# hw3_soln3 - between TOST time and RBOT time(b The value of...

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Problem 3.11 (a) SS xy = 5530.92 - (1950)(47.92)/18 = 339.586667, SS xx = 251,970 - (1950) 2 /18 = 40,720,and SS yy = 130.6074 - (47.92) 2 /18 = 3.033711, so r = 033711 . 3 40720 586667 . 339 = .9662 There is a very strong positive correlation between the two variables. (b) Because the association between the variables is positive, the specimen with the larger shear force will tend to have a larger percent dry fiber weight. (c) Changing the units of measurement on either (or both) variables will have no effect on the calculated value of r , because any change in units will affect both the numerator and denominator of r by exactly the same multiplicative constant. Problem 3.12 (a) Using R: ## Read in the data file dat=read.csv(file.choose(),header=T) ## Assign variable names x=dat[,1] y=dat[,2] ## Calculate correlation coefficient cor(x,y)

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A value of r = .9233 means that there is a strong positive linear relationship
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Unformatted text preview: between TOST time and RBOT time. (b) The value of r does not depend on which of the two variables is labeled as the x variable. Thus, had we let x = RBOT time and y = TOST time, the value of r would have remained the same. (c) The value of r does not depend on the unit of measure for either variable. Thus, had we expressed RBOT time in hours instead of minutes, the value of r would have remained the same. Problem 3.16 The value of the sample correlation coefficient using the squared y values would not necessarily be approximately 1. If the y-values are greater than 1, then the squared y-values would differ from each other by more than the y-values differ from one another. Hence, the relationship between x and y 2 would be less like a straight line, and the resulting value of the correlation coefficient would decrease....
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hw3_soln3 - between TOST time and RBOT time(b The value of...

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