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 0.82 1.39 1.48 0.95 1.15 1.06 1.00 1.82 Temp. 181 181 181 181 181 182 182 183 Ratio 1.35 1.52 1.55 2.19 2.17 0.92 1.45 0.82 Temp. 183 183 183 185 185 186 187 189 Ratio 1.85 2.04 2.70 1.59 2.54 3.04 1.89 3.12 (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, 0.82) (183, 1.85) (183, 2.04) (183, 2.70) 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 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. 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. 171 173 174 175 175 176 177 178 Ratio 0.82 1.39 1.48 0.95 1.15 1.06 1.00 1.82 Temp. 181 181 181 181 181 182 182 183 Ratio 1.35 1.52 1.55 2.19 2.17 0.92 1.45 0.82 Temp. 183 183 183 185 185 186 187 189 Ratio 1.85 2.04 2.70 1.59 2.54 3.04 1.89 3.12 (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, 0.82) (183, 1.85) (183, 2.04) (183, 2.70) 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 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. 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.)

Materials Science And Engineering Properties

1st Edition

ISBN:9781111988609

Author:Charles Gilmore

Publisher:Charles Gilmore

Chapter4: Temperature Effects On Atom Arrangements And Atom Motion

Section: Chapter Questions

Problem 4.5P

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