Question

For many firms, expenses are linear functions of sales. That appears to be the case for Adridorf Manufacturing, a company that markets industrial plastics. The table below shows Adridorfs annual sales in hundreds of thousands of dollars (x) and expenses in thousands of dollars ) for the years 1993 through 2012.rough 2012 vear 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 x 19 1927 25 25 17 22 16 22 20 355 576 739 585 590 515 669 423 509 519 vear 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 x 29 25 18 20 18 302323 30 25 734 708 418 500 569 806 654 506 908 624 (a) Plot the scatterplot ofthe data. (b) Compute the estimates of α and β, and the equation of the regression line. (c) Replot the scatterplot ofthe data and superimpose on it the regression line. (d) Draw the qq-plot and qq-line of the residuals, and compute the p-value for the Shapiro-Wilk's test. What can you conclude from these results? (e) Draw the plot of the residuals versus sales (x values). Does it suggest that fitting a straight line through these data would be appropriate?

Answer 1

a) scatter plot

scatter plot 1000 900 8 800 600 500 2 400 드300 200 100 10 15 20 25 漠) 35 sales in hundreds of thousands of dollars

b) $\alpha$ = -24.57381   $\beta$ = 27.3697, equation is   ŷ = 27.3697X - 24.57381

c) scatter plot and regression line

scatter plot n 1000 900 y 27.37x-24.574 R3 0.7268 8 800 E 600 4 500 2 400 드300 200 100 10 15 20 25 漠) 35 sales in hundreds of thousands of dollars

d) qq-plot and qq- line. Shapiro-Wilk's value is 0.948043 and p-value is 0.338362.hence, if we would reject H₀, the chance of type1 error (rejecting a correct H₀) would be too high: 0.3384 (33.84%).

Normal Q-Q Plot o o Oo 3 O 2 -2 Theoretical Quantiles

e) residual plot. fitting a straight line through these data not would be good predictor because of large residual error.

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