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.173175176177177178179180Ratio0.861.371.321.130.971.101.101.78Temp.183183183183183184184185Ratio1.471.541.532.152.050.801.390.96Temp.185185185187187188189191Ratio1.732.002.701.452.423.101.793.10(a)Determine the equation of the estimated regression line. (Round all numerical values to four decimal places.)y = (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 two decimal places.)(185, 0.96)(185, 1.73)(185, 2.00)(185, 2.70)Why do they not all have the same sign?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 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 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 three decimal places.) The invasive diatom species Didymosphenia geminata has the potential to inflict substantial ecological and economic damage in rivers. An article described an investigation of colonization behavior. One aspect of particular interest was whether y = colony density was related to x = rock surface area. The article contained ascatterplot and summary of a regression analysis. Here is representative data.50 7155 50 33 58 79 26y 157 1934 53 27 7 10 40 12x 69 44 37 70 20 45 49y 274 43 176 18 48 190 30(a) Fit the simple linear regression model to this data. (Round your numerical values to three decimal places.)y =Predict colony density when surface area = 70 and calculate the corresponding residual. (Round your answers to the nearest whole number.)colony densitycorresponding residualPredict colony density when surface area = 71 and calculate the corresponding residual. (Round your answers to the nearest whole number.)colony densitycorresponding residualHow do the residuals compare?O The residual for the first point is positive, while the residual for the second point is negative.O The residuals for both points are positive.O The residuals for both points are negative.O The residual for the first point is negative, while the residual for the second point is positive.(b) Calculate the coefficient of determination. (Round your answer to three decimal places.)Interpret the coefficient of determination.O The coefficient of determination is the increase in rock surface area due to an increase in one unit of rock surface area.O The coefficient of determination is the proportion of the total variation in colony density that can be explained by a linear regression model with rock surface area as the predictor.O The coefficient of determination is the increase in colony density due to an increase in one unit of colony density.O The coefficient of determination is the probability that the regression model fits the data.O The coefficient of determination is the proportion of the total variation in rock surface area that can be explained by a linear regression model with colony density as the predictor.(c) The second observation has a very extreme y value (in the full data set consisting of 72 observations, there were two of these). This observation may have had a substantial impact on the fit of the model and subsequent conclusions. Eliminate it and recalculate the equation of the estimated regression line.(Round your values to three decimal places.)Does it appear to differ substantially from the equation before the deletion?O The new equation is substantially different.O The new equation is not substantially different.What is the impact on 2 and s?O² and s are both smaller.O2 is smaller, while s is larger.O² and s are both larger.O2 is larger, while s is smaller.

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Answered: The efficiency for a steel specimen…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Related questions

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	0.86	1.37	1.32	1.13	0.97	1.10	1.10	1.78

Temp.	183	183	183	183	183	184	184	185
Ratio	1.47	1.54	1.53	2.15	2.05	0.80	1.39	0.96

Temp.	185	185	185	187	187	188	189	191
Ratio	1.73	2.00	2.70	1.45	2.42	3.10	1.79	3.10

(a)

Determine the equation of the estimated regression line. (Round all numerical values to four decimal places.)

y =

(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 two decimal places.)

(185, 0.96)(185, 1.73)(185, 2.00)(185, 2.70)

Why do they not all have the same sign?

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 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 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 three decimal places.)