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. 170 172 173 174 174 175 176 177 Ratio 0.88 1.41 1.34 0.97 1.01 1.02 1.08 1.82 Temp. 180 180 180 180 180 181 181 182 Ratio 1.37 1.54 1.65 2.21 2.05 0.82 1.33 0.80 Temp. 182 182 182 184 184 185 186 188 Ratio 1.87 1.92 2.78 1.47 2.50 3.08 1.89 3.14 (a) Determine the equation of the estimated regression line. (Round all numerical values to five decimal places.) y = (b) Calculate a point estimate for true average efficiency ratio when tank temperature is 182. (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 182. (Round your answers to four decimal places.) (182, 0.80) (182, 1.87) (182, 1.92) (182, 2.78) 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 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 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 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. Correct: Your answer is correct. (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 four decimal places.)

Answer 1

(d)

The value of R² obtained from regression analysis is 44.3%.

Therefore, 44.3% variation is observed in efficiency ratio due to changes in tank temperatures.

Part d