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	0.86	1.37	1.50	1.07	1.07	1.16	1.08	1.82

Temp.	180	180	180	180	180	181	181	182
Ratio	1.37	1.54	1.51	2.07	2.11	0.78	1.47	0.98

Temp.	182	182	182	184	184	185	186	188
Ratio	1.81	2.04	2.76	1.51	2.50	2.98	1.97	3.10

(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, 0.98)
(182, 1.81)
(182, 2.04)
(182, 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 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.

(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

a) y = -14.95656+0.09271* temperature

b) x=182

y= -14.95656+0.09271*182

y= 1.9167

c) y = -14.95656+0.09271* temperature

y=  -14.95656+0.09271* 182

y= 1.9167

(182, 0.98) e = y-y(hat)= 0.98-1.9167= -0.9367
(182, 1.81) e= 1.81-1.9167 = -0.1067
(182, 2.04) e= 2.04-1.9167 = 0.1233
(182, 2.76) e= 2.76-1.9167= 0.8433

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.

d) 0.4409  proportion of the observed variation in efficiency ratio can be attributed to the simple linear regression relationship between the two variables.

NOTE: I USED MS EXCEL FOR ANALYSIS.