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(a) Determine the equation of the estimated regression line. (Round all numerical values to four decimal places.)

(a) Determine the equation of the estimated regression line. (Round all numerical values to four decimal places.)

Materials Science And Engineering Properties
Materials Science And Engineering Properties
1st Edition
ISBN:9781111988609
Author:Charles Gilmore
Publisher:Charles Gilmore
Chapter9: Time, Temperature, And Mechanical Properties
Section: Chapter Questions
Problem 2ETSQ
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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. 171 Ratio 0.78 1.29 1.34 y = 173 174 Ratio Temp. 181 Ratio 1.47 1.62 1.63 2.09 181 181 Temp. 183 183 183 175 1.83 1.98 2.78 1.13 181 185 175 1.17 181 2.21 185 176 1.14 182 0.86 186 177 1.02 182 1.45 187 178 1.82 183 0.82 189 1.59 2.42 3.10 1.97 3.00 (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 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, 1.83) (183, 1.98) (183, 2.78) 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 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 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. 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. (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. 171 Ratio 0.78 1.29 1.34 y = 173 174 Ratio Temp. 181 Ratio 1.47 1.62 1.63 2.09 181 181 Temp. 183 183 183 175 1.83 1.98 2.78 1.13 181 185 175 1.17 181 2.21 185 176 1.14 182 0.86 186 177 1.02 182 1.45 187 178 1.82 183 0.82 189 1.59 2.42 3.10 1.97 3.00 (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 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, 1.83) (183, 1.98) (183, 2.78) 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 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 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. 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. (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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