.51 1.00 Temp. 183 183 183 185 185 186 187 189 Ratio 1.71 1.96 2.58 1.57 2.60 3.02 1.79 3.06 (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 183. (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 183. (Round your answers to two decimal places.) (183, 1.00) (183, 1.71) (183, 1.96) (183, 2.58)

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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Question

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.
171
173
174
175
175
176
177
178
Ratio
0.78
1.33
1.44
1.11
0.97
0.98
1.10
1.76
Temp.
181
181
181
181
181
182
182
183
Ratio
1.47
1.58
1.69
2.23
2.25
0.86
1.51
1.00
Temp.
183
183
183
185
185
186
187
189
Ratio
1.71
1.96
2.58
1.57
2.60
3.02
1.79
3.06
(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 183. (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 183. (Round your answers to two decimal places.)
(183, 1.00)
(183, 1.71)
(183, 1.96)
(183, 2.58)

Why do they not all have the same sign?
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 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.
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.
(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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