Larry Martinet, a manufacturing supervisor at Warbler Widgets reports to Diane F
ID: 3209088 • Letter: L
Question
Larry Martinet, a manufacturing supervisor at Warbler Widgets reports to Diane Feinberg, the Regional Vice President, that 500 dollars worth of copper wiring is missing from the plant. He suspects a night shift employee. Diane tells Larry that if he can find out who is stealing the wiring before the night shift returns to duty, she will promote him to Department Head. Larry goes back to the manufacturing area and discovers that next to the cabinet a set of muddy footprints, made by a size 11 shoe. He realizes that these prints could have been made only by a worker on the night shift and that he could narrow down his list of suspects if only he knew the shoe size of each night shift employee. Larry knows that, although shoe size is not provided on each workers employment record, their height is. Thinking fast, he rightly concludes that he can identify the thief if he can figure out the relationship between shoe size and height. Accordingly, he asks each worker on the day shift to list their height and shoe size and comes up with the following data: Assist Larry to find his copper wire thief by answering the following questions. Calculate a Pearson r for the relationship between shoe size and height. Make shoe size your X and height your Y, and remember to show all of your work, including your work for the XY column total (notice that the totals for X, Y, X^2, and Y^2 are already provided). Based on your r value, describe exactly how height and shoe size covary relative to one another and indicate whether the magnitude of their relationship is small, medium, or large Derive the formula for the regression line for the relationship between shoe size (X) and height (Y). Make sure that you show your calculations for the sum of squares or standard deviations for X and Y as well as the slope and intercept of the line.Explanation / Answer
a. Using the given information, Xbar=Sigma X/N, where, N is sample size, and X denote shoe size.
=105.50/11=9.59
Similarly, Ybar=774/11=70.36
Complete the following table.
Pearson correlation coefficient, r={Sigma xy-(Sigma x*Sigma y)/n}/[sqrt {{ Sigma X^2-(Sigma X)^2/n} {Sigma Y^2-(Sigma Y)^2/n}}]
={7462.5-(105.5*774)/11}/[sqrt{ {1024.25-(105.5)^2/11} {54629-(774)^2/11}}]
=39.136/[sqrt (12.409*167.545)]
=0.858~0.86 (ans)
b. The correlation coefficient is positive is sign, and is above 0.5. Therefore, there exists a strong, positive correlation among the variables-shoe size and height.
c. To formulate the regression equation, compute slope b and Y intercept, a as follows.
b1=Sxy/Sxx
={Sigma XY-(Sigma X*Sigma Y)/n}/{Sigma X^2-(Sigma X)^2/n}
={7462.5-(105.5*774)/11}/{1024.25-(105.50)^2/11}
=3.15
Y intercept, a=Ybar-beta1*Xbar
=70.36-3.15*9.59
=40.15
Therefore, the regression equation is as follows:
Yhat=40.15+3.15X
XY 607.5 685 777 512 674 825 715 885.5 552.5 612 616.5 Sum: 7462.5Related Questions
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