These are the answers I just need the work The relationship between correlation

Question

These are the answers I just need the work The relationship between correlation coefficient can be used to detect any two variables. and effect is very close to either +1or-1,then there is a cause relationship between a and y Note: Exercises through few observations and are suitable for manual computation, which can very against computer The remainder of the problems are be checked outpu best performed by a computer EMERCISES 1. The data of Table 7.13 represent the thickness of oxidation on a metal alloy for different settings of temperature in a curing oven. The values of Data for Exercise 1 temperature have been coded so that zero is the "normal" temperature, r Temperature manual cumputation easier osidation regression line to predict oxidation based on temperature. Explain the meaning of the c efficients and the variance of residuals. (b) Calculate the estimated oxidation thickness for each of the tempera- tures in the experiment. (c) Calculate the residuals and make a residual plot. Discuss the distribu- tion of residuals. (d) Test the hypothesis that Bi 0, using both the analysis of variance and t tests. 2. The data of Table7.14 show the sugar content ofafruit (Sugar) for different Table 7.14 numbers of days after picking (Days). Data for Exercise 2 (a) obtain the estimated regression line to predict sugar content based on the number of days the fruit is left on the tree. Sugar Days (b) Calculate and plot the residuals against days. Do the residuals suggest a fault in the model? 79 3. The grades for 15 students on midterm and final examinations in an English course are given in Table 7.15. 11.3 (a) obtain the least-squares regression to predict the score on the final 11.8 examination from the midtermexamination score. Test forsignificance 11.3 of the regression and interpret the results. (b) It is suggested that if the regression is significant, there is no need to 0.4 have a final examination. Comment. (Hint: Compute one or two 95% prediction intervals)

Explanation / Answer

1 a)

so from graph the regression line will be

y = -0.5x + 2.8

b) the estimated potential can be obtained by putting the values in the obtained regression line as

(i) y (oxidation) = -0.5 x(temperature) + 2.8

temperature = -2

oxidation = 0.5 X 2 +2.8 = 3.8

(ii) temperature -1

oxidation = 0.5 X 1 + 2.8 = 3.3

(iii) temperature = 0

oxidation = -0.5 X 0 2.8 = 2.8

(iv) temperature = 1

oxidation = -0.5 X 1 +2.8 = 2.3

(v) temperature = 2

oxidation = -0.5 X 2 +2.8 = 1.8

c) Residual is the difference int the expected oxidation and actual oxidation

The residuals seem to have an even variability

d) test the hypothesis

standard deviation of residue and studentized residue will be

Oxidation Temperature 4 -2 3 -1 3 0 2 1 2 2

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