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 y = Ratio Ratio Temp. 183 183 183 1.47 1.70 1.67 Temp. Ratio 176 0.88 1.37 1.40 0.97 1.09 185 185 185 (185, 1.98) (185, 2.74) 177 1.89 1.98 2.74 183 177 187 178 0.98 183. 184 179 1.00 1.70 184 180 2.15 2.11 0.90 1.53 0.80 187 188 189 1.51 2.56 3.02 1.77 185 191 (a) Determine the equation of the estimated regression line. (Round all numerical values to four decimal places.) 3.16 (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, 0.80) (185, 1.89) 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 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 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 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.)
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 y = Ratio Ratio Temp. 183 183 183 1.47 1.70 1.67 Temp. Ratio 176 0.88 1.37 1.40 0.97 1.09 185 185 185 (185, 1.98) (185, 2.74) 177 1.89 1.98 2.74 183 177 187 178 0.98 183. 184 179 1.00 1.70 184 180 2.15 2.11 0.90 1.53 0.80 187 188 189 1.51 2.56 3.02 1.77 185 191 (a) Determine the equation of the estimated regression line. (Round all numerical values to four decimal places.) 3.16 (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, 0.80) (185, 1.89) 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 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 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 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.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 68E
Related questions
Question
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
Temp. 183
Ratio
175 176
Ratio
183 183
1.47 1.70 1.67
177
177
0.88 1.37 1.40 0.97 1.09 0.98 1.00 1.70
183 183
2.15
Temp. 185 185 185 187
2.11
178
187
184
179
0.90
184
180
1.53
185
0.80
188 189 191
1.89 1.98 2.74 1.51 2.56 3.02 1.77 3.16
(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, 0.80)
(185, 1.89)
(185, 1.98)
(185, 2.74)
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 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 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 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.)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step 1: Write the given information.
VIEWStep 2: Construct the table and determine the regression equation.
VIEWStep 3: Determine the point estimate for true average efficiency ratio when tank temperature is 185.
VIEWStep 4: Determine the values of residual from the least squares line for the four observations.
VIEWStep 5: Determine proportion of observed variation in efficiency ratio attributed to the linear regression.
VIEWSolution
VIEW
Step by step
Solved in 6 steps with 15 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning