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. Ratio 172 0.80 174 1.41 175 1.40 176 176 0.93 0.99 177 178 1.16 1.06 179 1.74 Temp. Ratio 182 1.47 182 1.66 182 1.65 182 2.07 182 2.11 183 0.86 183 1.39 184 0.86 Temp. Ratio 184 1.85 184 1.96 184 2.74 186 1.53 186 2.54 187 2.96 188 1.85 190 3.00 (a) Determine the equation of the estimated regression line. (Round all numerical values to five decimal places.) y = -15.39838 + (0.09402 )x (b) Calculate a point estimate for true average efficiency ratio when tank temperature is 184. (Round your answer to four decimal places.) 1.9013 V (c) Calculate the values of the residuals from the least squares line for the four observations for which temperature is 184. (Round your answers to four decimal places.) (184, 0.86) -1.0413 (184, 1.85) -0.0513 (184, 1.96) 0.0587 (184, 2.74) 0.8387 ✓ Why do they not all have the same sign? 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. 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 four decimal places.) 0.6731

Answer 1

Using Excel<data<data analysis<regression

Here is the output:

Regression Analysis
	r²	0.4531
	r	0.673
	Std. Error	0.494
	n	24
	k	1
	Dep. Var.	Ratio,y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	4.4550	1	4.4550	18.23	.0003
Residual	5.3771	22	0.2444
Total	9.8322	23
Regression output				confidence interval
variables	coefficients	std. error	t (df=22)	p-value	95% lower	95% upper
Intercept	-15.3980	4.00	-3.85	0.00	-23.69	-7.11
Temp,x	0.0940	0.0220	4.269	.0003	0.0483	0.1397

Your all answers are correct.

You are almost correct. The observed variation is expressed by r^2 not r.

Answers:

d) 0.4531