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.	173	175	176	177	177	178	179	180
Ratio	0.92	1.39	1.40	1.05	0.97	0.98	1.10	1.78

Temp.	183	183	183	183	183	184	184	185
Ratio	1.39	1.60	1.65	2.21	2.09	0.78	1.53	0.80

Temp.	185	185	185	187	187	188	189	191
Ratio	1.87	2.04	2.76	1.53	2.50	3.08	1.93	3.18

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

−16.11770+0.09757x

  

(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 four decimal places.)

(185, 0.80)
(185, 1.87)
(185, 2.04)
(185, 2.76)

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 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 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 four 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 (). Temp.173 175 176 177 177 178 179 180 Ratio 0.92 1.39 1.40 1.05 0.97 0.98 1.10 1.78 Temp. 183 183 183 183 183 184 184 18S Ratio 1.39 1.60 1.65 2.21 2.09 0.78 1.53 0.80 Temp 185 185 185 187 187 18 189 191 Ratio 1.87 2.04 2.76 1.53 2.50 3.08 1.93 3.18 (a) Deternine the equation of the estimated regression line. (Round all numerical values to five decimal places.) y-1-16.11770 + 0.09757x | v' (b) Calculate ฮ point estimate for true average efficiency ratio when tank temperature is 185, (Round your answer to four decimal places.) 1.9327 (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 four decimal places.) (185, 0.80) -1.1388X (185, 1,87) 0.0698 (185, 2.04) 0.1012 (185, 2.76) 212 y 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 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 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 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 rogression relationship between the two variables? (Round your answer to four decimal places.) .0ogs

Answer 1

From qiven dea4 Ex4380 Ey0.2+1.39+ - .. +-1.93 t3.18 ery : (143)(0.92) t (145) (1.30 t t ( R) ( 3 , 18) EX: F99854 bot br bo rn 40.53 15.9) -4380 x e 68846 34 998 54 L4380 19 196496-19 ,84400

: 18o.2 9096 o40 53 009757 x 438o 94 I. 6888-0.09子5 I. 68#8-1子"806520 : Given χ:185 --16-1HỊ t 18.05045 : 938 15

-1、13075 I.93015 93875 1. 93915 O062+ 0.82 95 1.93215 (04x F445.9)- (4380 x 4053 4x7998 54 -l4380j)a4[19.3645)-(40-53 1180 2 62,139) 12096 x 3110834 554

180.9 180. 683132 2 O. 4393 Th u of 043 Hence the paopostion ooatiai 0.4393