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 artide gave the accompanying data on tank temperature (x) and efficiency ratio (y). Temp. Ratio 174 176 177 0.81 1.32 1.51 Temp. 184 184 184 Ratio 1.52 1.57 1.54 178 178 1.12 0.98 184 184 2.08 2.20 Temp. 186 186 186 1.84 1.97 2.61 Ratio (a) Determine the equation of the estimated regression line. 188 188 1.56 2.53 179 1.15 185 189 181 1.09 1.79 180 185 1.42 190 186 0.93 192 2.95 1.86 3.05 (b) Calculate a point estimate for true average efficiency ratio when tank temperature is 186. (c) Calculate the values of the residuals from the least squares line for the four observations for which temperature is 186. Why do they not all have the same sign? (d) What proportion of the observed variation in efficiency ratio can be attributed to the simple linear regression relationship between the two variables?

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